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Logical Reasoning & Problem Solving Practice Questions
Four friends take turns rolling a die, numbered from 1 to 6. Each friend rolls a different number. Each friend then makes a statement about the number they rolled.
- Ruby: I rolled a 4.
- Sam: My number's higher than Ruby's.
- Tori: My number's lower than Sam's.
- Umar: My number's lower than Tori's.
If exactly one of these statements is a lie, it is possible to determine which number each friend rolled if we know for sure that
Tails with three kinds of joints (ball-and-socket; peg-and-socket; gliding) have an unusual shape that allows for wide-ranging mechanical performance in grasping ability and also provide significant crushing resistance – that is, the tails are far less likely to be crushed when they collide with another object. By contrast, the cylindrical tails found in most animals are not prehensile (capable of grasping) or resilient to crushing because their plates translate and rotate upon impact. Seahorses, unlike most animals, have tails shaped like square prisms. Their tails are prehensile and resistant to impact.
From this information it follows that
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Excessive weight gain during pregnancy has been linked to increased risk of gestational diabetes, high blood pressure, large babies (who have a higher risk of childhood obesity) and birth interventions. The US Institute of Medicine (IOM) has therefore set out guidelines for pregnancy weight gain (listed in the table). The guidelines are tied to body mass index (BMI), which is an expression of body weight-for-height and determines a person's weight category.
A research group studied gestational weight gain in deliveries of full-term singleton births (excluding twins, triplets, etc.) in several different years and compiled the data, as shown in the figure below.
Excessive weight gain during pregnancy has been linked to increased risk of gestational diabetes, high blood pressure, large babies (who have a higher risk of childhood obesity) and birth interventions. The US Institute of Medicine (IOM) has therefore set out guidelines for pregnancy weight gain (listed in the table). The guidelines are tied to body mass index (BMI), which is an expression of body weight-for-height and determines a person's weight category.
A research group studied gestational weight gain in deliveries of full-term singleton births (excluding twins, triplets, etc.) in several different years and compiled the data, as shown in the figure below.
Of the following, the results of the research would least support the conclusion that
If a typical gestational period is 39 weeks, the IOM's weight gain recommendations assume that a pregnant woman with a prepregnancy BMI of 23.5 must gain no more than
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You are working as a gate agent for Pacific Air. Due to a glitch in your reservations system, none of the passengers booked into first class for the flight to Tokyo have been given seat assignments. The first class compartment includes four rows of seats (A, E, F, K). The aircraft includes two aisles from the rear up to row 3, after which the aisles merge into one, due to the narrowing of the plane.
All the first class passengers are waiting at the boarding gate, and you note their travelling companions and seating preferences as follows. (Note: Solo passengers can sit anywhere, except where restricted by their preferences. Everyone must be seated according to their preferences.)
- Georgia and Harrison, a couple on honeymoon, prefer to sit across the aisle in the same row.
- A mother, Kirstie, with two small children, Lily and Max, prefers that they sit in adjacent seats in the same row, with Kirstie next to one or both children.
- Lily wants a window seat, while Max refuses to sit by a window.
- There are two businessmen, each travelling as a solo passenger.
- Three airline employees – a pilot and two flight attendants – are travelling as solo passengers.
- The pilot and one of the businessmen want window seats on the left side of the plane.
- The other businessman will not sit in a row adjacent to any small children.
You must work quickly to figure out the seat assignments, as boarding is about to begin!
You are working as a gate agent for Pacific Air. Due to a glitch in your reservations system, none of the passengers booked into first class for the flight to Tokyo have been given seat assignments. The first class compartment includes four rows of seats (A, E, F, K). The aircraft includes two aisles from the rear up to row 3, after which the aisles merge into one, due to the narrowing of the plane.
All the first class passengers are waiting at the boarding gate, and you note their travelling companions and seating preferences as follows. (Note: Solo passengers can sit anywhere, except where restricted by their preferences. Everyone must be seated according to their preferences.)
