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![If p and q are integers, is the number [m]10^p + q[/m] divisible by 3?](/forum/styles/gmatclub_light/imageset/icon_post_target_unread.svg "If p and q are integers, is the number [m]10^p + q[/m] divisible by 3?"){kind=icon}
26 Jul 2019, 11:53
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C
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Difficulty:
65%
(hard)
Question Stats:
25% (01:03) correct
75%
(00:51)
wrong
based on 85
sessions
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If p and q are integers, is the number \(10^p + q\) divisible by 3?
(1) p = 5
(2) q = 2
(1) p = 5
(2) q = 2
GMATbuster's Collection
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
Statement1:
p=5
(10^5+q):3=??
—> if q=1, then remainder will be 2
—> if q=2, the remainder will be 0
Insuffiient
Statement2:
q=2
(10^p+2):3
—> the remainder will be always 0 if p >=0.
Otherwise, if p=-1, then (1/10+2) cannot be divided by 3
Insufficient
Taken together 1 and 2, p=5, q=2 —> (10^5+2) is divided by 3.
(Rule: If the sum of the digits is divide by 3, the number will be divided by 3 itself)
Sufficient
The answer choice is C.
Posted from my mobile device
p=5
(10^5+q):3=??
—> if q=1, then remainder will be 2
—> if q=2, the remainder will be 0
Insuffiient
Statement2:
q=2
(10^p+2):3
—> the remainder will be always 0 if p >=0.
Otherwise, if p=-1, then (1/10+2) cannot be divided by 3
Insufficient
Taken together 1 and 2, p=5, q=2 —> (10^5+2) is divided by 3.
(Rule: If the sum of the digits is divide by 3, the number will be divided by 3 itself)
Sufficient
The answer choice is C.
Posted from my mobile device
26 Jul 2019, 12:17
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gmatbusters
\(10^p + q\)
2 parts here.
\(10^(anything)\) is divided by 3 will always yield a reminder of 1. but we don't know q.
q is vital for this question.
Statement 1: p =5. we don't have idea regard q. NOT sufficient.
Statement 2: q=2.
\(10^0\) + 2 = 3
\(10^1\)+ 2 = 12
\(10^2\) + 2 = 102
\(10^3\) + 2 = 1002
In all cases , the reminder is 0.
Sufficient .
B is the correct answer.
