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Choose the best answer from the choices given. All numbers used are real numbers. 
1. What is the value of ^(−7)^, given that ^m^ = m^{3} − m^{2} − m? • −399
• −385 • −301
• −287
• 301
Answer: −385(−7)^{3} = (−7) x (−7) x (−7) = −343 (−7)^{2} = (−7) x (−7) = 49 ∴ Substituting in the given function, ^(−7)^ = −343 − 49 − (−7) = −343 − 49 + 7 = −385 2. How many multiples of both 3 and 6 are there between 27 and 78 exclusive? • 8 • 9
• 10
• 16
• 18
Answer: 8A multiple of 3 is not necessarily a multiple of 6, e.g., 27. On the other hand, a multiple of 6 is necessarily a multiple of 3. So, only the multiples of 6 need to be considered. The multiples of 6 between 27 and 78 exclusive are 30, 36, 42, 48, 54, 60, 66 and 72. ∴ Number of multiples of both 3 and 6 between 27 and 78 exclusive = 8. 3. How many twodigit numbers can be written using the digits 0 through 5, given that 0 can be the first digit, but no digit can be repeated? • 11
• 20
• 25
• 30 • 36
Answer: 30There are 6 possibilities (0, 1, 2, 3 and 4, 5) for the first digit of the number, because 0 can be the first digit. There are 5 possibilities for the second digit, because no digit can be repeated. ∴ Total possibilities (twodigit numbers) = 6 x 5 = 30
4. If ab < 0, which of these must be true? • a > 0
• b > 0
• a/b < 0 • a/b > 0
• a + b < 0
Answer: a/b < 0If ab < 0, either a or b is definitely less than 0, but both cannot be less than 0 (because the product of two negative numbers is always positive). ∴ a/b < 0 must be true (the other choices may or may not be true depending on the actual numbers). 5. What is the value of p − q, given that (0.5 x 10^{p} ) / (25 x 10^{q} ) = 0.2 x 10^{13} • 10
• 12
• 13
• 14 • 15
Answer: 14Evaluating the lefthand side of the equation, (0.5 x 10^{p} ) / (25 x 10^{q} ) = 0.02 x 10^{p − q} = 0.2 x 10^{p − q − 1} Thus, 0.2 x 10^{p − q − 1} = 0.2 x 10^{13} or p − q − 1 = 13 ∴ p − q = 14 6. If c^{2} − 4c − 45 = 0, which of these could be the value of c? • −9
• −4
• 4
• 5
• 9
Answer: 9Factoring c^{2} − 4c − 45 gives(c + 5)(c − 9). If (c + 5)(c − 9) = 0, then c = −5 or c = 9. ∴ The correct answer is 9, because −5 is not a listed choice. 7. The average (arithmetic mean) of 8 numbers is 7.5. When two more numbers are added to the 8 numbers, the new average of all the 10 numbers is 8.8. What is the average of the two numbers added? • 1.3
• 2.6
• 3.3
• 14 • 28
Answer: 14The average (arithmetic mean) of nnumbers is their sum divided by n. Sum of 8 numbers = 8 x 7.5 = 60 Sum of 10 numbers = 10 x 8.8 = 88 Sum of the two numbers added = 88 − 60 = 28 ∴ Average of the two numbers added = 28 / 2 = 14 8. Four members of a family want to raise funds for a Hawaiian vacation. They distribute 600 icecream packs equally among themselves, and decide that each pack is to be sold for $4. If two of them manage to sell 75% of their icecream packs and the other two manage to sell only 40% of their packs, how many dollars did they collect? • 225
• 345
• 1020
• 1380 • 2400
Answer: 1380Number of packs sold by two family members = 75% x 300 = 225 Number of packs sold by the other two family members = 40% x 300 = 120 Total packs sold by the 4 family members = 345 ∴ Funds collected = 345 x $4 = $1380 9. If the length of a rectangle is decreased by 25% and its width is increased by 40%, what is the percentage increase or decrease in its area, if any? • Decrease of 5%
• Increase of 5% • Decrease of 15%
• Increase of 15%
• There is neither an increase nor a decrease.
