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GMAT Test Prep : Quantitative Problem Solving Test II

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Choose the best answer from the choices given.
All numbers used are real numbers.

1. 'The Football Store' sells an average of 120 footballs per month in the first half of the year 2004. In the next 2 months, it sells an average of only 80 footballs per month. What is the average football sales for the first 8 months of 2004?
• 90
• 95
• 100
• 105
• 110
Answer: 110
Number of footballs sold in the first half of the year (6 months) = 120 x 6 = 720
Number of footballs sold in the next 2 months = 80 x 2 = 160
Total number of footballs sold in 8 months = 720 + 160 = 880
∴ Average number of footballs sold per month (in the first 8 months) = 880 / 8 = 110


2. If p and q are negative integers, which of these could be a positive integer?
p + q
p + q + 1
p + q − 1
• 2(p + q)
p / q
Answer: p / q
The sum of two negative integers is negative, so 'p + q' is not the answer, e.g., (−4) + (−2) = −6.
The sum of two negative integers and 1 is also negative, so 'p + q + 1' is not the answer, e.g., (−4) + (−2) + 1 = −5.
When 1 is subtracted from the sum of two negative integers, a negative number is obtained and so 'p + q − 1' is not the answer, e.g., (−4) + (−2) − 1 = −7.
Twice the sum of two negative integers is also negative, so '2(p + q)' is not the answer, e.g., 2((−4) + (−2)) = −12.
The quotient of two negative integers is always positive, so 'p / q' is the answer, e.g., (−4) / (−2) = 2.


3. The price of a pair of baseball gloves is increased by 15%. The next month, its price is further increased by 40%. This double increase in the price of the pair of baseball gloves would be equivalent to a single increase of
• 25%
• 49%
• 51%
• 55%
• 61%
Answer: 61%
Taking the original price of the pair of baseball gloves as $100
($100 is chosen because it is easier to convert into a percentage later),
New price after first increase = $115, i.e., 1.15 x 100
New price after second increase = $161, i.e., 1.4 x 115
∴ Increase in price = $61 and so the increase is 61%



4. If a rectangle having an area of 32 cm2 is formed when one side of a square is decreased by 7 cm and another side of the same square is increased by 7 cm, what is the perimeter of the original square (in cm)?
• 18
• 32
• 36
• 49
• 81
Answer: 36
Taking the side of the original square as x cm,
Area = (x − 7)(x + 7) = 32
x2 − 49 = 32
x2 = 81 or x = √81 = 9
∴ Perimeter of the original square = 4 x side = 4 x 9 cm = 36 cm


5. 'The Deli & Pastry Shop' sold cakes, brownies, cookies and croissants in the ratio of 8 : 2 : 4 : 6 last Monday. If customers purchased 27 croissants, how many cakes and brownies together were sold?
• 9
• 18
• 27
• 36
• 45
Answer: 45
Cakes sold = (8/6) x 27 = 36; Brownies sold = (2/6) x 27 = 9; Total = 36 + 9 = 45
Alternatively, each part of the ratio = 27/6 = 4.5
Cakes and brownies together equal 10 parts (8 + 2) of the ratio.
∴ Number of cakes and brownies sold = 4.5 x 10 = 45


6. What is 0.003 x 0.07 as a percentage?
• 0.0021%
• 0.021%
• 0.21%
• 2.1%
• 21%
Answer: 0.021%
0.003 x 0.07 = 0.00021
Converting to percentage gives 0.00021 x 100% = 0.021%.


7. The ratio of the number of boys to girls in a science class is 5 : 6. If the class has a total of 66 students, how many more girls are there as compared to boys ?
• 4
• 6
• 8
• 12
• None of these
Answer: 6
Sum of the parts of the ratio = 5 + 6 = 11.
Total number of students = 66; Each part of the ratio = 66 / 11 = 6.
Number of boys = 5 x 6 = 30; Number of girls = 6 x 6 = 36.
Thus, the girls outnumber the boys by 6.
Alternatively, let b and g denote the number of boys and girls, respectively.
Then, b/g = 5/6 and b + g = 66.
Eliminating b gives (5/6)g + g = 66 or (11/6)g = 66.
Thus, g = 36 and b = 30 giving gb = 6.


