A tank contains 30 litres of diesel, 6 litres are drawn out and filled

Question

A tank contains 30 litres of diesel, 6 litres are drawn out and filled by kerosene. This process is repeated three times. What will be the proportion of diesel to kerosene in the resulting mixture ?

A. 64/61

B. 1

C. 20/25

D. 64/125

E. 1/2

GMATinsight · Accepted Answer

CONCEPT  :
 \frac{Diesel-Left}{Original-Diesel} = (1- \frac{x}{100})^n 
 
Here, x = percentage of the quantity replaced
n = Number of iterations

Here,  x = \frac{6}{30}*100 = 20 %

i.e.  \frac{Diesel-Left}{30} = (1- \frac{20}{100})^3

i.e. Diesel Left  = 30*\frac{64}{125} = 15.36 
Karosene = 30-15.36 = 14.64

Diesel is greater than karosene and only Option A gives us the ratio greater than 1

Answer: Option A

Please check the following Video for learning the concept of successive replacement

https://www.youtube.com/watch?v=PchJCUHfB4w

Vivek1707 · Answer

To avoid lengthly calculations, the fastest way of solving this would be to find the % of Diesel remaining ---> using that you ll get an idea of what the ratio should be.

% Diesel remaining after 3 replacement would be

24^3 / 30^3 * 100

Which is (0.8)^3 *100 or 0.512 * 100 = 51.2%

Hence ratio would be 51.2/ 48.8 i.e slighly more than 1 i.e A so the only answer is A

To understand the mechanics of how we got the % of diesel check out my explanation on the question below
https://gmatclub.com/forum/8-litres-of- ... 99413.html

Vivek1707 · Answer

Hi  GMATinsight

One doubt I have here. When its that the process is  "repeated 3 times ", shouldnt this be 1 + 3 i.e  total 4 times  in total. The word " repeat " ideally  shouldnt include  the first time the operation is done. Simlar questions avoid this ambiguity by adding the word ' more ' i.e repeated 3 more times. Please guide.

egmat · Answer

Hi Vivek1707,

This is a fair language worry, and you're right that some writers add "more" to remove the ambiguity. Let me show you how the question itself settles it.

In these mixture problems, the phrase  "this process is repeated three times"  is meant as  3  operations in total, where each operation = (draw out  6  L) + (refill with kerosene). The sentence isn't describing one operation and  then  three more - it's naming the process once and saying it happens three times. So the exponent in the posted solution, n =  3 , is correct.

The cleanest way to be sure  is to let the answer choices decide for you. The diesel left is:

- With  n = 3 : 30 × (4/5)^3 =  15.36 , kerosene =  14.64 , ratio =  64/61  - that's option  A .
- With  n = 4 : 30 × (4/5)^4 = 30 ×  256/625  =  12.288 , kerosene =  17.712 , ratio ≈  0.694  -  no listed option matches .

That's the tell. If the intended count were  4 , the test would have to give you a choice that fits it. Since only  n = 3  produces an answer on the list (and produces exactly  A ), the question clearly intends three total operations.

So whenever the wording feels ambiguous like this on a GMAT-style question,  plug both readings and see which one lands on an answer choice  - the options are built around the intended interpretation, so they quietly tell you which count the writer meant.

Nice instinct spotting the ambiguity, by the way - that habit will protect you on trickier wordings.

Answer: A

Vivek1707 · Answer

Sure, thank you for your response. This was helpful.

Just that under the time pressure this can cause some trouble. But again as you mentioned we will need to be a bit flexible and having exposure to such questions and such language will definately help.

Thanks again.

A tank contains 30 litres of diesel, 6 litres are drawn out and filled

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