GMAT PREP Questions help

[earnest10]

Hello All:

Please I need help once again .

[Night reader]

Hello All:

Please I need help once again .

[GMATGuruNY]

On a certain sight-seeing tour, the ratio of the number of women to the number of children was 5 to 2. What was the number of men on the sight-seeing tour?

1). On the sight-seeing tour, the ratio of the number of children to the number of men was 5 to 11.
2). The number of women on the sight-seeing tour was less than 30.

This question is restricted to positive integers because it is about people. We can't have 2/3 of a child.

Given info is W:C = 5:2.

Question: M?

Statement 1: C:M = 5:11.
To combine this ratio with the first ratio, the common element (C) must be represented by the same value in each ratio.
W:C = 5:2 = 25:10
C:M = 5:11 = 10:22
Thus, W:C:M = 25:10:22.
Since we know only the ratio, no way to determine the actual value of M.
Insufficient.

Statement 2: W<30.
No way to determine M.
Insufficient.

Statements 1 and 2 together:
Given that W:C:M = 25:10:22 and W<30, we know that W=25 (because if we use a multiple of the ratio, the number of women will be at least 2*25 = 50).
Since W=25 and W:C:M = 25:10:22, M=22.
Sufficient.

The correct answer is C.

[Night reader]

Thanks Mitch! For the 2nd time, I was trying to solve a simple ac ratio conversion quest. brutally ...

On a certain sight-seeing tour, the ratio of the number of women to the number of children was 5 to 2. What was the number of men on the sight-seeing tour?

1). On the sight-seeing tour, the ratio of the number of children to the number of men was 5 to 11.
2). The number of women on the sight-seeing tour was less than 30.

This question is restricted to positive integers because it is about people. We can't have 2/3 of a child.

Given info is W:C = 5:2.

Question: M?

Statement 1: C:M = 5:11.
To combine this ratio with the first ratio, the common element (C) must be represented by the same value in each ratio.
W:C = 5:2 = 25:10
C:M = 5:11 = 10:22
Thus, W:C:M = 25:10:22.
Since we know only the ratio, no way to determine the actual value of M.
Insufficient.

Statement 2: W<30.
No way to determine M.
Insufficient.

Statements 1 and 2 together:
Given that W:C:M = 25:10:22 and W<30, we know that W=25 (because if we use a multiple of the ratio, the number of women will be at least 2*25 = 50).
Since W=25 and W:C:M = 25:10:22, M=22.
Sufficient.

The correct answer is C.

[Anurag@Gurome]

Question 2:

Simple way is to use the following shortcuts:
If a line has a positive slope, it will pass through quadrants I and III.

If a line has a negative slope, it will pass through quadrants II and IV.

(1) Since the slope is -1/6, which is negative, so the line k will pass through quadrant II. So, (1) is SUFFICIENT.

(2) y-intercept is -6 implies line k passes through (0, -6). In this case the line may or may not pass through quadrant II. So, (2) is NOT SUFFICIENT.

The correct answer is A.

[Anurag@Gurome]

Question 3:

Statements 1 and 2 are independently NOT SUFFICIENT to answer the question.

It is known that for any two positive integers X and Y, X*Y = (LCM of X and Y) * (GCF of X and Y), this fact can be very easily used in these type of questions.

So, when you combine both the statements, to answer the question.

So, the correct answer is C.

[Anurag@Gurome]

Question 4:

Easiest way is to plug in values for a and b: Let a = 3 and b = 4

Choice A: f(3 + 4) = (3 + 4)^2 = 12^2 = 144, and f(3) + f(4) = 3^3 + 4^2 = 9 + 16 = 25; clearly f(a + b) is not equal to f(a) + f(b).

Choice B: f(3 + 4) = 3 + 4 + 1 = 8, f(3) + f(4) = 3 + 1 + 4 + 1 = 9; clearly f(a + b) is not equal to f(a) + f(b).

Choice C: f(3 + 4) = √(3 + 4) = √7, f(3) + f(4) = √3 + √4; clearly f(a + b) is not equal to f(a) + f(b).

Choice D: f(3 + 4) = 2/7, f(3) + f(4) = 2/3 + 2/4; clearly f(a + b) is not equal to f(a) + f(b).

Choice E: f(3 + 4) = -3(7) = -21, f(3) + f(4) = -3(3) - 3(4) = -9 - 12 = -21; here f(a + b) = f(a) + f(b)

The correct answer is E.

[Anurag@Gurome]

Question 5:

If p is a prime number, then p + 1 cannot be a prime number (as 2 and 3 are the only consecutive prime numbers, but it is given that p is a prime number greater than 2).

(1) It is given that there are 100 primes between 1 and p+1, so p is the 100th prime number. Hence, (1) is SUFFICIENT.

(2) We can write all prime numbers between 1 and 3912 to get the value of p. So, (2) is SUFFICIENT.

The correct answer is D.