8. If a factory makes 108000 buttons every hour, how many buttons does it make in a second?
• 3
• 18
• 30
• 50
• 180
Answer: 30
There are 3600 seconds in an hour.
The factory makes 108000 buttons in one hour; so, in one second, it makes 108000 / 3600 = 30 buttons.


9. (1 / 4) + (1 / 7) + (1 / y) = 13, then y =
• 7 / 90
• 7 / 91
• 14 / 177
• 14 / 181
• 28 / 353
Answer: 28 / 353
1 / y = 13 − (1 / 4) − (1 / 7)
1 / y = (13 x 28 − 7 − 4) / 28 = (364 − 11) / 28= 353 / 28
y = 28 / 353


10. Ehud was supposed to submit his homework assignment by Thursday, the 15th of September. Unfortunately, he fell ill and his homework submission date was postponed by 33 days. On which day of the week was Ehud supposed to now submit his homework?
• Monday
• Tuesday
• Wednesday
• Thursday
• Friday
Answer: Tuesday
33 days is 2 days less than 5 weeks, since (7 x 5) − 2 = 33.
Had Ehud's homework assignment date been postponed by 35 days (5 weeks), the new submission date would have fallen on a Thursday.
Since the date was postponed by 33 days, he was supposed to now submit his homework on a Tuesday.


11. Avi worked for three straight hours solving GRE questions. He solved 30 questions in the third hour, which was 2½ times the number of questions he solved in the second hour, and three times the number he solved during the first hour. How many questions did he solve in all?
• 46
• 48
• 52
• 56
• 156
Answer: 52
Number of questions solved during the second hour = 30/2.5 = 300/25 = 12.
Number of questions solved during the third hour = 30/3 = 10.
Total number of questions solved = 30 + 12 + 10 = 52.


12. The average of 7 numbers is 83. The average of 5 of these numbers is 95. What is the average of the other 2 numbers?
• 53
• 57
• 64
• 69
• 71
Answer: 53
The average (arithmetic mean) of n numbers is their sum divided by n.
The sum of all the 7 numbers is 83 x 7 = 581.
The sum of the 5 numbers is 95 x 5 = 475.
So, the sum of the other 2 numbers is (581 − 475) = 106.
Thus, the average of the other 2 numbers is (106 / 2) = 53.


13. A motor-boat can travel upstream at a speed of 10 miles per hour and downstream at a speed of 14 miles per hour. If the boat travels at a constant speed, what is the speed at which the stream is flowing?
• 1 mile per hour
• 2 miles per hour
• 3 miles per hour
• 4 miles per hour
• None of these
Answer: 2 miles per hour
Let v be the speed at which the boat is moving (relative to the ground) and u be the speed at which the stream is flowing (also relative to the ground).
When the boat travels upstream, its speed (relative to the ground) is reduced because the stream opposes the motion of the boat. So, the speed of the boat is vu = 10.
On the other hand, when the boat travels downstream, its speed (also relative to the ground) increases and is equal to v + u = 14.
Subtracting vu = 10 from v + u = 14 gives 2u = 4 or u = 12 miles per hour.


14. What is the probability that when a pair of six-sided die are thrown, the sum of the numbers does not equal 12?
• 35 / 36
• 5 / 36
• 1 / 36
• 1 / 18
• 1 / 9
Answer: 35 / 36
There are 36 possible outcomes when a pair of die are thrown as explained below.
For each number that the first dice rolls, there are 6 possible outcomes for the second dice.
For example, if the first dice rolls a 1, the second dice can roll 1, 2, 3, 4, 5 or 6.
Since the first dice can roll 6 different numbers, there are 6 x 6 = 36 different possibilities.
The only way that the numbers rolled by the two dice can sum upto 12 is if each dice rolls a 6.
Since the sum of the numbers does not equal 12 in 35 out of the total 36 possibilities, the required probability is 35 / 36.


