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To find the total amount of water in 3 glasses

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To find the total amount of water in 3 glasses

by gmattesttaker2 » Wed Dec 25, 2013 6:25 pm
Hello,

Can you please assist with this:

If three glasses contain 1/6 liter, 1/8 liter, and 1/9 liter of water, respectively,
then the total amount of water in the three glasses is between...


(A) 0 and 1/3 liters
(B) 1/3 and 1/2 liters
(C) 1/2 and 2/3 liters
(D) 2/3 and 5/6 liters
(E) 5/6 and 1 liters

OA: B

I tried to solve as follows:

1/6 + 1/8 + 1/9

= (12 + 9 + 8)/72

= 29/72

However, I was not sure how to proceed further. Can you please assist?

Thanks,
Sri
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by Uva@90 » Wed Dec 25, 2013 7:09 pm
Hi Sri,
You arrived till 29/72
72*4 = 288 <290
so 29/72 should be approximate .4
Come to options now,
A = 0-0.33
Not in our eliminate
B = 0.33-0.5
Yes
Hence Ans is B

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Uva.
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by Stuart@KaplanGMAT » Wed Dec 25, 2013 9:24 pm
gmattesttaker2 wrote:Hello,

Can you please assist with this:

If three glasses contain 1/6 liter, 1/8 liter, and 1/9 liter of water, respectively,
then the total amount of water in the three glasses is between...


(A) 0 and 1/3 liters
(B) 1/3 and 1/2 liters
(C) 1/2 and 2/3 liters
(D) 2/3 and 5/6 liters
(E) 5/6 and 1 liters

OA: B

I tried to solve as follows:

1/6 + 1/8 + 1/9

= (12 + 9 + 8)/72

= 29/72

However, I was not sure how to proceed further. Can you please assist?

Thanks,
Sri
Hi!

Uva did a great job saying what you could do next, so I want to discuss what you could have done instead - everyone taking the GMAT should strive to follow the Lazy Test-taker Rule: Do the least amount of work possible to answer each question.

On questions that ask you to find a range, focusing on limits is often a huge time saver. Such is the case on this question.

If our 3 fractions had all been 1/6, the sum would be 3/6 = 1/2
If our 3 fractions had all been 1/9, the sum would be 3/9 = 1/3

Since our 3 fractions are between 1/6 and 1/9 (inclusive), the answer must be between 1/3 and 1/2 - choose (B)!

Note that it's not a coincidence that things worked out so nicely - the GMAT wants to reward you for strategic thinking, so many questions are designed to be quickly solvable with logic and common sense.
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by GMATGuruNY » Wed Dec 25, 2013 9:28 pm
gmattesttaker2 wrote:Hello,

Can you please assist with this:

If three glasses contain 1/6 liter, 1/8 liter, and 1/9 liter of water, respectively,
then the total amount of water in the three glasses is between...


(A) 0 and 1/3 liters
(B) 1/3 and 1/2 liters
(C) 1/2 and 2/3 liters
(D) 2/3 and 5/6 liters
(E) 5/6 and 1 liters

OA: B
If all 3 glasses each contained 1/9 liter, then the total volume = 3(1/9) = 1/3 liter.
Since 2 of the glasses each contain MORE than 1/9 liter, the ACTUAL total volume must be GREATER than 1/3 liter.

If all 3 glasses each contained 1/6 liter, then the total volume = 3(1/6) = 1/2 liter.
Since 2 of the glasses each contain LESS than 1/6 liter, the ACTUAL total volume must be LESS than 1/2 liter.

Thus, the actual total volume must be BETWEEN 1/3 and 1/2 liter.

The correct answer is B.
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by Brent@GMATPrepNow » Thu Dec 26, 2013 7:25 am
gmattesttaker2 wrote: If three glasses contain 1/6 liter, 1/8 liter, and 1/9 liter of water, respectively,
then the total amount of water in the three glasses is between...

(A) 0 and 1/3 liters
(B) 1/3 and 1/2 liters
(C) 1/2 and 2/3 liters
(D) 2/3 and 5/6 liters
(E) 5/6 and 1 liters
I'd typically solve this question using the same approach used by Mitch and Stuart, but here's another approach that wouldn't take long.

All students should know the following conversions from fraction to decimal:
1/2 = 0.5
1/3 ≈ 0.33
1/4 = 0.25
1/5 = 0.2
1/6 ≈ 0.17
1/7 ≈ 0.14
1/8 = 0.125
1/9 ≈ 0.11

So, 1/6 + 1/8 + 1/9 ≈ 0.17 + 0.125 + 0.11
From here, we can "eyeball" this sum to see that we get approximately 0.4, so the answer must be B

Cheers,
Brent
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by abhasjha » Thu Dec 26, 2013 10:49 am
Brent@GMATPrepNow wrote:
gmattesttaker2 wrote: If three glasses contain 1/6 liter, 1/8 liter, and 1/9 liter of water, respectively,
then the total amount of water in the three glasses is between...

(A) 0 and 1/3 liters
(B) 1/3 and 1/2 liters
(C) 1/2 and 2/3 liters
(D) 2/3 and 5/6 liters
(E) 5/6 and 1 liters
I'd typically solve this question using the same approach used by Mitch and Stuart, but here's another approach that wouldn't take long.

All students should know the following conversions from fraction to decimal:
1/2 = 0.5
1/3 ≈ 0.33
1/4 = 0.25
1/5 = 0.2
1/6 ≈ 0.17
1/7 ≈ 0.14
1/8 = 0.125
1/9 ≈ 0.11

Hi Brent ,

I just want to add that these fractions can be memorised quickly if you know percentage - fraction equivalent .... this is what is mean ...

100/2 = 50 and 1/2 = .5
100/3 = 33.33 so 1/3 = .33
100/4 = 25 so 1/4 = .25

and if one wants to remember 1/7 = then 7 x 2 =14 and 14 x 2 = 28

therefore 1/7 = .1428.....

else 100/7 ... 7x14 + 2 ... therefore 1/7 = .14

similarly 1/8 , 1/9 .... etc

one need not memorise anything ....

if u know 1/3 then 2/3 can be calculated easily like this ...

since 1/3 = .33 so 2/3 = .33x2 = .66
and for 5/6 since 1/6 = .1666 so 5/6 = .1666x5 = .833...

this way one can convert also the option choice into decimals and the figurue given in question into decimal too and see what the answer is ...

though not a preferable method as this is time consuming ... just an alternate method to solve question.
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