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rakshitsood21
Joined: 27 Aug 2018
Last visit: 18 Dec 2021
Posts: 27
Given Kudos: 16
Location: India
Concentration: Strategy, Leadership
Schools: ISB'22 (A) Fuqua '23 (D) IIMA PGPX'22 (WL)
GMAT 1: 670 Q51 V29
GMAT 2: 740 Q51 V38 (Online)
GPA: 4
30 Aug 2020, 09:20
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
42% (01:48) correct
58%
(01:51)
wrong
based on 304
sessions
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Is it possible for a wooden block in the shape of a rectangular solid measuring l by w by h centimeter to pass through a square hole with sides of length 4 centimeters?
1) The volume of the wooden block is 16 cm3.
(2) L > w > h > 1
Source: Advanced Quant Manhattan Prep 2020
1) The volume of the wooden block is 16 cm3.
(2) L > w > h > 1
Source: Advanced Quant Manhattan Prep 2020
30 Aug 2020, 09:49
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Given: dimension of the square is 4cm x 4cm
Statement 1:
The volume of the block is 16
This could mean the dimensions are:
64 * 1/2 * 1/2 - Possible
4 * 4 * 1 - Possible
8 * 2 * 1 - Possible
Sufficient
Statement 2:
L > w > h > 1
It could be 1.1 * 1.2 * 1.3 that is possible OR 100 * 100 * 100 that is impossible
Thus, answer is A
Statement 1:
The volume of the block is 16
This could mean the dimensions are:
64 * 1/2 * 1/2 - Possible
4 * 4 * 1 - Possible
8 * 2 * 1 - Possible
Sufficient
Statement 2:
L > w > h > 1
It could be 1.1 * 1.2 * 1.3 that is possible OR 100 * 100 * 100 that is impossible
Thus, answer is A
30 Aug 2020, 10:50
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As long as two of the three dimensions of the block are less than 4 cm, the block will be able to pass through the square. Using Statement 1, it's certainly possible that two of the dimensions are less than 4 cm - it could measure 2x2x4, say. But it's also possible that only one of the dimensions is less than 4 cm. Maybe the height is 1/1,000,000 cm, and the other two dimensions are both 4000 cm, which would look like an enormous square sheet of paper. Without bending the sheet, you couldn't pass that sheet through a small square hole no matter how you rotate it.
Statement 2 is clearly insufficient alone, but using both Statements, if it were true that two of the block's dimensions were greater than 4, then since the third dimension must be greater than 1, then the volume would automatically be greater than 16 cm^3. So it's impossible for two (or all three) of the dimensions to exceed 4 cm. So at most one dimension exceeds 4 cm, and we know if only one dimension is greater than 4 cm, the block can fit through the square. So the answer is C.
Statement 2 is clearly insufficient alone, but using both Statements, if it were true that two of the block's dimensions were greater than 4, then since the third dimension must be greater than 1, then the volume would automatically be greater than 16 cm^3. So it's impossible for two (or all three) of the dimensions to exceed 4 cm. So at most one dimension exceeds 4 cm, and we know if only one dimension is greater than 4 cm, the block can fit through the square. So the answer is C.
