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25 Sep 2020, 23:29
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E
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Difficulty:
95%
(hard)
Question Stats:
42% (02:41) correct
58%
(02:24)
wrong
based on 142
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If n is a positive integer, is (n+2)(n+3) divisible by 8?
(1) n+2 is divisible by 3
(2) n-1 is divisible by 4
(1) n+2 is divisible by 3
(2) n-1 is divisible by 4
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
25 Sep 2020, 23:42
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DisciplinedPrep
CONCEPT: (n+2)(n+3) is a product two consecutive integers (one even and other odd) which will be divisible by 8 if
1) One of them (n+2 or n+3) is divisible by 8
Statement 1: n+2 is divisible by 3
i.e. n+2 may be 3, 6, 9, 12, 15, 18... etc
i.e. n may be 1, 4, 7, 10, 13, 16, 19, 22.... etc.
(n+2)(n+3) may be NO
3*4 Not divisible by 8
6*7 Not divisible by 8
9*10 Not divisible by 8
12*13 Not divisible by 8
15*16 divisible by 8 YES
NOT SUFFICIENT
Statement 2:n-1 is divisible by 4
i.e. n may be 1, 5, 9, 13, 17, 21, 25, 29, 33.... etc
(n+2)(n+3) may be
7*8 divisible by 8 YES
11*2 Not divisible by 8 NO
NOT SUFFICIENT
Combining the statements
statement 1: i.e. n may be 1, 4, 7, 10, 13, 16, 19, 22, 25.... etc.
STatement 2: i.e. n may be 1, 5, 9, 13, 17, 21, 25, 29, 33.... etc
i.e. n may be 1, 13, 25... etc
i.e.(n+2)(n+3) may be
3*4 Not divisible by 8 NO
15*16 divisible by 8 YES
NOT SUFFICIENT
ANswer: Option E
Target4bschool
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26 Sep 2020, 05:58
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What is the error in my methodology?
n+2, n+3 are consecutive numbers
(1) n+2 is divisible by 3
if n+2 = 3
n+3 =4
So, (n+2)(n+3) is not divisible by 8
But if n+2 = 15
n+3 =16
So, (n+2)(n+3) is divisible by 8
Not sufficient.
(2) n-1 is divisible by 4
if n-1 is divisible by 4
then,
n-1 is divisible by 4
n is divisible by 5
.
.
n+3 is divisible by 8
Sufficient.
Answer B.
n+2, n+3 are consecutive numbers
(1) n+2 is divisible by 3
if n+2 = 3
n+3 =4
So, (n+2)(n+3) is not divisible by 8
But if n+2 = 15
n+3 =16
So, (n+2)(n+3) is divisible by 8
Not sufficient.
(2) n-1 is divisible by 4
if n-1 is divisible by 4
then,
n-1 is divisible by 4
n is divisible by 5
.
.
n+3 is divisible by 8
Sufficient.
Answer B.
