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# GRE Quantitative General Questions

Hi, I recently took a GRE class (not with powerscore but I heard you guys can help). Here are three questions that I am sure are so easy, but I just can’t see it:

1. In a certain group of people, 87 people indicated they like raspberries, 91 indicated they like strawberries, and 91 people indicated they like blueberries. Of the people surveyed, 9 liked only raspberries, 10 liked strawberries, and 40 liked all three. How many of the people surveyed liked both strawberries and blueberries, but not raspberries?

A. 21 B. 26 C. 31 D. 36 E. 41

2. There are 20 rows of seats in an auditorium. If the first row has 20 seats and each successive row has 6 more seats then the previous row, how many seats are in the auditorium?

On this question, the answer was given as 1540, but that is including the extra 6 seats starting in the first row as far as I can see it. Am I wrong on this?

3. x–(1/y) where x-(1/y) does not equal 0

What is the reciprocal?

A. 1/x – y B. –y/x C. y/(x-1) D. x/(xy–1) E. y/(xy-1)

Thank
you so much!

## Posts

Hey Roxy,

Great questions. Let's tackle them individually:

Question 1)This problem deals with "Sets and Groups." Unlike many sets and groups problems, this question has three groups (raspberries, strawberries, and blueberries), as opposed to the more typical combination of only two. To set it up, draw three overlapping circles - one for each type of berry - that will represent the different combinations of the groups, and then begin filling in the information that you are given:

Now you are left with only unknowns x, y, and z (which stand for the groups who like exactly two of the three berry types). The question asks for the number of people who like S and B, but not R; this is the overlapping segment represented above by y (includes S and B, but not R). You know that the four pieces that make up each circle will add up to the total size of each circle (91 for two of them, and 87 for the third), so you have these equations:

1) For S: 91 = x + y + 40 + 10 à 91 = x + y + 50 à x + y = 41

2) For B: 91 = y + z + 40 + 12 à 91 = y + z + 52 à y + z = 39

3) For R: 87 = x + z + 40 + 9 à 87 = x + z + 49 à x + z = 38

Now solve for y:

From the third equation (x + z = 38), you can find that x = 38 – z. Substituting (38 – z) in for x in the first equation (x + y = 41) gives:

(38 – z) + y = 41 à y – z + 38 = 41 à y – z = 3

You can combine this equation (y – z = 3) with the second equation above (y + z = 39):

y – z = 3

+ y + z = 39

2y = 42, so y = 21

So y, the number of people who like strawberries and blueberries, but not raspberries, is 21. The correct answer is A.

Question 2)You know that there are 20 rows of chairs, each of which has at least 20 chairs (after the first row you start adding 6 chairs to each row). So you have 400 chairs (20 chairs x 20 rows) to start. The question is: how many more chairs do you add to this 400? To calculate this, picture the following:

6 chairs added to row 2

6(2) chairs added to row 3 (12 extra chairs in row 3)

6(3) chairs added to row 4 (18 extra chairs in row 4)

and so on until…

6(19) chairs added to row 20 (114 extra chairs in row 20)

To get the total number of extra chairs, you must find: 6(19 + 18 + 17 + 16 +…+ 3 + 2 + 1) = ?

19 + 18 +…+ 2 + 1 is known as consecutive number counting, where a sum of numbers is needed. To find the sum, take the average of the group of numbers x the number of numbers in the group:

Average = 10, number of numbers from 1 to 19 (inclusive) = 19. The sum of the numbers from 1 to 19 = 10(19) = 190

So the number of extra chairs is 6(190) = 1140. These extra chairs, in addition to the 20 rows of 20 (400 chairs), gives the total: 1140 + 400 = 1540

Question 3)A reciprocal is a number or term that, when multiplied by the original number or term, gives a product of 1.

The correct answer, E, does just that:

(x – (1/y)) (y/(xy – 1)) = (xy/(xy – 1) – (y/(xy2 – y))

Cancels the y’s in the term on the right: (xy/(xy – 1) – (y/(xy2 – y)) = (xy/(xy – 1) – (1/(xy – 1))

Now you can combine the two terms (both have a common denominator of (xy – 1):

(xy/(xy – 1) – (1/(xy – 1)) = (xy – 1)/(xy – 1), and this is equal to 1

Since you get a product of 1 after multiplying the original term by answer choice E, answer choice E is a reciprocal.

I hope this helps and good luck with your studies!