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 BWhen 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.
