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Difficulty:
15%
(low)
Question Stats:
78% (01:14) correct
22%
(01:24)
wrong
based on 151
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Is the sum of n odd integers odd?
(1) n is even.
(2) The sum is divisible by 3.
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(1) n is even.
(2) The sum is divisible by 3.
Pure algebraic questions like this one are no longer part of the GMAT Data Sufficiency syllabus.
For relevant Data Sufficiency questions, please check the Data Sufficiency forum:
Data Sufficiency Forum
Data Sufficiency Forum
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We need to check whether the sum of n odd integers odd or not.
If n=odd => e.g 3 odds => Sum will be odd.
If n=even => e.g 4 odds => the sum will be even.
So we actually need to check whether n is odd or even.
Statement 1=>N is even => Sum will be even => Sufficient
Statement 2 => sum is divisible by 3
Sum =6
Sum=15
Hence Insufficient
Hence A
If n=odd => e.g 3 odds => Sum will be odd.
If n=even => e.g 4 odds => the sum will be even.
So we actually need to check whether n is odd or even.
Statement 1=>N is even => Sum will be even => Sufficient
Statement 2 => sum is divisible by 3
Sum =6
Sum=15
Hence Insufficient
Hence A
Abhishek009
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Bunuel
FROM STATEMENT - I ( SUFFICIENT )
Sum of even number of odd integers is always even...
Hence, The sum of even numbers of Odd integers will be Even.
FROM STATEMENT - II ( INSUFFICIENT )
Let n = 3 ( Odd )
Sum of first 3 Odd numbers is 9 ( ie, 1 + 3 + 5 ) which is divisible by 3
Let n = 6 (Even)
Sum of first 6 Odd numbers is 36 ( ie, 1 + 3 + 5 +7 + 9 + 11 ) which is divisible by 3
Thus no unique solution can be obtained...
Hence, Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked., answer will be (A)
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Bunuel
IMO A
from statement 1
n is even. Sum of even number of odd numbers is even. Answers No
Hence sufficient.
From statement 2
the sum is divisible by 3
n=3 1+3+5= 9
n=6 1+3+5+7+9+11= 36
n can be odd/ even
Insufficient
Hence A
1)n is even..
For example take n=2,4 and take examples to verify the satement
if n=2 then 1+3=4 (Even)
if n=4 then 1+3+5+7 = 16(even)
took 1,3,5,7 because n odd integers mentioned. So A is sufficient
2)n is divisible by 3.
Now take n=2,3 (didn't mentioned even or odd so to get a precise answer we'll take one even and one odd number)
if n=2 then 1+3=4 not divided by 3
if n=3 then 1+3+5=9 divided by 3.
So it's working for only some numbers hence insufficient
For example take n=2,4 and take examples to verify the satement
if n=2 then 1+3=4 (Even)
if n=4 then 1+3+5+7 = 16(even)
took 1,3,5,7 because n odd integers mentioned. So A is sufficient
2)n is divisible by 3.
Now take n=2,3 (didn't mentioned even or odd so to get a precise answer we'll take one even and one odd number)
if n=2 then 1+3=4 not divided by 3
if n=3 then 1+3+5=9 divided by 3.
So it's working for only some numbers hence insufficient
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