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# Q is a set of four distinct prime numbers. If the sum of the integers

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Math Expert
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Q is a set of four distinct prime numbers. If the sum of the integers  [#permalink]

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23 Dec 2014, 10:01
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Difficulty:

15% (low)

Question Stats:

91% (01:07) correct 9% (01:14) wrong based on 127 sessions

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Tough and Tricky questions: Word Problems.

Q is a set of four distinct prime numbers. If the sum of the integers in Q is even and the number x is a member of Q, then what is the least value that x can be?

A. 2
B. 3
C. 4
D. 5
E. 7

Kudos for a correct solution.

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Re: Q is a set of four distinct prime numbers. If the sum of the integers  [#permalink]

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23 Dec 2014, 10:29
1
Sum of the 4 Prime integers in set Q is even, implies none of the number is even (as there is only one even prime number).
So the least value of any number in set Q is 3 , Answer B
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Re: Q is a set of four distinct prime numbers. If the sum of the integers  [#permalink]

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23 Dec 2014, 10:38
1
X should be the least prime no.
So,
2+3+5+7=17...............Odd
2+3+5+11=21...............Odd Now something rang in my empty head sum of odd+even=odd and sum of odd+odd=even
lets try all odd then
3+5+7+11=16 ............ bingo 3 is the answer
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Re: Q is a set of four distinct prime numbers. If the sum of the integers  [#permalink]

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23 Dec 2014, 21:33
1
Bunuel wrote:

Tough and Tricky questions: Word Problems.

Q is a set of four distinct prime numbers. If the sum of the integers in Q is even and the number x is a member of Q, then what is the least value that x can be?

A. 2
B. 3
C. 4
D. 5
E. 7

Kudos for a correct solution.

Sum of 4 prime integers is Even

So all four integers should be odd numbers as including 2 in the set will make the sum Odd

Smallest odd prime number is 3

So Ans B
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Re: Q is a set of four distinct prime numbers. If the sum of the integers  [#permalink]

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24 Dec 2014, 01:58
1

2 + 3 + 5 + 7 = 17 (Discard as sum is ODD)

3 + 5 + 7 + 11 = 26 (Sum is even)

Least number = 3
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Re: Q is a set of four distinct prime numbers. If the sum of the integers  [#permalink]

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08 Jan 2015, 07:37
Bunuel wrote:

Tough and Tricky questions: Word Problems.

Q is a set of four distinct prime numbers. If the sum of the integers in Q is even and the number x is a member of Q, then what is the least value that x can be?

A. 2
B. 3
C. 4
D. 5
E. 7

Kudos for a correct solution.

OFFICIAL SOLUTION:

(B) We are told that Q is a set of four distinct prime numbers, and the sum of the numbers in Q is even. Since the question involves odds, evens and the smallest possible prime, you should immediately think of 2, the smallest prime number and the only even prime number.

If 2 were a member of the set, then we would have one even number and three odd numbers. Since this sum would always be odd, 2 cannot be a member of the set. Thus, all the members of Q must be odd to yield an even sum.

Since all the members of the set must be odd prime numbers, the answer is the smallest odd prime number, which is 3.

Note: 1 is not a prime number.
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Re: Q is a set of four distinct prime numbers. If the sum of the integers  [#permalink]

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23 Aug 2015, 13:39
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Re: Q is a set of four distinct prime numbers. If the sum of the integers  [#permalink]

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23 Aug 2015, 13:43
dina98 wrote:

Thank you for noticing. Edited.
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Re: Q is a set of four distinct prime numbers. If the sum of the integers  [#permalink]

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05 Aug 2019, 17:26
Bunuel wrote:

Tough and Tricky questions: Word Problems.

Q is a set of four distinct prime numbers. If the sum of the integers in Q is even and the number x is a member of Q, then what is the least value that x can be?

A. 2
B. 3
C. 4
D. 5
E. 7

Kudos for a correct solution.

Since the sum of the integers is even, we must have 4 odd prime numbers. Thus, the least value of x is 3.

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Re: Q is a set of four distinct prime numbers. If the sum of the integers   [#permalink] 05 Aug 2019, 17:26
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