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605-655 Level|   Geometry|      
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alimad
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A small cubical aquarium has a depth of 1 foot. In the small Updated on: 17 Apr 2014, 09:15
Originally posted by alimad on 06 Jun 2008, 11:02.
Last edited by Bunuel on 17 Apr 2014, 09:15, edited 1 time in total.
Renamed the topic, edited the question, added the OA and moved to PS forum.
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C
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72% (03:13) correct 28% (02:54) wrong based on 342 sessions

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A small cubical aquarium has a depth of 1 foot. In the small aquarium there is a big fish with volume 44 cubic inches. A big cubical aquarium has depth of 2 feet and 88 fish, each with a volume of 2 cubic inches. What is the difference in the amount of water between the two aquariums if they are both completely filled?

(A) 246 cubic inches
(B) 300 cubic inches
(C) 11,964 cubic inches
(D) 13,824 cubic inches
(E) 16,348 cubic inches
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C
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A small cubical aquarium has a depth of 1 foot. In the small 06 Mar 2011, 21:40
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A small cubical aquarium has a depth of 1 foot. In the small aquarium there is a big fish with volume 44 cubic inches. A big cubical aquarium has depth of 2 feet and 88 fish, each with a volume of 2 cubic inches. What is the difference in the amount of water between the two aquariums if they are both completely filled?

(A) 246 cubic inches

(B) 300 cubic inches

(C) 11,964 cubic inches

(D) 13,824 cubic inches

(E) 16,348 cubic inches

While I got the answer correct, I would very much like to know if there is a shortcut to the deriving the answer, as the calculations are time-consuming and tedious?
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Notice that while the answer options are wide apart, volume of fish is very small as compared to volume of aquariums.

Just do \(24^3 - 12^3 = 12^3(2^3 - 1) = 144*12*7 = 12096\)
now the actual difference will be less than 12096 but around this number. So answer has to be (C).

In case the answer options were close, the last digit of the options would have been different so you could have just figured out the last digit.

In case the answer options were close and multiple options had the same last digit as the answer, then it would not have been a GMAT question at all. GMAT doesn't expect you to do such calculations. Even the one done above is a little extreme.
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A small cubical aquarium has a depth of 1 foot. In the small 06 Jun 2008, 11:29
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11964.
In small aq. there are 12^3-44 cubic inches of water. In big one: 24^3-88*2 c.i.
For difference subtract the small from the large, this will give 11964.
(you need to know that 1 foot = 12 inches).
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A small cubical aquarium has a depth of 1 foot. In the small Updated on: 21 Oct 2014, 15:04
Originally posted by MRHDK1 on 06 Mar 2011, 06:27.
Last edited by Bunuel on 21 Oct 2014, 15:04, edited 1 time in total.
RENAMED THE TOPIC.
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A small cubical aquarium has a depth of 1 foot. In the small aquarium there is a big fish with volume 44 cubic inches. A big cubical aquarium has depth of 2 feet and 88 fish, each with a volume of 2 cubic inches. What is the difference in the amount of water between the two aquariums if they are both completely filled?

(A) 246 cubic inches

(B) 300 cubic inches

(C) 11,964 cubic inches

(D) 13,824 cubic inches

(E) 16,348 cubic inches

While I got the answer correct, I would very much like to know if there is a shortcut to the deriving the answer, as the calculations are time-consuming and tedious?
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A small cubical aquarium has a depth of 1 foot. In the small 06 Mar 2011, 06:43
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I ft = 12 inch

Volume of bigger aquarium = \(24^3\)
Volume of water in the bigger aquarium = \(24^3 - (88*2) = 24^3 - 176\)

Volume of smaller aquarium = \(12^3\)
Volume of water in the smaller aquarium = \(12^3 - 44 = 12^3 - 44\)

Difference of water in two aquariums:

\(24^3 - 176 - (12^3 - 44) = (2*12)^3 - 176 - 12^3 + 44 = 12^3(2^3-1) - 132 = 12^3*7-132 = 12096 - 132 = 11964\) cubic inches

Ans: "C"
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A small cubical aquarium has a depth of 1 foot. In the small 06 Mar 2011, 06:45
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I am going to calc approx

V1 = Eff volume of small aq = 12 * 12 * 12 - 44
V2 = Eff volume of big aq= 8 * 12 * 12 * 12 - 88 * 2
V2 - V1 = 7 * 12 * 12 * 12 - 176 + 44 = (7 * 12 * 12 * 12) - 132

Unit digit of V2 - V1 is 7 * 2 * 2 * 2 - 2 = 6 - 2 = 4

Hence the answer is C or D.
V2 -V1 (ignore 132 for now) = (7 * 12 * 12 * 12)
12 * 12 = 144
12 * 144 = (10 + 2)*144 = 1440 + 288 = 1728
1728 * 7 = 11.9K something.
V2 - V1 = 11.9K approx