- Georgia and Harrison, a couple on honeymoon, prefer to sit across the aisle in the same row.
- A mother, Kirstie, with two small children, Lily and Max, prefers that they sit in adjacent seats in the same row, with Kirstie next to one or both children.
- Lily wants a window seat, while Max refuses to sit by a window.
- There are two businessmen, each travelling as a solo passenger.
- Three airline employees – a pilot and two flight attendants – are travelling as solo passengers.
- The pilot and one of the businessmen want window seats on the left side of the plane.
- The other businessman will not sit in a row adjacent to any small children.
You must work quickly to figure out the seat assignments, as boarding is about to begin!
If Lily sits in 3A, and 1K is empty, who must sit in a K seat?
Answer: (D)
This set of 3 questions is a Logic Puzzle, requiring you to work out deductions based on the initial rules, and potential further deductions with the added info in each question. Take a minute to read over the rules and look for any initial deductions. As you do so, you‟ll want to make a rough sketch of the scenario on your test paper. Even though one is provided, it will be easier to do a sketch of your own, as you‟ll need to re-draw a sketch for each question. In the first class compartment, there are 4 rows: two with two seats (A and K), and two with four seats (A, E, F and K). There‟s an aisle between A/E and F/K seats in the back two rows, merging to one aisle between the A/K seats in the first two rows. Perhaps the simplest sketch would be
Now, consider what we know about the passengers. Georgia and Harrison must sit together, across an aisle. You could note this as G/H. Also, Lily, Max and Kirstie have to be in the same row in adjacent seats, with Lily in a window seat and Max not in a window seat. Thus, Lily must be in an A or K seat, and Max in an E/F seat. Since they must be in three adjacent seats, Kirstie must also be in an E/F seat, and they must be in Row 3 or Row 4. The second businessman, who will not sit in a row adjacent to small children, therefore cannot be in Row 3 or 4; he (call him 2B) must be in Row 1 (if L/K/M are in Row 3), or he could be in Row 1 or 2 if they are in Row 4. We also know that the pilot (P) and the first businessman (1B) must be A seats. This means that P and 1B can‟t be in the same row; also, if Lily is in an A seat, then we have three of the A seats taken. We don‟t know anything about the flight attendants (FA, FA) – they could go anywhere. However, we do know that there are 10 passengers total, and 12 seats – so there will be two empty seats. Knowing which seats are empty could be very useful, since it would limit where people could sit. Also, the groups that must sit in the same row – G/H and L/M/K – could be quite limited in where they will fit, although we may not know the exact seats for each.
Moving onto the details in question 5, which gives two further special conditions for this question only: Lily sits in 3A and 1K is empty. Add these details to the sketch:
We know that Max and Kirstie have to sit in the E and F seats in Row 3; we don‟t know which goes in which seat, and it really doesn‟t matter, since we now know that Kirstie (answer B) cannot sit in a K seat. We also know that the second businessman‟s seating depends on L/M/K‟s: since they are in Row 3, then 2B must be in Row 1 – and there is only one seat he can take in that row, 1A. Add these to the sketch:
Note the use of slashes when there are two options for who could go into a seat. Now, the next passengers to slot in are the pilot and the first businessman. They have to take A seats, and there are two left – 2A and 4A. The only remaining passengers who are restricted at all are Georgia and Harrison – they have to sit across the aisle from each other. With 2A and 4A taken, the only remaining seats for G/H are 4F and 4K. Add these in:
Notice the wrong answer trap: (A) is not something that must be true. Georgia could sit in a K seat, 4K. However, she could just as easily sit in 4F, which is NOT a K seat. Both are equally possible, so (A) is wrong. We have already assigned Kirstie and both businessmen to seats, none of which are K seats. Thus, answer (D) must be correct. As the sketch shows, there are three seats remaining: 2K, 3K and 4E. The two flight attendants can sit in any two of these seats, but at least one of them will be in a K seat.
