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Each of the 23 mangoes in box X weighs less than each of the 22 mangoe

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Math Expert
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Each of the 23 mangoes in box X weighs less than each of the 22 mangoe  [#permalink]

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25 Oct 2018, 02:23
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76% (01:06) correct 24% (01:47) wrong based on 48 sessions

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Each of the 23 mangoes in box X weighs less than each of the 22 mangoes on box Y. What is the median weight of the 45 mangoes in the boxes?

(1) The heaviest mango in box X weighs 100 grams
(2) The lightest mango in box Y weighs 120 grams

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Re: Each of the 23 mangoes in box X weighs less than each of the 22 mangoe  [#permalink]

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25 Oct 2018, 04:25
The answer is A.
We can solve this question Precisely - the data given is sufficient to easily find the answer.
If there are 45 mangoes, the median mango is the 23rd in weight. The question stem tells us the 23rd lightest one is the heaviest of box X.
1) tells us the weight of this median. Sufficient! 2) only tells us the weight of the next-largest one after the median: this only tells us the median is less than 120 - but how much is it?? Insufficient!
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Re: Each of the 23 mangoes in box X weighs less than each of the 22 mangoe  [#permalink]

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25 Oct 2018, 06:33

Solution

Given:
• The weight of each of the 23 mangoes in box X < the weight of each of the 22 mangoes in box Y

To find:
• The median weight of the 45 mangoes

Approach and Working:
• Let’s arrange the mangoes in increasing order of weights
• So, the 23 mangoes in box X occupies the first 23 places, then the remaining 22 places are occupied by mangoes in box Y
• Median = 23rd term = the 23rd mango(heaviest mango) of box X

Analysing Statement 1
• Given the weight of heaviest mango in box X = 100 grams, which is the median weight

Therefore, Statement 1 alone is sufficient to answer this question

Analysing Statement 2
• Given the weight of the lightest mango in box Y = 120 grams
• Implies, the 24th term = 120, we can just say that the median is ≤ 120, but we cannot find the exact value.

Therefore, Statement 2 alone is not sufficient to answer this question

Hence, the correct answer is Option A.

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Re: Each of the 23 mangoes in box X weighs less than each of the 22 mangoe   [#permalink] 25 Oct 2018, 06:33
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Each of the 23 mangoes in box X weighs less than each of the 22 mangoe

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