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Will the first 10 volumes of a 20-volume encyclopedia fit

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Will the first 10 volumes of a 20-volume encyclopedia fit

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Source: GMAT Paper Tests



Will the first 10 volumes of a 20-volume encyclopedia fit upright in the bookrack shown above?

1) \(x=50\) centimeters.
2) Twelve of the volumes have an average (arithmetic mean) thickness of 5 centimeters.

The OA is E

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BTGmoderatorLU wrote:
Source: GMAT Paper Tests



Will the first 10 volumes of a 20-volume encyclopedia fit upright in the bookrack shown above?

1) \(x=50\) centimeters.
2) Twelve of the volumes have an average (arithmetic mean) thickness of 5 centimeters.

The OA is E
Target question: Will the first 10 volumes of a 20-volume encyclopedia fit upright in the bookrack shown above?

Statement 1: x = 50 centimeters.
We have no idea how THICK the first 10 volumes are.
They COULD each be 1 mm thick, in which case the 10 volumes will easily fit in the 50 cm rack
Or they COULD each be 1 km thick, in which case the 10 volumes will NOT fit in the 50 cm rack
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: Twelve of the volumes have an average (arithmetic mean) thickness of 5 centimeters.
We have no idea how wide the book rack is.
Statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
We have no info about the thickness of the 10 volumes to be placed in the rack.
Consider these two possible cases:
Case a: Each of the 12 volumes noted above in statement 2 are 5 cm thick. Two of those 5-cm-thick volumes are added to eight volumes that are each 1 mm thick. In this case, the 10 volumes will easily fit in the 50 cm rack
Case b: Each of the 12 volumes noted above in statement 2 are 5 cm thick. Two of those 5-cm-thick volumes are added to eight volumes that are each 1 km thick. In this case, the 10 volumes will NOT fit in the 50 cm rack

Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer: E

Cheers,
Brent

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Statement 1
50 centimeter the relationship between x and the volume of then encyclopedia is not known, statement 1 is INSUFFICIENT.

Statement 2
Twelve of the volumes have an average ( arithmetic mean) thickness of 5 centimeters.
There is no information about the thickness of the thickness of the 10 volumes to be placed on the rack, hence statement 2 is INSUFFICIENT.

Combining statement 1 and 2 together.
Book rack Length = 50 cm
12 volumes have an average of 5 cm
Therefore,
$$\frac{\left(sum\ of\ 12\ volumes\right)}{12}=5$$
8 volumes remaining
The thickness of the remaining 8 volumes is not known, hence both statements together is INSUFFICIENT.

$$answer\ is\ option\ E$$

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