Suppose that the two businessmen sit in the same row, with a flight attendant seated directly in front of one of them. Which of the following could be true?
Answer: (B)
This question gives further information, and asks for something that could be true. This means that the correct answer could be one of the possible options, such as those indicated by a slash in the previous sketch. The further info says that the two businessmen sit in the same row, with a flight attendant directly in front of one of them. We know from our original deductions that the second businessman can only sit in Row 1 or Row 2; if a flight attendant is seated in front of one of them, then the FA is in Row 1, and 1B and 2B are in Row 2. We also know that Kirstie and her kids must be in Row 4, since 2B will not sit in Row 2 if they are in Row 3. Add all these details into a sketch:
We don‟t know whether the flight attendant in Row 1 is in 1A or 1K, or whether Lily‟s in 4A or 4K. There are four people who still need seats: the pilot, Georgia, Harrison and the other flight attendant. The pilot will have to take 1A or 3A. Georgia and Harrison need to be seated across the aisle in the same row; there are no seats for them in Row 1 (FA has one), Row 2 (both seats taken by businessmen) or Row 4 (Kirstie and her kids), so G/H must go into Row 3, either 3A/3E or 3F/3K. Thus, it is possible that Harrison could be seated directly in front of Max. The answer is (B)
For the record: Georgia and Harrison would have to take 3A or 3K as one of their seats, so at least one businessman would not be seated in front of an empty seat. If the pilot takes 1A, he won‟t be in the same row as Georgia; if the pilot takes 3A, then Georgia and Harrison would take 3F and 3K, so there would be at least one seat between Georgia and the pilot. If the pilot takes 1A, no one is seated in front of him; if the pilot takes 3A, he is seated directly behind the first businessman, not a flight attendant.
If the flight attendants sit in 2K and 3F, the empty seats could not be
Answer: (C)
This question assigns both flight attendants to specific seats, then asks which seats could not be empty. This means that if there are multiple possible options, we‟ll have to ensure that the seats in the correct answer are taken by someone (if not necessarily the same person) in all those options. First, redraw the sketch:
This means that Kirstie, Lily and Max must sit in Row 4. However, there are three possible seats (1A, 2A, 3A) for the pilot and the first businessman; the second businessman can then take any remaining seat in Row 1 or Row 2. Thus, you can‟t do much with P, 1B and 2B at this point. That leaves Georgia and Harrison. If Kirstie and the kids are in Row 4, that means G/H can‟t be in Row 4; they also can‟t be in Row 2, or on the right side of Row 3. The only possible seats for G/H are 1A/1K or 3A/3E – both of which would severely limit the pilot and businessmen‟s seating options. Draw a quick sketch for each option for G/H, starting with them in Row 1:
In this option, there is only one possible seat for the second businessman: 2A, as it‟s the only seat that is not in a row adjacent to the children. This means that the pilot and first businessman must take 3A and 4A, and that Lily must take 4K. Amending the sketch:
The deductions have accounted for all the assigned seats, even if we‟re not sure who is in each seat; thus, in Option I, we see that 3E and 3K are empty seats; answer (D) is incorrect, as these could be the empty seats.
However, there‟s a second option to consider: what if Georgia and Harrison are in Row 3? Sketch this option:
This option isn‟t nearly as tidy as Option I; there are no further seats that must be assigned. However, we know that the pilot and first businessman must take A seats (1A, 2A or 4A), that Lily must take 4A or 4K, and that the second businessman must be in 1A, 1K or 2A, as he will not sit in a row adjacent to the children.
If 2B takes 1A or 2A, then P and 1B must be in the other two A seats, putting Lily in 4K; the empty seats are thus 1K and 3K. These could be the empty seats, so (A) is incorrect.
If 2B takes 1K, then Lily could take 4A or 4K, and P and 1B could take any two of 1A/2A/4A; the empty seats would therefore be 3K and either 1A, 2A, 4A or 4K. Thus, 2A and 3K could be the empty seats, ruling out (B).
