The ratio by weight, measured in pounds, of books to clothes

Question

The ratio by weight, measured in pounds, of books to clothes to electronics in Jorge's suitcase initially stands at 8 to 5 to 3. Jorge then removes 4 pounds of clothing from his suitcase, thereby doubling the ratio of books to clothes. Approximately how much do the electronics in the suitcase weigh, to the nearest pound?

A. 3
B. 4
C. 5
D. 6
E. 7

A. 3
B. 4
C. 5
D. 6
E. 7

saiesta · Accepted Answer

Given =

B : C : E 
 8 : 5 : 3

\frac{8x}{5x-4}  =  \frac{16}{5}  --->  8x(5) = 16(5x - 4)  --->  40x = 80x - 64  --->  -40x = -64  --->  x = 1.6

1.6 * 3 = 4.8

Answer C

ywilfred · Answer

Ratio
B:C:E = 8:5:3

Total weight of items = x

Weight of books = 8x/16
Weight of clothes = 5x/16
Wegith of electronics = 3x/16

New total weight of items = (x-4)
Weight of clothes = 5x/16 - 4 = (5x-64)/16

New Ratio B:C:E = 
8x/16(x-4) : (5x-64)/16(x-4) : 3x/16(x-4)
8x : 5x-64 : 3x

We're told B:C = 16:5
So B/C = 16/5 = 8x/5x-64
80x - 1024 = 40x
40x = 1025
x = 25.6

Electronics = 3x/16 = 4.8 pounds ~ 5 pounds

kidderek · Answer

Maybe I'm misunderstanding the question, but if the weights of the B:C:E is 12.8 : 8 : 4.8, and you take four pounds of clothes away, aren't you left with 12.8 : 4 : 4.8? But 12.8 is more than double 4.

hosam · Answer

By removing the 4 pounds, you're doubling the original ratio - not making B double C. So the new ratio is 16/5

bipolarbear · Answer

I was wondering if anyone else experienced confusion during the question. Take this example from MGMAT:

The ratio by weight, measured in pounds, of books to clothes to electronics in Jorge's suitcase initially stands at 8 to 5 to 3. Jorge then removes 4 pounds of clothing from his suitcase, thereby doubling the ratio of books to clothes. Approximately how much do the electronics in the suitcase weigh, to the nearest pound?

A. 3
B. 4
C. 5
D. 6
E. 7

a) 3
 b) 4
 c) 5
 d) 6
 e) 7

When I hear, thereby "doubling" the ratio of books to clothes, I think that the book to clothes ratio become 2:1, which is colloquial but not correct.

Their answer:
Initially the ratio of B: C: E can be written as 8x: 5x: 3x. (Recall that ratios always employ a common multiplier to calculate the actual numbers.)
After removing 4 pounds of clothing, the ratio of books to clothes is doubled. To double a ratio, we double just the first number; in this case, doubling 8 to 5 yields a new ratio of 16 to 5. This can be expressed as follows:

8x/5x – 4 = 16/5.
Cross multiply to solve for x:
40x = 80x – 64
40x = 64
x = 8/5
The question asks for the approximate weight of the electronics in the suitcase. Since there are 3x pounds of electronics there are 3 × (8/5) = 24/5 or approximately 5 pounds of electronics in the suitcase.
The correct answer is C.

However, I did 8x/5x – 4 = 2. => choice d)

I see how they mean "double" due to the technicalities of the english sentence but I would be really ticked off if this appeared on an actual GMAT. Is this MGMAT's lack of clarity or will the real GMAT use this tricky language?

IanStewart · Answer

There are quite a few details of the wording here which make it unlike a real GMAT question. The ratio in the question is unitless (it's the same ratio whether you measure the weights in nanograms, pounds or tons), so the phrase 'measured in pounds' is redundant and misleading. The phrase 'stands at' is a colloquialism, and not something that would appear in a real test question. When the question says Jorge's action doubles 'the ratio of books to clothes', that phrase is also misleading. The intended meaning is that it doubles 'the ratio of the weight of the books to the weight of the clothes'. One could easily think the statement was referring to the number of books, for example, and not their weight. No real GMAT question is ever so imprecise with its wording.

However, I don't have an issue with the phrase 'doubling the ratio'; ratios are fractions, so if you double a ratio, you're multiplying the first part of the ratio -- the numerator -- by 2.

JeffTargetTestPrep · Answer

We are given that the ratio of books to clothes to electronics = 8x : 5x : 3x. We are also given that Jorge removes 4 pounds of clothing from his suitcase, thereby doubling the ratio of books to clothes, from 8/5 to (2)(8)/5. Thus:

2(8)/5 = 8x/(5x - 4)

16(5x - 4) = 40x

80x - 64 = 40x

40x = 64

x = 64/40 = 1.6

Thus, we see the electronics weigh 3 x 1.6 = 4.8 or about 5 pounds.

Answer: C

Kinshook · Answer

@kidderekGiven: The ratio by weight, measured in pounds, of books to clothes to electronics in Jorge's suitcase initially stands at 8 to 5 to 3. Jorge then removes 4 pounds of clothing from his suitcase, thereby doubling the ratio of books to clothes.
Asked: Approximately how much do the electronics in the suitcase weigh, to the nearest pound?
Before removing clothing: -
Books : Clothes = 8 : 5
Books / Clothes = 8x/5x

After removing 4 pounds of clothing: - 
Books : Clothes = 16: 5
Books / Clothes = 8x/(5x-4) = 16/5
8x / (5x - 4) = 16/5
5x = 10x - 8
x = 8/5

Electronics = 3x = 3*8/5 = 4.8 pounds = 5 pounds approx

IMO C

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The ratio by weight, measured in pounds, of books to clothes

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