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20 Jun 2017, 02:52
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84% (02:10) correct
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The ratio of blue to black jeans at a certain shop is 15:16. If there were 35 additional black jeans in the shop, the ratio of blue to black jeans would be 15:21. How many blue jeans does the shop have?
A) 100
B) 103
C) 105
D) 107
E) 110
A) 100
B) 103
C) 105
D) 107
E) 110
Updated on: 01 Feb 2021, 07:56
Originally posted by BrentGMATPrepNow on 20 Jun 2017, 08:42.
Last edited by BrentGMATPrepNow on 01 Feb 2021, 07:56, edited 1 time in total.
Last edited by BrentGMATPrepNow on 01 Feb 2021, 07:56, edited 1 time in total.
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danlew
We can actually solve this question WITHOUT using the information in the second sentence.
The ratio of blue to black jeans at a certain shop is 15:16
There are many possibilities. Here are a few:
- There are 15 blue jeans and 16 black jeans
- There are 30 blue jeans and 32 black jeans
- There are 45 blue jeans and 48 black jeans
- There are 60 blue jeans and 64 black jeans
- There are 75 blue jeans and 80 black jeans
etc
Notice that, since the number of each type of jeans must be an INTEGER, the number of blue jeans must be a multiple of 15
Check the answer choices....only one answer choice is a multiple of 15
Answer:
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20 Jun 2017, 03:04
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danlew
Let number of Blue jeans be \(= X\)
Let number of Black jeans be \(= Y\)
Blue jeans / Black jeans \(= \frac{X}{Y} = \frac{15}{16}\)
\(Y = \frac{16}{15} * X\) --------- (i)
Blue jeans / Black jeans + 35 additional black jeans \(= \frac{X}{Y + 35} = \frac{15}{21}\)
\(\frac{X}{Y + 35} = \frac{15}{21}\)
\(21 X = 15 (Y + 35)\)
\(21 X = 15 Y + 525\) ---------- (ii)
Substituting value of Y from (i) in (ii), we get;
\(21 X = 15 (\frac{16}{15} * X) + 525\)
\(21 X = 16 X + 525\)
\(21 X - 16 X = 525\)
\(5 X = 525\)
\(X = \frac{525}{5} = 105 .\) Answer (C) ...