15. What is the probability that a card drawn at random from a pack will be a red card?
• 1 / 2
• 1 / 4
• 3 / 4
• 4 / 13
• 6 / 13
Answer: 1 / 2
A pack of cards typically has totally 52 cards (26 red and 26 black).
Probability = Number of favorable outcomes / Total number of possible outcomes
Number of favorable outcomes (for drawing a red card) = 26; Total number of possible outcomes = 52.
So, the required probability = 26 / 52 = 1 / 2.


16. Ilhan wants a pizza and a drink for lunch. If his school cafeteria has 3 different choices of pizza and 7 different choices of drinks, in how many different ways can he order his lunch?
• 10
• 14
• 16
• 21
• None of these
Answer: 21
Ilhan can order a pizza in 3 different ways.
For each pizza order, he has a choice of 7 drinks.
So, the total number of different orders that he can place is 3 x 7 = 21.


17. If the price of a stock rises from $50 to $70, what is the percentage increase in its price?
• 20%
• 29%
• 30%
• 32%
• 40%
Answer: 40%
Rise in price = New Price − Original Price = $70 − $50 = $20.
So, percentage increase = (20/50) x 100% = 40%.


18. A teacher is paid a monthly interest of $2000 on his pension fund of $400000. What is the annual rate of simple interest?
• ½%
• 4%
• 6%
• 8%
• 12%
Answer: 6%
Annual interest income = $2000 x 12 = $24000.
Interest rate = Annual interest income / Amount on which interest is being earned
= (24000/400000) x 100% = 6%.


19. What is the next term in the sequence 1, 1, 2, 3, 5, 8, 13, 21...?
• 27
• 28
• 30
• 32
• 34
Answer: 34
Observe that with the exception of the first 2 terms of the sequence, every term of the sequence is equal to the sum of the preceeding two terms.
So, the term appearing after 21 in the sequence is (13 + 21) = 34.
Note that this is a very well-known sequence of numbers, and is called the 'Fibonacci sequence'.


20. A bus travels between two villages 200 miles apart in 7 hours. The return trip takes 3 hours. What is the average speed of the bus in miles per hour?
• 18
• 20
• 24
• 40
• 48
Answer: 40
Average speed = Total distance traveled / Total time taken.
Total distance traveled = 200 + 200 = 400 miles.
Total time taken to complete both the journeys = 7 + 3 = 10 hours.
So, average speed = 400 / 10 = 40 miles per hour.


21. Joshua can paint a car in 40 minutes while Ariel can do the same job in 60 minutes. If they both work together, how long will they take to finish the job ?
• 16 minutes
• 18 minutes
• 24 minutes
• 30 minutes
• 32 minutes
Answer: 24 minutes
To solve such problems, consider the rate at which a person or group does a particular job.
Joshua does the job at the rate of (1/40)th of the job per minute.
Ariel does the job at the rate of (1/60)th of the job per minute.
When working together, their rates can be added. So, (1/40) + (1/60) = (3/120) + (2/120) = 5/120.
Joshua and Ariel together do the job at the rate of (5/120)th of the job per minute.
Thus, time taken to complete the job working together = 120/5 = 24 minutes.


22. Lamp posts are being placed at 50-foot intervals along a bridge 1200 feet long. If the first lamp post is placed at one end of the bridge, how many lamp posts are needed?
• 23
• 24
• 25
• 26
• 27
Answer: 25
Since lamp posts are being placed at 50-foot intervals along a 1200 feet long bridge, the bridge is divided into 1200 / 50 = 24 sections.
If each section is associated with the lamp post at its end, 24 lamp posts are required.
However, one lamp post is placed at the beginning (one end) of the bridge.
So, the total number of lamp posts required is 24 + 1 = 25.
Note : In such counting problems, care must be taken to include the first and the last items that have to be counted.



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