Since 3K must be empty in all possibilities, the two empty seats could not be 2A and 4K. Answer (C) is correct.
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Attention Deficit Hyperactivity Disorder (ADHD) causes hyperactivity and difficulties with concentration in children and young adults. In the following study, children were given an approved drug for a number of weeks at 20mg, 40mg or 80mg. One group of children were given a placebo, which contained 0mg of the drug.
Prior to starting treatment, all children were given a test to determine their level of concentration; this became their baseline score. In this test, a higher score corresponds to a higher level of concentration and a lesser severity of ADHD. The same test was then repeated every two weeks for the duration of the 12-week study. The graph shows the results from the study.
Attention Deficit Hyperactivity Disorder (ADHD) causes hyperactivity and difficulties with concentration in children and young adults. In the following study, children were given an approved drug for a number of weeks at 20mg, 40mg or 80mg. One group of children were given a placebo, which contained 0mg of the drug.
Prior to starting treatment, all children were given a test to determine their level of concentration; this became their baseline score. In this test, a higher score corresponds to a higher level of concentration and a lesser severity of ADHD. The same test was then repeated every two weeks for the duration of the 12-week study. The graph shows the results from the study.
The drug is least likely to be effective based on the data from
Which of the following is most strongly supported by the results of the experiment?
Interpersonal Understanding Practice Questions
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In the passage below, a female patient has come to the emergency department complaining of abdominal pains.
The patient was half-sitting up on the table, a pillow in a plastic case behind her head, watching as the two doctors leafed through her notes. Although they were of a similar age, the taller doctor held an air of superiority. He, obviously the slightly more senior of the two, had some sort of seniority over the shorter doctor, even if he was only mere months older.
'The patient is complaining of abdominal pains. What do you do?' asked the taller doctor.
'Indigestion?' The shorter doctor barked the word right after her, as if it were a command and she were a dog. He glanced to his taller, apparently senior, colleague, then back at her, firing away: "Are you suffering from gas? Constipation? Nausea? Vomiting?‟
'Diarrhoea,' sighed the taller doctor. 'Not vomiting. You should've asked about diarrhoea.'
'Well?' the younger doctor was clicking his pen in and out, in and out, staring at her now. 'What about it? Have you had any diarrhoea?‟
12 The patient reddened. She‟d never have come to hospital for such a simple, obvious problem. It was as though these boys were playing guessing games and using her as the object of inquiry. They‟d barely given her a chance to answer.
'No.' The meekness of her reply annoyed her. It was met with more sighs from Dr Big.
'No. Of course not. You can‟t make a diagnosis from something as vague as “abdominal pains”; you need to determine where specifically the pain is coming from, how severe the pain is, whether the area is swollen. Come on, you know all this – it‟s so basic, even the nurses can do it. What are other causes of abdominal pains?' Shorty rattled off the list, counting on his fingers. 'Bowel cancer, intestinal obstruction, problems with the liver and kidneys, menstruation or pregnancy. Although this patient is too old to be menstruating or pregnant.'
'Right. Good. Now you‟re making observations. The next step is to do a thorough inspection of the area.‟ He turned his head to the patient, his hands already hovering over her. 'You don't mind do you?' he asked, almost as an afterthought.
Not trusting her voice, she merely shook her head.
The taller doctor nodded, pulled the patient‟s shirt up into her armpits and began to press different areas of her stomach firmly. Thank God I wore a new bra, she couldn't help thinking.
'Can you tell me please, in numbers from 1 to 10, the level of pain in each area I‟m touching?' His words were brisk and confident, his hands the same – though so cold on her skin. She could only nod in consent.
'Zero,' she said, as his cold, clinical fingers pressed at her left side. He pushed against her again and again, moving closer and closer to the sensitive area.
'Five,' she said. Then, she couldn't help squeaking as he moved round the area in rapid sucession: 'Seven… eight… ten…ten…ten!'
