GMAT MATH - DATA SUFFICIENCY

GMAT MATH - DATA SUFFICIENCY

Question

If r, s, and t are all positive integers, what is the remainder of 3^p/10 if p = qst?

(1) s is even
(2) p = 4t

A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C) Both statements TOGETHER are sufficient, but NEITHER one ALONE is sufficient.
D) EACH statement ALONE is sufficient.
E) Statements (1) and (2) TOGETHER are NOT sufficient.

Solution

Answer B

When a number is divided by 10, the remainder is simply the units digit of that number. For example, 243 divided by 10 has a remainder of 3.

Statement 1 INSUFFICIENT: If s is even, we know that the product qst is even and so is p. Knowing that p is even does not help us with definate value to find the reminder.

Statement 2 is SUFFICIENT: If p = 4t and t is an integer, p must be a multiple of 4. so any possible value for p will be (0,4,8,12...). Since at any point we know a definite value of p we know the value of 3 ^ p. So we can find reminder by dividing it by 10.

GMAT Math : Data Sufficiency

GMAT Math : Data Sufficiency 

 Question

 How must is 60 percent of a certain number

Statement 1 : 25 percent of twice the number is equal to half the number.
Statement 2 : 50 percent of the number is 20 less than the number.

A) If statement 1 alone is sufficient to answer the question, but statement 2 alone is not sufficient.
(B) If statement 2 alone is sufficient to answer the question, but statement 1 alone is not sufficient.
(C) If both statements together are needed to answer the question, but neither statement alone is sufficient.
(D) If either statement by itself is sufficient to answer the question.
(E) If not enough facts are given to answer the question.

Solution:

 Answer B

Evaluating Statement 1: 25 percent of twice the number is equal to half the number.

 To determine what is 60 of a certain number (say x), you need to know what the value of that number (x) is. Statement 1 seems to provide that equation to solve for the value of x, but when you read this statement closely it is bogus leads you nowhere.

it states as
2 (0.25x ) = 0.5x
0.5x = 0.5x

You cannot solve for the value of x.

 Evaluating Statement 2: 50 percent of the number is 20 less than the number. 

 The Equation for this statement will be

0.5x = x-20
This implies,
x-0.5x= 20
Solving for 
0.5x =20
x=40

Since we know the value of X we can now find 60 percent of x.
So the correct choice is answer B