Problem Solving

BTGmoderatorLU wrote:Source: e-GMAT

If the ratio of the present age of Anna and Paula is 1:2, what could be the ratio of their respective ages 8 years ago??

A. 3 : 8
B. 4 : 7
C. 3 : 5
D. 2 : 3
E. 4 : 5

The OA is A

Say the present age of Anna and Paula are x and 2x, respectively.

Thus, their ages 8 years ago would be (x - 8) and (2x - 8), respectively.

Thus, the ratio of their ages after 8 years would be (x - 8) : (2x - 8). Note that x is a positive integer and is greater than 8.

Note that the current ratio of the ages is 1 : 2, so 8 years ago, then the ratio of their ages must be less than 1 : 2. We see that only Option A (3 : 8 = 1: (8/3) = 1 : 2.67) is less than 1 : 2; thus option A is the correct answer.

To quickly compare options against 1 : 2, we must see that say for a ratio a : b, if b is greater than double of a, then a : b is less than 1 : 2, else not.

Let's visit all the options.

A. 3 : 8: We see that double of 3 is 6 and 8 is greater than 6, so 3 : 8 is less than 1 : 2. The correct answer.
B. 4 : 7: We see that double of 4 is 8 and 7 is not greater than 8, so 4 : 7 is NOT less than 1 : 2.
C. 3 : 5: We see that double of 3 is 6 and 5 is not greater than 6, so 3 : 5 is NOT less than 1 : 2.
D. 2 : 3: We see that double of 2 is 4 and 3 is not greater than 4, so 2 : 3 is NOT less than 1 : 2.
E. 4 : 5: We see that double of 4 is 8 and 5 is not greater than 8, so 4 : 5 is NOT less than 1 : 2.

The correct answer: A

Hope this helps!

-Jay
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Hi All,

We're told that the ratio of Anna's and Paula's CURRENT ages is 1:2. We're asked which of the following COULD have been the ratio of their respective ages 8 years ago. This question can be solved in a couple of different ways, including by 'brute force' Arithmetic.

Since we're asked about their ages 8 years ago, we know that both Anna and Paula are older than 8 right now. Given the 1:2 ratio in their current ages, the ages of the two girls could be...

Anna = 9, Paula = 18
Anna = 10, Paula = 20
Anna = 11, Paula = 22
Anna = 12, Paula = 24
Etc.

When we subtract 8 from each of the values in one of those pairs of numbers, we'll get the correct answer, so we just have to do enough work to find that answer...

9 & 18 would lead to 1 and 10 --> 1:10 Not an option
10 & 20 would lead to 2 and 12 --> 2:12 = 1:6 Not an option
11 & 22 would lead to 3 and 14 --> 3:14 Not an option
12 & 24 would lead to 4 and 16 --> 4:16 = 1:4 Not an option
13 & 26 would lead to 5 and 18 --> 5:18 Not an option
14 & 28 would lead to 6 and 20 --> 6:20 = 3:8 This IS an option

Final Answer: A

GMAT assassins aren't born, they're made,
Rich

BTGmoderatorLU wrote:Source: e-GMAT

If the ratio of the present age of Anna and Paula is 1:2, what could be the ratio of their respective ages 8 years ago??

A. 3 : 8
B. 4 : 7
C. 3 : 5
D. 2 : 3
E. 4 : 5

The OA is A

Some possible ratios of ages are:

A/P = 8/16, 9/18, 10/20, 11/22, 12/24, 13/26, 14/28, 15/30, 16/32, 17/34, 18/36, 19/38, 20/40

So 8 years ago, these ratios would be:

A/P = 0/8, 1/10, 2/12, 3/14, 4/16, 5/18, 6/20, 7/22, 8/24, 9/26, 10/28, 11/30, 12/32.

We see that if Anna is 20 and Paula is 40, the ratio of their ages 8 years ago is 12/32 = 3/8.

Alternate Solution:

Let x = Ann's present age. Since the ratio of Ann's present age to Paula's present age is 1:2, Paula's present age must be 2x.

8 years ago, Ann's age was (x - 8), and Paula's age was (2x - 8); therefore, the ratio of their ages was (x - 8)/(2x - 8). Let's set this expression equal to each answer choice and see which one gives a positive integer value for x:

A) 3:8

(x - 8)/(2x - 8) = 3/8

8x - 64 = 6x -24

2x = 40

x = 20

We see that answer choice A gives us a positive integer value for x, so it must be the correct answer choice. Indeed, the ratio of Ann's present age to Paula's present age is 20/40, and the ratio of Ann's age 8 years ago to Paula's age 8 years ago is 12/32 = 3/8.

Answer: A