Question Number 1:



Given: Angle PSR = 90°
In triangle PRQ, PRQ + PQR + QPR = 180°
Thus, PQR + QPR = 180° - PRQ = PRS

Statement 1: QPR = 30°
As, PQR + QPR = PRS => PRS - PQR = QPR = 30°

Sufficient.

Statement 2: PQR + PRQ = 150° => QPR = 180° - 150° = 30°
Thus statement 2 is equivalent to statement 1.

Sufficient.

The correct answer is D.

Question Number 2:

If r and s are positive integer, is r/s is an integer?

• (1) Every factor of s is also a factor of r.
  (2) Every prime factor of s is also a prime factor of r.

Statement 1: As every factor of s is also a factor of r, r is completely divisible by s. Thus, r/s is an integer.

Sufficient.

Statement 2: Every prime factor of s is also a factor of r. But this doesn't mean that r is completely divisible by s, as it may be possible that the power of a prime in s is greater than that in r. For example, take r = 2*3^2 = 18 and s = 2^2*3^2 = 36. Every prime factor of s, i.e. 2 and 3 is also a prime factor of r. But r/s (=1/2) is not an integer.

Not sufficient.

The correct answer is A.

Question Number 3:

Refer to this post: https://www.beatthegmat.com/gmat-prep-70 ... tml#311730

Question Number 4:

Is (m + z) > 0?

• (1) (m - 3z) > 0
  (2) (4z - m) > 0

Statement 1: (m - 3z) > 0 => m > 3z

Not sufficient.

Statement 2: (4z - m) > 0 => 4z > m

Not Sufficient.

1 & 2 Together: (1) + (2) => (m - 3z) + (4z - m) > 0 => z > 0
Now, combination of the inequalities results in, 4z > m > 3z> 0
Addition of z to each terms results, (4z + z) > (m + z) > (3z + z) > z > 0
Thus, (m + z) > 0.

Sufficient.

The correct answer is C.

Question Number 5:

If x is a positive number less than 10, is z greater than the average (arithmetic mean) of x and 10?

• (1) On the number line, z is closer to 10 than it is to x.
  (2) z = 5x.

Given: x < 10.
Average of x and 10 = (x + 10)/2

Statement 1: On the number line, z is closer to 10 than it is to x.



Referring to the above picture, z must lie between (x + 10)/2 and 10.
Thus, z > (x + 10)/2

Sufficient.

Statement 2: z = 5x
For z to be greater than (x + 10)/2,
5x > (x + 10)/2 => 10x > (x + 10) => 9x > 10 => x > 9/10

But x may not be greater than 9/10!

Not sufficient.

The correct answer is A.