Answer: Increase of 5%Let original length = L and original width = W. Then, original area = LW Now, new length = 0.75L and new width = 1.4W. So, new area = (0.75 x 1.4) LW = 1.05 LW ∴ Increase = (1.05 LW − LW)/(LW) = 1.05 − 1 = 0.05 = 0.05 x 100% = 5% 10. Faucet C fills a tank in 3 hours, whereas faucet D independently fills the same tank in 9 hours. What fraction of the tank will be filled, if both the faucets are kept running for 1½ hours, and the tank is originally onefourth full? • 1/6
• 1/3
• 4/9
• 5/9
• 11/12
Answer: 11/12Faucet C fills 1/3 of the tank in 1 hour. Faucet D fills 1/9 of the tank in 1 hour. Fraction of tank filled by both faucets in 1 hour = 1/3 + 1/9 = 3/9 + 1/9 = 4/9 Fraction of tank filled by both faucets in 1½ hours = 4/9 x 3/2 = 2/3 ∴ Fraction of tank filled (including original ¼th fraction) = 2/3 + 1/4 = 8/12 + 3/12 = 11/12 11. If the radius of a circle is halved, what is the percentage decrease in its area? • 10%
• 25%
• 50%
• 75% • 90%
Answer: 75%Let original radius = r. Then, original area = π r^{2}. Now, new radius = 0.5r. So, new area = π (0.5r)^{2} = 0.25π r^{2} ∴ Decrease = (π r^{2} − 0.25π r^{2} )/(π r^{2}) = 1 − 0.25 = 0.75 = 0.75 x 100% = 75% 12. If x@y = 2x^{2} − y^{3}, then (−4)@(−3) = • −59
• −5
• 5
• 41
• 59
Answer: 59(−4)^{2} = (−4) x (−4) = 16 (−3)^{3} = (−3) x (−3) x (−3) = −27 ∴ Substituting in the given function, (−4)@(−3) = 2(16) − (−27) = 32 + 27 = 59 13. In how many different ways can the digits 2, 2, 7 and 9 be arranged, so that there is at least one 2 between 7 and 9 always? • 3
• 4
• 6 • 9
• 12
Answer: 6There are three possibilities (2, 7, 9) for the first digit. If the first digit is 2, there are two arrangements: 2729 and 2927. If the first digit is 7, there are two arrangements: 7292 and 7229. If the first digit is 9, there are two arrangements: 9272 and 9227. ∴ There are 6 arrangements possible. 14. What is the minimum value of b for which [b^{3} + 8][(64/b) + 16] = 0? • − 4 • − 2
• − ¼
• ¼
• 2
Answer: − 4Taking each factor of the lefthand side of the equation as 0 and evaluating : b^{3} + 8 = 0 or b^{3} = −8 giving b = −2 (64/b) + 16 = 0 or 64/b = −16 giving b = 64/(−16) = −4 ∴ The minimum value of b is −4. 15. If 2^{2} x 3^{3} = 3^{2} x n, then n = • 4
• 8
• 12 • 21
• 36
Answer: 12Evaluating the given equation, we get: 4 x 27 = 9 x n So, n = (4 x 27) / 9 = 4 x 3 = 12 16. Corporation A hired only chemical engineers and mechanical engineers in the year 2003. If 55% of the employees hired were chemical engineers, and the remaining 450 employees hired were mechanical engineers, how many employees were hired totally? • 100
• 450
• 505
• 550
• 1000
Answer: 1000Percentage of mechanical engineers hired = 100% − 55% = 45% Taking the employees hired totally as x, we get(45/100)x = 450 So, x = (450 x 100) / 45 = 1000 17. If a tractor covers 4 miles in 20 minutes, what is its speed in miles per hour? • 1/5
• 1/4
• 5
• 12 • 60
Answer: 12Speed = Distance / Time So, Speed of tractor (in miles per minute) = 4/20 = 1/5 To convert to miles per hour, multiply by 60, and get: (1/5) x 60 = 12 miles per hour 18. If m is an even integer, which of these must be an odd integer? • m + 2
• m + 4
• 2m − 1 • 2m − 2
• 3m
Answer: 2m − 12m is an even integer and (2m − 1) is an odd integer. Alternatively, taking an even integer (say, 2), and evaluating all the choices given, we get: m + 2 = 2 + 2 = 4 (even) m + 4 = 2 + 4 = 6 (even) 2m − 1 = 4 − 1 = 3 (odd) 2m − 2 = 4 − 2 = 2 (even) 3m = 3 x 2 = 6 (even) 19. 'The Golf Company' purchased clubs and balls in the ratio 2 : 9. If it purchased a total of 34 clubs, how many balls did it purchase? • 68
• 102
• 136
• 153 • 187
Answer: 153Each part of the ratio = 34 / 2 = 17 ∴ Number of balls purchased = 17 x 9 = 153 20. Brian took a loan of $4000 from his friend at a simple interest of 6% per year. If he has to pay off the entire loan amount and the interest in equal installments within 8 months, how much would he have to pay every month? • $480
• $500
• $520 • $660
• $740
Answer: $520Loan amount to be paid every month = $4000 / 8 = $500 Interest payable per month = (6/100) x $4000 / 12 = $20 ∴ Payment every month = $500 + $20 = $520. 21. A certain integer n when divided by 5 yields a remainder of 4. Which of these cannot be an integer? • n / 9
• n / 10 • n / 14
• n / 19
• n / 24
Answer: n / 10Since n when divided by 5 yields a remainder of 4, n must be the sum of 4 and a multiple of 5, i.e., n could be 9 (4 + 5 x 1), 14 (4 + 5 x 2), 19 (4 + 5 x 3), 24 (4 + 5 x 4), etc. Thus, n has either a 4 or 9 in the units place. Integers (except multiples of 10 with a 0 in the units place) when divided by 10 give rise to decimal numbers and not integers. ∴ (n / 10) cannot be an integer (since no n is a multiple of 10).
Alternatively, substitute the following values for n in the choices given, to form integers: If n = 9 (4 + 5 x 1), then n / 9 = 1 (an integer) If n = 14 (4 + 5 x 2), then n / 14 = 1 (an integer) If n = 19 (4 + 5 x 3), then n / 19 = 1 (an integer) If n = 24 (4 + 5 x 4), then n / 24 = 1 (an integer) 22. 'The DryFruit Company' sells a dryfruit mixture containing 12 pounds of raisins, 4 pounds of almonds, and 4 pounds of walnuts. If the price of raisins, almonds and walnuts per pound is $a, $b, and $c respectively, what is the price (in dollars) of 1 pound of the dryfruit mixture? • (a + 3b + 3c) / 5
• (3a + b + c) / 5 • (a + 4b + 4c) / 20
• (12a + b + 4c) / 20
• (12a + 4b + c) / 20
Answer: (3a + b + c) / 5Weight of mixture produced = 20 pounds Price of raisins = $(12a); Price of almonds = $(4b); Price of walnuts = $(4c) Total price of mixture produced = $(12a + 4b + 4c) Price (in dollars) of 1 pound of mixture = (12a + 4b + 4c) / 20 ∴ On simplifying (dividing the numerator and denominator by 4), we get: (3a + b + c) / 5
Try the Quiz : GMAT Test Prep : Quantitative Math Problem Solving Test V
