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23 May 2020, 08:52
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
5%
(low)
Question Stats:
88% (01:03) correct
12%
(01:12)
wrong
based on 185
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Is the sum of four different positive prime integers an odd integer?
(1) One of the integers is 11.
(2) One of the integers is 2.
DS20442
(1) One of the integers is 11.
(2) One of the integers is 2.
DS20442
23 May 2020, 09:04
Kudos
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Bunuel
Is the sum of four different positive prime integers an odd integer?
(1) One of the integers is 11.
(2) One of the integers is 2.
DS20442
(1) One of the integers is 11.
(2) One of the integers is 2.
DS20442
Target question: Is the sum of four different positive prime integers an odd integer?
This is a good candidate for rephrasing the target question.
The key concept involved here is that 2 is the only EVEN prime number, and all other prime numbers are ODD
So, if 2 is among the four primes, then the sum = EVEN + ODD + ODD + ODD = ODD
If 2 is NOT among the four primes, then the sum = ODD + ODD + ODD + ODD = EVEN
So, in order for the sum to be ODD, 2 must be among the four primes.
This means we can rephrase the target question as follows:
REPHRASED target question: Is 2 among the four primes?
Statement 1: One of the integers is 11.
Since we have no information about the other three primes, 2 may or may not be among them.
Since we cannot answer the REPHRASED target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: One of the integers is 2.
Perfect!
The answer to the REPHRASED target question is YES, 2 is among the four primes
Since we can answer the REPHRASED target question with certainty, statement 2 is SUFFICIENT
Answer: B
Cheers,
Brent
VIDEO ON REPHRASING THE TARGET QUESTION:
23 May 2020, 09:32
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Bunuel
Is the sum of four different positive prime integers an odd integer?
(1) One of the integers is 11.
(2) One of the integers is 2.
DS20442
(1) One of the integers is 11.
(2) One of the integers is 2.
DS20442
CONCEPT:
1) There is only One EVEN Prime number i.e. 2. Rest of the prime numbers are ODD
2) Sum of 4 odd integers will be even i.e. for Sum of 4 prime to be ODD one of them MUST be 2
1) There is only One EVEN Prime number i.e. 2. Rest of the prime numbers are ODD
2) Sum of 4 odd integers will be even i.e. for Sum of 4 prime to be ODD one of them MUST be 2
STatement 1: One of the integers is 11.
Prime may be {2, 3, 5, 11} i.e. Sum ODD
Prime may be {3, 5, 7, 11} i.e. Sum EVEN
NOT SUFFICIENT
STatement 2: One of the integers is 2
Now remaining three prime will have to be ODD hence sum of the four primes must be ODD
SUFFICIENT
Answer: Option B
