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17 Sep 2021, 05:45
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
25%
(medium)
Question Stats:
75% (01:23) correct
25%
(01:48)
wrong
based on 111
sessions
History
Date
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Not Attempted Yet
Which of the following numbers is NOT the sum of three consecutive odd integers?
(A) 15
(B) 75
(C) 123
(D) 297
(E) 313
(A) 15
(B) 75
(C) 123
(D) 297
(E) 313
17 Sep 2021, 06:18
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Bunuel
To get a feel for what the sum of three consecutive ODD integers looks like, let's:
Let x = the smallest of the three odd integers
Let x + 2 = the next integer (since each consecutive odd integer is 2 greater than the odd integer before it)
Let x + 4 = the last integer
So, the sum = x + (x + 2) + (x + 4) = 3x + 6 = 3(x + 2)
We can now see that the sum of any three consecutive odd integers will be divisible by 3.
Useful property: If a number is divisible by 3, then the sum of its digits will be divisible by 3.
So let's check each answer choice to see whether the sum of its digits is divisible by 3.
(A) 1+5 = 6, which is divisible by 3
(B) 7+5 = 12, which is divisible by 3
(C) 1+2+3 = 6, which is divisible by 3
(D) 2+9+7= 18, which is divisible by 3
(E) 3+1+3 = 7, which is NOT divisible by 3
Since 313 is not divisible by 3, it can't be the sum of three consecutive odd integers.
Answer: E
17 Sep 2021, 09:19
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(E) 313
as it is not divisible by 3
as it is not divisible by 3
