Question: John ordered 4 pairs of black socks and some additional pair of blue socks. The price of the black socks per pair was twice that the blue. When the order was filled, it was found that the number of pairs of the two colors has been interchanged. This increased the bill by 50%. The ratio of the number if pairs of black socks of the number of pairs of blue socks in the original order was:

1. 4 : 1
2. 2 : 1
3. 1 : 4
4. 1 : 2
5. 1 : 8

Answer:
Solution with Explanation:
Approach Solution (1):

For the purpose of exam techniques: Can set up a table for (where Bla. is Black, Blu. is Blue, Q. is Quantum, P. is Price, T. is Total and Rev. T is Reverse Total

…Q…P…T…Rev.T
Black…4…2(2)…16…4
Blu…1…2…2…8
T…………..18…12

Luckily A fits in but we need to remember that we need the original or reversed.

Correct Option: C

Approach Solution (2):

Let price of Black socks be P and Let price of Blue socks be Q

So from question we know, P = 2Q --- (1)

Let ‘x’ be the number of Blue socks ordered.

So we can formulate equation(s) in the below way

Expected Bill (original bill) = 4P + xQ --- (2)
Interchange Bill (Final Bill) = 4Q + xP --- (3)

Now, we know form the question:

Interchange Bill (Final Bill) = 1.5 * Expected Bill (original bill) --- (4)

From (2), (3), and (4)

4Q + xP = 1.5 [4P + xQ] --- (5)

From (1) and (5),

4Q + 2xQ = 1.5 [8Q + xQ]

On solving, we get:

x = 16

So original ratio becomes:

Count of black : Count of blue = 4 : 16 or 4 : 1

Correct Option: C

“John ordered 4 pairs of black socks and some additional pair of blue socks. The price of the black socks per pair was twice that the blue. When the order was filled, it was found that the number of pairs of the two colors has been interchanged. This increased the bill by 50%. The ratio of the number if pairs of black socks of the number of pairs of blue socks in the original order was:”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “GMAT Official Guide Quantitative Review”. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. The GMAT Quant topic in the problem-solving part requires calculative mathematical problems that should be solved with proper mathematical knowledge.

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