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Sample 1: Table of Contents
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Math Word Problems for the GMAT

Sample 1: Table of Contents
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Sample 3: Sample Problems with Statistics
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Guerrilla Review for the GMAT

Table of Contents
Sample Section: Math 4
Sample Section: Answer Key for Math 4

 

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Answer Key for Math Section 4

1. To answer this question, we need to know the ratio of shrimp eaters to roast beef eaters, which is provided in Statement 2. The information in Statement 1 is interesting, but extraneous. Choice B is correct.

2. To answer this question, we need to know the amount of people that the original recipe served. Neither statement gives us this information. Choice E is correct.

3. To answer this question, we need to know the exact number of CDs that one of the boys owns AND enough information to write an equation to solve for the number that belong to Joe. Neither of these statements gives us an exact number for any of the boys; additionally, there is insufficient information to write an equation to solve for the unknown. Choice E is correct.

4. To answer this question, we need to know the relationship of the five numbers, which Statement 1 provides. Statement 2, however, is NOT enough information for us to find the middle number, because it only gives us an average of the 5 values, not the spread. Choice A is correct.

5. The two statements, if taken together, provide enough information for us to answer the question. Choice C is correct.

6. In this case, we can answer the question using either statement. Choice D is correct.

7. Choice E is correct. We do not have enough information to determine definite values for A and B. Therefore, we cannot answer the question.

8. Choice B is correct. Statement 2 is sufficient to answer the question.

9, Let x = the # of Victorian Lady gowns sold and 450 - x = the # of Summer Delight gowns sold. The total profit ($44,995) is the sum of the two gowns, which makes our equation:

75x + 140 (450 -x) = 44,995
75x + 63,000 - 140x = 44,995
-65x = -18005
x = 277 Victorian Lady Gowns; 450 -277 = 173 Summer Delight Gowns. Choice D is correct.

10. The first step is to draw a quick chart of what we know:

Driver Distance Rate Time
Jack 75x 75 x
Jill 45x 45 x

In this case, Jack and Jill will drive the same amount of time at different speeds. We want to know the amount of time it will take for Jack to be 45 miles ahead of Jill, which can be represented by:

75x - 45x = 45
30x = 45
X = 3/2 hours. Choice B is correct.

Because this is a relatively simple scenario, it is easier for some students to think it through without the chart. If Jack drives 75 miles per hour while Jill drives 45 miles per hour, then he travels 76 - 45 = 30 additional miles each hour. The time required for Jack to be 45 miles ahead of Jill is therefore 1.5 times 30 = 1.5 hours.

11. In this decimal, the repeating pattern is 9876321, which is a string of 7 digits. The first 49 digits will be 7 repetitions of this pattern. Then, in the eight repetition of the pattern, the 54th digit to the right of the decimal point will be the fifth number in the series, which is 3. Choice C is correct.

12. This problem is a combination of two sub-series. In the first one, each number increase by 1 (3,4,5,6); in the second, each number increases by 2 (5,7,9,11). The next number would be 6 + 1, or 7. Choice D is correct.

13. First, let's define our variables. We will let x = the smaller number and 12 - x equal the larger number. Six times the smaller number is therefore 6x. Three times the larger number is 3(18 - x).
Further, we know that the difference between these two quantities is equal to 2. We must therefore solve the following equation:
6x - 4(12-x) = 3, so 6x -48 + 4x = 2, or 10x =50, or x = 5 and 12 - 5 = 7. Choice D is correct.

14. (x + 7) + (x + 9) = 2x + 16. Choice C is correct.

15. According to the triangle inequality theorem, the length of one side of a triangle must be greater than the difference and less than the sum of the lengths of the other two sides.
Therefore, in Triangle D, the length of the third side must be greater than 36 - 21 = 15 and less than 36 + 21 = 57. The only answer choice between 15 and 57 is Choice C.

16. 30 yards x 3 feet/yard x 12 inches/foot = 1,080 inches / 4 = 270 4-inch segments. Choice B is correct

17. The relationship of the groups is defined as follows: Group 1 + Group 2 + Neither - Both = 100. Once we establish this simple equation, we can plug in numbers to solve for the unknown, which in this case is the group defined as Both.
Group 1 + Group 2 + Neither - Both = 100
60 + 35 + 20 - Both = 100
Both = 15, which is answer choice D.

