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Andy and Brenda...!

Expert replies
by chaitanya.bhansali » Thu Aug 07, 2014 10:09 am
Andy and Brenda have a total sum of $1330. If 3/23 of Andy's amount is equal to 9/26 of
Brenda's amount, approximately what percent more money does Brenda need to have in order to have an amount equal to that of Andy?
A) 26.5 B) 38
C) 52 D) 126.5 E) 165
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Source: — Problem Solving |

by [email protected] » Thu Aug 07, 2014 10:25 am
Hi chaitanya.bhansali,

This question can be solved in a couple of different ways. You could set it up as a long-form "system" question (2 variables and 2 unique equations), but here's a way that requires considerably less "math":

Since we're told that 3/23 of A = 9/26 of B, it does NOT actually matter what A + B is. We have the relationship that we need to answer the given question. Here's why/how:

3A/23 = 9B/26

We can reduce this immediately (both numerators are divisible by 3):

A/23 = 3B/26

Now cross-multiply:

26A = 69B

To make the next steps as easy as possible, I'm going to TEST VALUES for A and B....

A = 69
B = 26

The question asks what approximate PERCENT MORE money would Brenda need to have the same amount as Andy....which is the PERCENTAGE CHANGE Formula....

(New - Old)/(Old) = (69 - 26)/26 = 43/26 = 1 17/26

1 17/26 is greater than 150%.....look at the answers....

Final Answer: E

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by GMATGuruNY » Thu Aug 07, 2014 11:11 am
chaitanya.bhansali wrote:Andy and Brenda have a total sum of $1330. If 3/23 of Andy's amount is equal to 9/26 of
Brenda's amount, approximately what percent more money does Brenda need to have in order to have an amount equal to that of Andy?
A) 26.5 B) 38
C) 52 D) 126.5 E) 165
Since the question stem asks for a PERCENT, the total sum can be ANY VALUE.

Let B = $26.
Then 9/26 of B = (9/26)(26) = 9.

Since 9/26 of B is equal to 3/23 of A, we get:
9 = (3/23)A
(9*23)/3 = A.
A = $69.

We need to determine what percent must be added to B=26 to get A=69.
Since the question stem asks for the APPROXIMATE percentage, test easy cases.
If 100% added to B, we get:
26 + 100% of 26 = 26 + 26 = 52.
Too small.
If 150% is added to B, we get:
26 + 150% of 26 = 26 + 39 = 65.
Still too small.
The correct answer must be greater than 150.

The correct answer is E.
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by shrivats » Thu Aug 07, 2014 8:31 pm
Here is a much easier method.
let the two amounts be A and B.

for the sake of calculations, 3/23 can be approximated to 1/8 and 9/26 can be approximated to 1/3.

A/8 = B/3

A = 8B/3
= B + 5B/3 (so B has to be increased by 5/3 to equal A )
5/3 = 1.67, in terms of % the increase would be around 167%..

Ans E, 165%
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