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Apr 2808:00 AM PDT
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24 Jun 2020, 05:16
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D
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Difficulty:
55%
(hard)
Question Stats:
38% (01:10) correct
63%
(02:07)
wrong
based on 8
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If bin A contains exactly twice as many potatoes as bin B, and if bin A contains exactly 11 more potatoes than bin C, does bin B contain more potatoes than bin C?
(1) The difference between the number of potatoes in bin A and the number in bin C is greater than the number of potatoes in bin B.
(2) If one potato were added to bin A and to bin C, bin A would contain exactly twice as many potatoes as bin C.
(1) The difference between the number of potatoes in bin A and the number in bin C is greater than the number of potatoes in bin B.
(2) If one potato were added to bin A and to bin C, bin A would contain exactly twice as many potatoes as bin C.
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yashikaaggarwal
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24 Jun 2020, 05:46
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Given: If bin A contains exactly twice as many potatoes as bin B, and if bin A contains exactly 11 more potatoes than bin C.
Let C contain P potatoes
A will have P+11
B have (P+11)/2
To find: does bin B contain more potatoes than bin C?
(1) The difference between the number of potatoes in bin A and the number in bin C is greater than the number of potatoes in bin B.
=> P+11-P > (P+11)/2
=> 11 > (P+11)/2
=> 22 > P+11
=> 11 > P
Case 1: if C have 10 potatoes
A will have 10+11 = 21 potatoes
B will have 21/2 = 10.5 potatoes.
Case 2: if C have 9 potatoes
A will have 9+11 = 20 potatoes
B will have 20/2 = 10 potatoes.
So B will contain more potatoes than C (Sufficient)
(2) If one potato were added to bin A and to bin C, bin A would contain exactly twice as many potatoes as bin C.
P+12 = 2(P+1)
P+12 = 2P+2
10 = P
If C have 10 potatoes
A will have 10+11 = 21 potatoes
B will have 21/2 = 10.5 potatoes.
B have more potatoes than C (Sufficient)
Answer is D
Posted from my mobile device
Let C contain P potatoes
A will have P+11
B have (P+11)/2
To find: does bin B contain more potatoes than bin C?
(1) The difference between the number of potatoes in bin A and the number in bin C is greater than the number of potatoes in bin B.
=> P+11-P > (P+11)/2
=> 11 > (P+11)/2
=> 22 > P+11
=> 11 > P
Case 1: if C have 10 potatoes
A will have 10+11 = 21 potatoes
B will have 21/2 = 10.5 potatoes.
Case 2: if C have 9 potatoes
A will have 9+11 = 20 potatoes
B will have 20/2 = 10 potatoes.
So B will contain more potatoes than C (Sufficient)
(2) If one potato were added to bin A and to bin C, bin A would contain exactly twice as many potatoes as bin C.
P+12 = 2(P+1)
P+12 = 2P+2
10 = P
If C have 10 potatoes
A will have 10+11 = 21 potatoes
B will have 21/2 = 10.5 potatoes.
B have more potatoes than C (Sufficient)
Answer is D
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24 Jun 2020, 09:11
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SajjadAhmad
If A contains twice as many potatoes as B, then the difference between the number in A and the number in B is exactly equal to the number in B (in other words, A - B = B). So Statement 1 says "the difference A - C is greater than the difference A - B", and if that's true, B > C must be true. So Statement 1 is sufficient.
Adding one potato to bins A and C doesn't change the difference of 11 between them, so we know if we add one potato to each, there will be 11 potatoes in C and 22 in A. So we currently have 10 in C, 21 in A, and thus 10.5 in B. Since we can find all our numbers, we can answer any question.
So the answer is D, but the question seems flawed - it doesn't seem like it should be possible to have a non-integer number of potatoes, but that's the consequence of Statement 2.