18. If f(p) = p/7 + 10 - (73)/p , then f (14) = 14/7 + 10 - 343/14 = 2 + 10 - 24.5 = -12.5 Choice A is correct.

19. Area = L x W = 5 x 5 = 25. Choice B is correct.

20. I and III are true. Choice E is correct.

21. 3/8 = 0.375. The closest answer choice is D, 7/19, which is 0.368.

22. This is a simple addition and subtraction problem, with a final conversion to dollars at the end. When we add and subtract the terms, we get: 1489 + 324 + 112 - 117 = 1808 nickels x ($1.00/20 nickels) = $90.40. Choice A is correct.

23. To solve this problem, we must check our answer choices against both criteria in the problem: they must 1) be divisible by 2 and 3 AND 2) they must leave a remainder of 4 when they are divided by 5. Choices C and D are not divisible by 2, so we do not need to examine them further. Of the remaining choices, only Choice E (54) meets both criteria. .

24. 110/220 = ½ = 50%. 22/220 = 1/10 = 10%. Therefore, 50% + 10% = 60% are from Hawaii & Canada. Therefore, 40% are not. Choice C is correct.

25. This can be solved by a simple equation: 8x - 25 = 215. x = 30. Choice C is correct.

26. To solve this problem, we must first calculate the total interest that Ronda will pay on the loan. To do so, we use the basic formula, Interest = Principal x Rate x Time. In this case, the Principal = $15000, the Rate = 0.09 and the Time = 4 years.
Hence, Interest = ($15000)(0.09)(4) = $5,400 in total interest over 4 years.
Now, we must convert this number to a monthly basis. If Ronda pays $5,400 in total interest over 4 years, then she pays $5,400/48 = $112.50 in interest per month. Choice B is correct.

27. First, we must define our variables. In this case, x = the number of dimes. Therefore, 320 - x = the number of quarters. Since the value of these two coins is $77.90, our equation becomes:
10x + 25(320 - x) = 7790
10x + 8000 - 25x = 7790
--15x = -210
x = 14 dimes. Choice A is correct.

28. Let x be the length of the base. Perimeter = sum of all three sides = 90 = x + 2(3x - 4) = 7x - 8. Thus, 7x = 98. x = 14. Choice B is correct.

29. Add the equations together, then divide by 2: 2x + 6y = 29. Choice C is correct.

30. If 11 - 4x = 3, then x = 2. 6 - (4)(2) = -2. Choice B is correct.

31. Our unknown is the total amount of time needed to fill the tank, which is the sum of the intake pipes, minus the drain pipe. Hence, our equation is 1/40 + 1/72 - 1/96 = 1/x
To solve, we must multiply both sides of the equation by 4320x, which is our least common denominator:
108x + 60x - 45x = 4320
123x = 4320
x = 35.12 hours. Choice B is correct.

32. The probability is 1/6, or Choice A.

33. Once again, this is a simple problem if we substitute numbers for letters. Let's assume that Yankee Stadium charges $20 for the first 8 hours and $5 for each additional hour. Let's also assume that Grace parked for 12 hours. If we do, then J = 20, P = 5, and S = 12.

Grace's total cost will be the basic charge for 8 hours, plus the additional cost for every hour over 8.
The basic cost = 20 = J. The additional cost per hour = 5(12 - 8) = P(S - 8).
Therefore, Grace's total cost = 20 + 5(12 - 8) = J + P(S - 8). Choice C is correct.

34.(0.6) 15,600= 9,360. Choice E is correct.

35. The easiest way to solve this problem is to try each answer choice. The largest one that divides evenly into 57 and 399 is 19, which is Choice D.

36. The data indicate that each 10% increase in solids decreases the flow by 50%. Therefore, the syrup with 10% solids would flow 8 times as fast (2 x 2 x 2) as the syrup with 40% solids. Hence, the correct answer choice is D.

37. A syrup with 50% solids would flow 50% as fast as a syrup with 40% solids. Choice B is correct.


 

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