Hence C
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A small cubical aquarium has a depth of 1 foot. In the small 06 Mar 2011, 21:28
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Volume of water small aquarium - (12 * 12 * 12) - 44

Volume of water big aquarium - (24 * 24 * 24) - 44 * 4

So the difference is - (24 * 24 * 24) - 44 * 4 - {(12 * 12 * 12) - 44}

= (12 * 12 * 12) ( 8 - 1) - 44* 4 + 44

= 144*12 * 7 - 3 * 44

= 12 ( 1008 - 11) = 12 * 997 = 11964
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A small cubical aquarium has a depth of 1 foot. In the small 17 Apr 2014, 08:56
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greenoak
11964.
In small aq. there are 12^3-44 cubic inches of water. In big one: 24^3-88*2 c.i.
For difference subtract the small from the large, this will give 11964.
(you need to know that 1 foot = 12 inches).
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how did you find out the big cubical aquarium has 24 inches?
Thanks !
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A small cubical aquarium has a depth of 1 foot. In the small 17 Apr 2014, 09:28
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yooky
greenoak
11964.
In small aq. there are 12^3-44 cubic inches of water. In big one: 24^3-88*2 c.i.
For difference subtract the small from the large, this will give 11964.
(you need to know that 1 foot = 12 inches).


how did you find out the big cubical aquarium has 24 inches?
Thanks !
Show more

1 foot = 12 inches, so the big cubical aquarium has depth of 2 feet = 24 inches.

A small cubical aquarium has a depth of 1 foot. In the small aquarium there is a big fish with volume 44 cubic inches. A big cubical aquarium has depth of 2 feet and 88 fish, each with a volume of 2 cubic inches. What is the difference in the amount of water between the two aquariums if they are both completely filled?

(A) 246 cubic inches
(B) 300 cubic inches
(C) 11,964 cubic inches
(D) 13,824 cubic inches
(E) 16,348 cubic inches

The volume of the small cubical aquarium = \(12^3\) cubic inches;
The amount of the water in the small cubical aquarium = \(12^3 - 44\) cubic inches.

The volume of the big cubical aquarium = \(24^3\) cubic inches;
The amount of the water in the small cubical aquarium = \(24^3 - 88*2=24^3-176\) cubic inches.

The difference = \((24^3-176)-(12^3 - 44)=24^3-12^3-132=12^3(2^3-1)-132=144*12*7-132=12096-132\)

Answer: C.
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A small cubical aquarium has a depth of 1 foot. In the small 06 Jun 2014, 06:18
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Ballpark it.

Start from the big tank: 24^3 = 13,824 which happens to be option d).
You know this can't be the answer since you have not even subtracted the other values.

Now take the small tank: 12^3 = 1,728.

13,824 - 1,728 has to be in the range of option c) and no other.
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A small cubical aquarium has a depth of 1 foot. In the small 06 Jun 2014, 11:49
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Hi Bunuel, tell me somthing, do we need to know that 1 foot = 12 inches because me and i`m pretty sure that all of students who are not used to the imperial system using inches yards, miles etc will be in problem with it.
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A small cubical aquarium has a depth of 1 foot. In the small 06 Jun 2014, 11:55
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murilomoraes
Hi Bunuel, tell me somthing, do we need to know that 1 foot = 12 inches because me and i`m pretty sure that all of students who are not used to the imperial system using inches yards, miles etc will be in problem with it.
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On the real test, such question would have a note saying that 1 foot = 12 inches.
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A small cubical aquarium has a depth of 1 foot. In the small 26 Dec 2016, 09:46
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A small cubical aquarium has a depth of 1 foot. In the small aquarium there is a big fish with volume 44 cubic inches. A big cubical aquarium has a depth of 2 feet and 88 fish, each with a volume of 2 cubic inches. What is the difference in the amount of water between the two aquariums if they are both completely filled?
(Note: 1 foot = 12 inches)

A. 246 cubic inches
B. 300 cubic inches
C. 11,964 cubic inches
D. 13,824 cubic inches
E. 16,348 cubic inches
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A small cubical aquarium has a depth of 1 foot. In the small 26 Dec 2016, 10:34
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interceptor77
A small cubical aquarium has a depth of 1 foot. In the small aquarium there is a big fish with volume 44 cubic inches. A big cubical aquarium has a depth of 2 feet and 88 fish, each with a volume of 2 cubic inches. What is the difference in the amount of water between the two aquariums if they are both completely filled?
(Note: 1 foot = 12 inches)

A. 246 cubic inches
B. 300 cubic inches
C. 11,964 cubic inches
D. 13,824 cubic inches
E. 16,348 cubic inches
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Merging topics. Please refer to the discussion above.
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A small cubical aquarium has a depth of 1 foot. In the small 07 Nov 2023, 19:52
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Hello from the GMAT Club BumpBot!

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