Hi ske,
While this question can be solved algebraically, it can also be solved with a bit of brute force and some Number Properties.
We're told that two numbers are in the ratio of 2:3. Thus, the two numbers could be...
2 and 3
4 and 6
6 and 9
8 and 12
10 and 15
Etc.
We're told that ADDING 4 to each number changes the ratio of the numbers to 5:7. We're asked for the DIFFERENCE between the original numbers.
Since adding 4 makes the first number a multiple of 5, this limits the possibilities....
2+4 = 6 NOT POSSIBLE
4+4 = 8 NOT POSSIBLE
6+4 = 10 This IS possible...Using this example, we would have...
"6 and 9", after adding 4 to each, becomes "10 and 13"...this is NOT a ratio of 5 to 7 though (even though it's pretty close), so we have to keep looking....
The next value that becomes a multiple of 5 when you add 4 to it is...16...
16 + 4 = 20
With "16 and 24", after adding 4 to each, we have "20 and 28." This IS a ratio of 5 to 7, so we have our pair of original numbers.
The difference between them is 8.
Final Answer:
GMAT assassins aren't born, they're made,
Rich
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