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18 Sep 2019, 00:27
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
74% (02:08) correct
26%
(02:41)
wrong
based on 136
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[GMAT math practice question]
A \(5\)-digits positive integer \(ab3cd\) is a multiple of \(225.\) What is maximum number?
\(A. 98325\)
\(B. 97325\)
\(C. 96320\)
\(D. 95325\)
\(E. 95320\)
A \(5\)-digits positive integer \(ab3cd\) is a multiple of \(225.\) What is maximum number?
\(A. 98325\)
\(B. 97325\)
\(C. 96320\)
\(D. 95325\)
\(E. 95320\)
18 Sep 2019, 01:00
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A 55-digits positive integer ab3cd is a multiple of 225
factorizing 225 we get = 5*5*3*3
since ab3cd is a multiple of 225 = ab3cd is divisible by --3, 9, 5, 15, 25, 75, 45, 225
-ab3cd to be divisible by 225 must be divisible by all factors
let's see the answer choice--
A.98325
--this is the correct answer (correct)
B.97325
-adding digits to check the divisibility by 3 = 9+7+3+2+5 = 26 (not the multiple of 3)
-so not divisible by 3
-hence, not the multiple of 225 (incorrect)
C.96320
-adding digits to check the divisibility by 3 = 9+6+3+2+0 = 20 (not the multiple of 3)
-so not divisible by 3
-hence, not the multiple of 225 (incorrect)
D.95325
--adding digits to check the divisibility by 3 = 9+5+3+2+5 = 24 (multiple of 3)
-so divisible by 3
let's check for 9 --adding digits to check the divisibility by 9 = 24 (not the multiple of 9)
-not divisible by 9
-hence, not the multiple of 225 (incorrect)
E.95320
---adding digits to check the divisibility by 3 = 9+5+3+2+0 = 19 (not the multiple of 3)
-not divisible by 3
-hence, not the multiple of 225 (incorrect)
factorizing 225 we get = 5*5*3*3
since ab3cd is a multiple of 225 = ab3cd is divisible by --3, 9, 5, 15, 25, 75, 45, 225
-ab3cd to be divisible by 225 must be divisible by all factors
let's see the answer choice--
A.98325
--this is the correct answer (correct)
B.97325
-adding digits to check the divisibility by 3 = 9+7+3+2+5 = 26 (not the multiple of 3)
-so not divisible by 3
-hence, not the multiple of 225 (incorrect)
C.96320
-adding digits to check the divisibility by 3 = 9+6+3+2+0 = 20 (not the multiple of 3)
-so not divisible by 3
-hence, not the multiple of 225 (incorrect)
D.95325
--adding digits to check the divisibility by 3 = 9+5+3+2+5 = 24 (multiple of 3)
-so divisible by 3
let's check for 9 --adding digits to check the divisibility by 9 = 24 (not the multiple of 9)
-not divisible by 9
-hence, not the multiple of 225 (incorrect)
E.95320
---adding digits to check the divisibility by 3 = 9+5+3+2+0 = 19 (not the multiple of 3)
-not divisible by 3
-hence, not the multiple of 225 (incorrect)
18 Sep 2019, 04:00
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MathRevolution
An integer is a multiple of 9 if its digit sum is a multiple of 9.
225 has a digit sum that is a multiple of 9:
2+2+5 = 9
Thus, 225 is a multiple of 9.
Implication:
For the correct answer to be divisible by 225, it must be divisible by 9 and thus must have a digit sum that is a multiple of 9.
Of the five answer choices, only A has a digit sum that is a multiple of 9:
9+8+3+2+5 = 27
