Problem Solving - 54

This year Henry will save a certain amount of his income, and he will spend the rest. Next year Henry will have no income, but for each dollar that he saves this year, he will have 1 + r dollars available to spend. In terms of r, what fraction of his income should Henry save this year so that next year the amount he was available to spend will be equal to half the amount that he spends this year?

(A) 1/(r+2)
(B) 1/2(r+2)
(C) 1/(3r+2)
(D) 1/(r+3)
(E) 1/(2r+3)


Answer: E

Let total income = x
Let saved = y
=> spent = x-y

Total dollars available that he can spend next year = y(1+r)

Given y(1+r) = (x-y)/2
=> y = x/(2r+3)

Fraction (y/x) = 1/(2r+3)

Hence E

Problem Solving - 36

Equal amounts of water were poured into two empty jars of different capacities, which made one jar 1/4 full and the other jar 1/3 full. If the water in the jar with lesser capacity is then poured into the jar with the greater capacity, what fraction of the larger jar will be filled with water?

A. 1/7

B. 2/7

C. 1/2

D. 7/12

E. 2/3

Answer: C

The jar that is 1/3 full is smaller
water in jar 1 = water in jar 2
jar 1 is now twice as full (1/4)*2 = 1/2

or

1/4 + 1/4 = 1/2

Manhatten Challenge Problem of the week ! - Aug 21

Question

What is the ratio of 2x to 3y?

(1) The ratio of x^2 to y^2 is equal to 36/25.

(2) The ratio of x^5 to y^5 is greater than 1.

(A) Statement (1) ALONE is sufficient to answer the question, but statement (2) alone is not.
(B) Statement (2) ALONE is sufficient to answer the question, but statement (1) alone is not.
(C) Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient.
(D) EACH statement ALONE is sufficient to answer the question.
(E) Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the question.

For the answer click on link below -
Ratios and exponents