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655-705 (Hard)|   Geometry|      
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Tank A and Tank B are hollow rectangular solids. Tank A is empty and T 14 Mar 2018, 02:24
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60% (02:30) correct 40% (02:23) wrong based on 159 sessions

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Tank A and Tank B are hollow rectangular solids. Tank A is empty and Tank B is filled with water to a depth of x feet. If water is transferred from Tank B to Tank A until either Tank A is completely filled or Tank B is completely empty, will there be any water left in Tank B?

(1) The area of the base of Tank A is 8 square feet
(2) The volume of water in Tank B is 64 cubic feet

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Tank A and Tank B are hollow rectangular solids. Tank A is empty and T 14 Mar 2018, 02:25
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Bunuel

Tank A and Tank B are hollow rectangular solids. Tank A is empty and Tank B is filled with water to a depth of x feet. If water is transferred from Tank B to Tank A until either Tank A is completely filled or Tank B is completely empty, will there be any water left in Tank B?

(1) The area of the base of Tank A is 8 square feet
(2) The volume of water in Tank B is 64 cubic feet

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23. Geometry




24. Coordinate Geometry




25. Triangles




26. Polygons




27. Circles




28. Rectangular Solids and Cylinders




29. Graphs and Illustrations



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Tank A and Tank B are hollow rectangular solids. Tank A is empty and T 14 Mar 2018, 13:25
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1) The area of the base of Tank A is 8 square feet
Here, wl = 8. We have no information about the height of Tank A
Also, we have no information about the volume of Tank B. (Insufficient)

(2) The volume of water in Tank B is 64 cubic feet
Here, 2l*2w*2h = 64 -> lwh = 8
But l = 4,w = 2, and h=1 or l = 2,w = 2,h = 2
Also, we don't know the value of x, it could be 0.5 or 1 or 2 (Insufficient)

Combining the information from both the statements, without
knowing the value of x, we can't say anything for sure

Since lwh = 8 and wl = 8 -> h=1,w=2,l=4

Case 1: If x = 0.5, tank B will have 8*4*0.5 = 16 cubic feet of water.
All the water cannot be transferred to Tank A(which has a volume of 8 cubic feet)
In this case, 8 cubic feet of water will remain in Tank B.

Case 2: If x = 0.25, tank B will contain 8*4*0.25 = 8 cubic feet of water.
In this case, the entire 8 cubic feet of water can be transferred and no water
remains in the Tank B (Insufficient - Option E)
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Tank A and Tank B are hollow rectangular solids. Tank A is empty and T 14 Nov 2019, 04:36
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Bunuel

Tank A and Tank B are hollow rectangular solids. Tank A is empty and Tank B is filled with water to a depth of x feet. If water is transferred from Tank B to Tank A until either Tank A is completely filled or Tank B is completely empty, will there be any water left in Tank B?

(1) The area of the base of Tank A is 8 square feet
(2) The volume of water in Tank B is 64 cubic feet
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\(vol_A=lwh;vol_B=8lwh;water=4lwx\)

\(Q:vol_A-water>0…vol_A>water…lwh>4lwx…h>4x?\)

(1) The area of the base of Tank A is 8 square feet insufic
\(lw=8\)

(2) The volume of water in Tank B is 64 cubic feet insufic
\(4lwx=64…lwx=16…x=16/lw\)

(1 & 2) insufic
\(lw=8;x=16/lw=16/8=2\)
\(vol_A>water…lwh>4lwx…h>4x…h>4(2)…h>8?\)

Ans (E)
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Tank A and Tank B are hollow rectangular solids. Tank A is empty and T 11 Feb 2021, 15:54
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Bunuel

Tank A and Tank B are hollow rectangular solids. Tank A is empty and Tank B is filled with water to a depth of x feet. If water is transferred from Tank B to Tank A until either Tank A is completely filled or Tank B is completely empty, will there be any water left in Tank B?

(1) The area of the base of Tank A is 8 square feet
(2) The volume of water in Tank B is 64 cubic feet
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A = LWH
B = (2L)(2W)(2H) = 8LWH
Implication:
A's capacity is \(\frac{1}{8}\) B's capacity.

Thus:
If the water in B constitutes more than \(\frac{1}{8}\) B's capacity, then a portion of the water will remain even after A has been filled.
Question stem, rephrased:
Does the water in B constitute more than \(\frac{1}{8}\) B's capacity?

Even when the statements are combined, the 64 cubic feet of water in B could constitute \(\frac{1}{2}\) B's capacity (in which case the answer to the question stem is YES) or \(\frac{1}{10}\) B's capacity (in which case the answer is NO).

Case 1: \(64 = \frac{1}{2}*B\) --> \(B=128\) --> \(A=\frac{1}{8}*128 = 16 =\) (base area of 8)(height of 2)
Case 2: \(64 = \frac{1}{10}*B \)--> \(B=640\) --> \(A=\frac{1}{8}*640 = 80 =\) (base area of 8)(height of 10)

Since the answer is YES in the first case but NO in the second case, the two statements combined are INSUFFICIENT.

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Tank A and Tank B are hollow rectangular solids. Tank A is empty and T 18 Aug 2022, 03:53
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