gre quant problemss ...

[sandeep641]

1. Given a rectangle of breadth 2m and area 26sq.m and
this rectangle is divided vertically with
two vertical lines(making it into 3 boxes).
If the length of first & second box is 5 and third is 'x',
then what is the value of 'x'?

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2. There was a survey of 500 persons.
Each person was given some questions, and for each question
they can answer either "YES" or "NO".
If 410 persons from the group answered "YES"
for the first question,
220 of the group answered "YES" for the second question
and if 'n' is the least number of persons
who answered "YES" to both the questions,
what is the value of 'n' provided if all the
500 persons answered both the questions?


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3. Given one pentagon with angles x, x, x, 2x-90 and 80
and was asked to find x value?


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4. Given three points of a triangle as (0,0), (x,0) and (4,3).
If the area is given as 12, then
Col A: x
Col B: 8


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5. Given x < y < 0
Col A: xy
Col B: y-x


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6. If the average of 'p' numbers in a list is 62
and the average of 'q' numbers in a list is 65,
and if the average of 'p+q' is 85, then the value of p/q is?


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7. Given a circle, with another circle inscribed in it and
the distance between bigger circle and
smaller circle was shaded.
If the bigger circle's radius was twice that of smaller circle.

Col A: area of bigger circle -
area of smaller circle (shaded part)

Col B: area of smaller circle.

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8. Given two line equations 5x - y - 3 = 0 and 5x + y + 3 = 0.
Col A: Slope of the first line
Col B: Slope of the second line.

[Goldust]

1.

Since the area is 26 sq.m and breadth is 2m, the length is 13 m. Since the length of the first two boxes is 5 each, the remaining box has a length of 3.

2.

I am not sure of this, but here goes. Drawing a Venn diagram, we get 410 - n people who answered (YES,NO), 220 - n people who answered (NO,YES) and n people who answered (YES,YES). Adding all of these together, we get 630 - n people who answered at least one question with a YES. However, we do not know the number of people who answered with (NO,NO). Let this be x. Then, we get 630-n+x = 500. Hence, n = 130 + x. For n to be minimum, x should be 0. Hence, n = 130.

3.

The sum of the interior angles of a pentagon is 540. Adding all the angles and solving for x, we get x = 110.

4.

The base of the triangle lies on the X-axis. The height of the triangle is 3. Hence, using Area = 1/2*base*height, we get base = 8. Hence, the two columns are equal.

5.

Plug in x = -1 and y = -.5. In the case of both the columns you get xy = y-x = 0.5. Some other case will give different values. Hence, the answer is D.

6.

I doubt the correctness of this question. I am hard pressed to think of any set of numbers with averages of 62 and 65 that when combined give an average of 85 ! I will assume you mean that the average of p+q numbers is 85. For the sake of a mathematical solution, here goes.
The average of p+q numbers is given by:-

(p*62+q*65)/(p+q)=85
i.e. p*62+q*65 = 85*p + 85*q
dividing throughout by q, we get,
p/q*62 + 65 = 85*p/q + 85.
Solving for p/q, we get, p/q = -20/23, which makes absolutely no sense, since p and q are the number of terms in each group and are therefore, positive.

7.

Firstly, you cannot inscribe a circle within a circle. Since the bigger circle's radius is twice that of the smaller radius (r), we get

Area of smaller circle = pi*r*r;
Area of bigger circle = 4*pi*r*r;
Hence, area of shaded region = 3*pi*r*r;
So, column A is greater.

8.

Putting both equations in the form y = mx + c. where m is the slope and c is the y-intercept, we get the first slope as positive and the second slope as negative. Hence, column A is greater.

Any queries or corrections are welcome.

[sandeep641]

in first problem , how did u get length as 13 , por favor, el señor specify detail formulae ?

[Goldust]

The area = 26 and the breadth = 2. Hence, length = area/breadth = 13

[gre320hex]

Q2. Isnt it enough to say :

Number of people who said yes for question 1 = 410
Number of people who said yes for question 2 = 220

That is in excess of 630 - 500 people , which is equal to 130. Therefore, atleast 130 people would have said 'Yes' more than once.

Or am I oversimplifying it and getting an answer by coincidence.

[gre320hex]

For Q4 . x can also be -8 . Since, it is the co-ordinate system. Therefore, D I guess.

[Goldust]

gre320hex,

For Q.2, you are right in saying that 130 people would have said "YES" at least once. However, you are assuming that there are no people who didn't answer YES to any of the questions. While it does work when you need to find the least value of n, it does not work always.

For Q.4, you are right, x could be 8 or -8. I just assumed that there must have been a diagram with the question, with (x,0) on the positive X-axis. Don't ask me why.

[gre320hex]

Goldust,

A'right got your point on Q.2 . I went back and thought about it. Another approach I could think of is

Total No's for 1 st question : 90
Total No's for 2 nd question : 280

Therefore, if all these no's were from different people, than 500 - 90 - 280 = 130 people who would have said Yes for both questions.

Does that make sense?

[Goldust]

Yup that makes perfect sense. It is the complement of the method that I used.