Practice Test Problems

[showoff16884]

Please help explain the answers to the following practice questions:

1. If [(1/5)^m *(1/4)^18] = [1/(2(10)^35)], what is the value of m?

A. 17
B. 18
C. 34
D. 35
E. 36


2. If (2^x) - (2^(x-2)) = (3(2^13)), x=?

A. 9
B. 11
C. 13
D. 15
E. 17


3. A perimeter of a certain isosceles right triangle is 16+(16 Sq root 2), what is the length of the hypotenuse?

A. 8
B. 16
C. 4 Sqrt 2
D. 8 Sqrt 2
E. 16 Sqrt 2

4. If n is a positive integer and the product of all the integers from 1 to n, is a multiple of 990, what is the least possible value of n?

A. 10
B. 11
C. 12
D. 13
E. 14



OA: 1 (D); 2 (D); 3 (B); 4 (B)

[camitava]

Q-1
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Already discussed in the section but forgot the link! I forgot the link ...

Q-2
-----
Suppose, 2^x = a

So a - a/4 = 3*2^13
or 3a = 3*2^15
x = 15.
Got the answer?
Q-3
----
Suppose, isocelses sides are a and hyp is h
so 2a^2 = h^2
so h = sqrt(2)

Again a + a + h = 16 + 16sqrt(2)
r a = (16 + 16*sqrt(2)) / (sqrt(2) + 1) = 8*sqrt(2).

h = sqrt(2) * 8*sqrt(2) = 16

Q - 4
------
990 = 9 * 10 * 11
11 is a prime number so in n 11 should be present. So B is the best answer to chose.

[showoff16884]

Here is the link to solution to problem # 1

https://www.beatthegmat.com/stuck-on-thi ... t6439.html

Its a tricky one!

[gmatrant]

I would like to know how to solve 1 & 4 as well, and I also have this question.

A furniture dealer purchased a desk for 150 and then set the selling price equals the purchase price plus the mark up that was 40% of the selling price. What was the amount of the dealer gross profit from the purchase and the sell of the desk? answer is 100. I solved this and got 60, please fill me in with the missing details.

The question is not very clear, but this is how its done

SP =150 + 40% of SP
SP - 2/5*SP = 150 [ 2/5SP is 40% SP, simplified]
3/5SP = 150
SP = 250
Profit = SP - CP
Profit = 250 - 150 =100