'Look closely,' he said to the short one. 'This area' – she winced as he pushed flames of pain into her again – 'is showing extensive swelling, and the patient is experiencing discomfort. Feel it.' He kept pressing into her,
35 shooting her through with fire, then instructing the other doctor to do the same. The patient inhaled sharply.
Just lie there, just lie there, she said to herself. Like a lamb at the butcher’s.
In the passage below, a female patient has come to the emergency department complaining of abdominal pains.
The patient was half-sitting up on the table, a pillow in a plastic case behind her head, watching as the two doctors leafed through her notes. Although they were of a similar age, the taller doctor held an air of superiority. He, obviously the slightly more senior of the two, had some sort of seniority over the shorter doctor, even if he was only mere months older.
'The patient is complaining of abdominal pains. What do you do?' asked the taller doctor.
'Indigestion?' The shorter doctor barked the word right after her, as if it were a command and she were a dog. He glanced to his taller, apparently senior, colleague, then back at her, firing away: "Are you suffering from gas? Constipation? Nausea? Vomiting?‟
'Diarrhoea,' sighed the taller doctor. 'Not vomiting. You should've asked about diarrhoea.'
'Well?' the younger doctor was clicking his pen in and out, in and out, staring at her now. 'What about it? Have you had any diarrhoea?‟
12 The patient reddened. She‟d never have come to hospital for such a simple, obvious problem. It was as though these boys were playing guessing games and using her as the object of inquiry. They‟d barely given her a chance to answer.
'No.' The meekness of her reply annoyed her. It was met with more sighs from Dr Big.
'No. Of course not. You can‟t make a diagnosis from something as vague as “abdominal pains”; you need to determine where specifically the pain is coming from, how severe the pain is, whether the area is swollen. Come on, you know all this – it‟s so basic, even the nurses can do it. What are other causes of abdominal pains?' Shorty rattled off the list, counting on his fingers. 'Bowel cancer, intestinal obstruction, problems with the liver and kidneys, menstruation or pregnancy. Although this patient is too old to be menstruating or pregnant.'
'Right. Good. Now you‟re making observations. The next step is to do a thorough inspection of the area.‟ He turned his head to the patient, his hands already hovering over her. 'You don't mind do you?' he asked, almost as an afterthought.
Not trusting her voice, she merely shook her head.
The taller doctor nodded, pulled the patient‟s shirt up into her armpits and began to press different areas of her stomach firmly. Thank God I wore a new bra, she couldn't help thinking.
'Can you tell me please, in numbers from 1 to 10, the level of pain in each area I‟m touching?' His words were brisk and confident, his hands the same – though so cold on her skin. She could only nod in consent.
'Zero,' she said, as his cold, clinical fingers pressed at her left side. He pushed against her again and again, moving closer and closer to the sensitive area.
'Five,' she said. Then, she couldn't help squeaking as he moved round the area in rapid sucession: 'Seven… eight… ten…ten…ten!'
'Look closely,' he said to the short one. 'This area' – she winced as he pushed flames of pain into her again – 'is showing extensive swelling, and the patient is experiencing discomfort. Feel it.' He kept pressing into her,
35 shooting her through with fire, then instructing the other doctor to do the same. The patient inhaled sharply.
Just lie there, just lie there, she said to herself. Like a lamb at the butcher’s.
Why does the patient redden (line 12)?
Regarding his feelings towards the shorter doctor, the taller doctor might best be described as
How does the patient feel about being examined physically by the shorter doctor (line 35)?
In the context of the passage as a whole, which of the following best describes the actions of the shorter doctor?
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Josh is Irene’s eldest son. Irene has recently been diagnosed with a terminal illness. They are discussing Irene’s decision to refuse treatment.
Josh: So basically, what you're trying to tell me is that you're giving up?
Irene: It's not about giving up. You and the boys all have families and jobs now. Your dad's been gone for almost 8 years. I've done my part. I don't want to hang on, in agony, making you all put up with me.
