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Difficulty:
55%
(hard)
Question Stats:
51% (01:18) correct
49%
(01:54)
wrong
based on 37
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Are all of the numbers in a set of 3 or more numbers equal?
(1) The sum of all 14 numbers in the set is 98.
(2) The sum of any 3 numbers in the set is 21.
This is re-worked Veritas Question. Check RonTargetTestPrep post HERE.
Similar official question is HERE.
(1) The sum of all 14 numbers in the set is 98.
(2) The sum of any 3 numbers in the set is 21.
This is re-worked Veritas Question. Check RonTargetTestPrep post HERE.
Similar official question is HERE.
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Updated on: 12 Sep 2022, 09:43
Originally posted by $!vakumar.m on 10 Sep 2022, 23:59.
Last edited by $!vakumar.m on 12 Sep 2022, 09:43, edited 1 time in total.
Last edited by $!vakumar.m on 12 Sep 2022, 09:43, edited 1 time in total.
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Are all of the numbers in a set of 3 or more numbers equal?
St1. The sum of all 14 numbers in the set is 98.
that is the set can consist of 14 numbers all 7's so that sum is 98 or it can consist of 14 different numbers such that their sum is 14.
st 1 is not sufficient
St2. The sum of any 3 numbers in the set is 21.
Interesting. st 2 implies if we pick any 3 numbers from the set their sum is 21 which is possible only if all the numbers are equal to 7. The number of elements in the set can be >= 3.
Hence, st 2 is Sufficient.
Answer: B
St1. The sum of all 14 numbers in the set is 98.
that is the set can consist of 14 numbers all 7's so that sum is 98 or it can consist of 14 different numbers such that their sum is 14.
st 1 is not sufficient
St2. The sum of any 3 numbers in the set is 21.
Interesting. st 2 implies if we pick any 3 numbers from the set their sum is 21 which is possible only if all the numbers are equal to 7. The number of elements in the set can be >= 3.
Hence, st 2 is Sufficient.
Answer: B
Updated on: 12 Sep 2022, 04:11
Originally posted by SaquibHGMATWhiz on 11 Sep 2022, 04:41.
Last edited by SaquibHGMATWhiz on 12 Sep 2022, 04:11, edited 1 time in total.
Last edited by SaquibHGMATWhiz on 12 Sep 2022, 04:11, edited 1 time in total.
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Bunuel
Solution:
We are asked if all the numbers in a set are equal or not
Statement 1: The sum of all 14 numbers in the set is 98
From this statement, we understand that there are 14 numbers in the set and the sum is 98.
There can be a case where all the numbers are \(\frac{98}{14}=7\) individually. However, we cannot be sure of it.
Thus, statement 1 alone is not sufficient and we can eliminate options A and D
Statement 2: The sum of any 3 numbers in the set is 21
According to this statement, the sum of ANY 3 numbers is 21. The word "ANY" plays a big role here. (It is ambiguous in terms of language and unlikely to be framed like this in GMAT)
From this, we can infer that every time we are picking the same set of 3 numbers and getting the same sum 21.
Each of those 3 numbers are \(\frac{21}{3}=7\).
From this, we can be sure that each number in the set is the same i.e., 7 each.
Thus, statement 2 alone is sufficient
Hence the right answer is Option B
