Sets for an overlapping sets problem it is best to use a double set matrix to organize the information and solve. Fill in the information in the order in which it is given
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GMAT Quant Topic 1 (General Arithmetic) Solutions
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- 180 – (1/6) T (1/2) T
(1) INSUFFICIENT: If we add the total number of students to the information from the question, we do not have enough to solve for .7x.
(2) INSUFFICIENT: If we add the fact that 20% of the sixteen year-olds who passed the practical test failed the written test to the original matrix from the question, we can come up with the relationship .7x = .8y. However, that is not enough to solve for .7x.
(1) AND (2) SUFFICIENT: If we combine the two statements we get a matrix that can be used to form two relationships between x and y:
.7x = .8y y + .3x = 188 This would allow us to solve for x and in turn find the value of .7x, the number of sixteen year-olds who received a driver license. The correct answer is C.
23.
The question is asking us for the ratio of the darkly shaded box to the lightly shaded box. INSUFFICIENT: Since one-half of all the guests had a house in Palm Beach, we can fill in the matrix as follows:
We cannot find the ratio of the dark box to the light box from this information alone. (2) INSUFFICIENT: Statement 2 tells us that two-thirds of all the guests had a house in the Hamptons. We can insert this into our matrix as follows:
We cannot find the ratio of the dark box to the light box from this information alone. (1) AND (2) INSUFFICIENT: we can fill in our matrix as follows.
The ratio of the number of people who had a house in Palm Beach but not in the Hamptons to the number of people who had a house in the Hamptons but not in Palm Beach (i.e. dark to light) will be:
This ratio doesn’t have a constant value; it depends on the value of T. We can try to solve for T by filling out the rest of the values in the matrix (see the bold entries above); however, any equation that we would build using these values reduces to a redundant statement of T = T. This means there isn’t enough unique information to solve for T. The correct answer is E. 24.
The problem gives us the following data to fill in the initial double-set matrix. We want to know if we can determine the maximum value of a, which represents the number of girls who ate chocolate ice cream.
(1) SUFFICIENT: Statement (1) tells us that exactly 30 children came to the party, so we'll fill in 30 for the grand total. Remember that we're trying to maximize a.
In order to maximize a, we must maximize b, the total number of chocolate eaters. Since b + d = 30, implying b = 30 - d, we must minimize d to maximize b. To minimize d we must minimize c. The minimum value for c is 0, since the question doesn't say that there were necessarily boys who had strawberry ice cream. Now that we have an actual value for c, we can calculate forward to get the maximum possible value for a. If c = 0, since we know that c + 9 = d, then d = 9. Since b + d = 30, then b = 21. Given that 8 + a = b and b = 21, then a = 13, the maximum value we were looking for. Therefore statement (1) is sufficient to find the maximum number of girls who ate chocolate. (2) INSUFFICIENT: Knowing only that fewer than half of the people ate strawberry ice cream doesn't allow us to fill in any of the boxes with any concrete numbers. Therefore statement (2) is insufficient. The correct answer is A. 25. Since we are dealing with overlapping sets and there are two independent criteria, the best way to solve this problem is with a double-set matrix. The first statement in the question stem tells us that of the students who speak French (represented by the first column), four times as many speak German as don't. This information yields the following entries in the double-set matrix:
The second statement in the question stem tells us that 1/6 of the of the students who don't speak German do speak French. This is fact represented in the double-set matrix as follows:
Now since x = y/6, we can get rid of the new variable y and keep all the expressions in terms of x.
Now we can fill in a few more boxes using the addition rules for the double-set matrix.
The main question to be answered is what fraction of the students speak German, a fraction represented by A/B in the final double-set matrix. So, if statements (1) and/or (2) allow us to calculate a numerical value for A/B, we will be able to answer the question.
(1) INSUFFICIENT: Statement (1) tells us that 60 students speak French and German, so 4x = 60 and x = 15. We can now calculate any box labeled with an x, but this is still insufficient to calculate A, B, or A/B. (2) INSUFFICIENT: Statement (2) tells us that 75 students speak neither French nor German, so 5x = 75 and x = 15. Just as with Statement (1), we can now calculate any box labeled with an x, but this is still insufficient to calculate A, B, or A/B. (1) AND (2) INSUFFICIENT: Since both statements give us the same information (namely, that x = 15), putting the two statements together does not tell us anything new. Therefore (1) and (2) together are insufficient. The correct answer is E.
The question is asking us if the total number of blue-eyed wolves (fourth column, second row) is greater than the total number of brown-eyed wolves (fourth column, third row). (1) INSUFFICIENT. This statement allows us to fill in the matrix as below. We have no information about the total number of brown-eyed wolves.
(2) INSUFFICIENT. This statement allows us to fill in the matrix as below. We have no information about the total number of blue-eyed wolves.
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