Josh: But we're all still your family! I just don't see how you can do this to us. What about your grandchildren? Okay, Dad is gone, but I‟m sure he wouldn't have wanted this. He would have wanted you to live as long as possible. It doesn't make any sense, Mum.
7 Irene: Josh. What's the use of me undergoing all that treatment? You saw how Uncle Fred was when he had the chemo. It gave him another two years of life. But it was unbearable for him. It took his hair and his appetite and his energy. That's what it's meant to do. It would do the same to me. And it was unpleasant for the rest of us, too. You boys were so frightened. That one time, we left the hospital and you were crying in the car. You couldn't stop crying. You can't honestly say that you‟d want to go through that again, love, can you?
Josh: Of course I would! Even if it only gave you another month it would be worth it. And from what the doctors are saying… you could see Parker graduate, and Matt's wedding. Matt and Emma are getting married next year. They'll want you there. Do it for them, Mum. For me. For us. Have the treatment. 15
Please. Please. Give it a go. And I won't cry this time, I promise! You can't just let yourself go…
17 Irene:I'm not scared, Josh. I feel ready for this. What's the point in me hanging on anymore?
Josh is Irene’s eldest son. Irene has recently been diagnosed with a terminal illness. They are discussing Irene’s decision to refuse treatment.
Josh: So basically, what you're trying to tell me is that you're giving up?
Irene: It's not about giving up. You and the boys all have families and jobs now. Your dad's been gone for almost 8 years. I've done my part. I don't want to hang on, in agony, making you all put up with me.
Josh: But we're all still your family! I just don't see how you can do this to us. What about your grandchildren? Okay, Dad is gone, but I‟m sure he wouldn't have wanted this. He would have wanted you to live as long as possible. It doesn't make any sense, Mum.
7 Irene: Josh. What's the use of me undergoing all that treatment? You saw how Uncle Fred was when he had the chemo. It gave him another two years of life. But it was unbearable for him. It took his hair and his appetite and his energy. That's what it's meant to do. It would do the same to me. And it was unpleasant for the rest of us, too. You boys were so frightened. That one time, we left the hospital and you were crying in the car. You couldn't stop crying. You can't honestly say that you‟d want to go through that again, love, can you?
Josh: Of course I would! Even if it only gave you another month it would be worth it. And from what the doctors are saying… you could see Parker graduate, and Matt's wedding. Matt and Emma are getting married next year. They'll want you there. Do it for them, Mum. For me. For us. Have the treatment. 15 Please. Please. Give it a go. And I won't cry this time, I promise! You can't just let yourself go…
17 Irene:I'm not scared, Josh. I feel ready for this. What's the point in me hanging on anymore?
Irene‟s example of Uncle Fred (line 7) suggests that she is refusing treatment primarily because
A day after the end of the passage, Josh accompanies Irene to her next doctor‟s appointment. The doctor asks if Irene has come to a decision about treatment, and Irene hesitates.
Based on his comments and feelings in the passage, how is Josh most likely to respond?
How does Irene ultimately feel about her decision (line 17)?
Non-Verbal Reasoning Practice Questions
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Next in the Series
Choose the option (A, B, C, D or E) that completes the sequence in the simplest and most logical way.
Next in the Series
Choose the option (A, B, C, D or E) that completes the sequence in the simplest and most logical way.
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Missing Segment
Choose the option (A, B, C, D or E) that completes the image in the simplest and most logical way.
Missing Segment
Choose the option (A, B, C, D or E) that completes the image in the simplest and most logical way.
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Middle of the Sequence
In this question, the five images can be rearranged into a logical sequence.
Choose the option (A, B, C, D or E) that occurs in the middle position of the simplest and most logical sequence.
Middle of the Sequence
In this question, the five images can be rearranged into a logical sequence.
Choose the option (A, B, C, D or E) that occurs in the middle position of the simplest and most logical sequence.
