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21 Oct 2020, 07:26
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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:
85%
(hard)
Question Stats:
30% (01:19) correct
70%
(01:23)
wrong
based on 99
sessions
History
Date
Time
Result
Not Attempted Yet
450 when multiplied with x results in the square of an integer. Find x?
1) x is positive
2) x<5
Source: www.GMATinsight.com
1) x is positive
2) x<5
Source: www.GMATinsight.com
Updated on: 21 Oct 2020, 08:11
Originally posted by VoltAmpere on 21 Oct 2020, 07:41.
Last edited by VoltAmpere on 21 Oct 2020, 08:11, edited 1 time in total.
Last edited by VoltAmpere on 21 Oct 2020, 08:11, edited 1 time in total.
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If x is an integer:
1) x>0
if x=2
450(2)=900=30^2
if x=8
450(8)=3600=60^2
at least 2 possible answers: INSUFFICIENT
2) x<5
only when x=2 results to a square of an integer
SUFFICIENT
We can also use the property of perfect squares: prime factors must have even number exponents
450x=(3^2)(5^2)(2)(x)
therefore: minimum value of x must be 2
next possible value is 2*2^2=8, which is greater than 5
if x is not an integer, which is the case since not mentioned
1) when x>0
if x=2
450(2)=900=30^2
if x=8
450(8)=3600=60^2
At least 2 possible answers: INSUFFICIENT
2) x<5
x=1/2, x=2, x=961/450...
multiple possible answers
INSUFFICIENT
IMO CORRECT ANSWER IS E
1) x>0
if x=2
450(2)=900=30^2
if x=8
450(8)=3600=60^2
at least 2 possible answers: INSUFFICIENT
2) x<5
only when x=2 results to a square of an integer
SUFFICIENT
We can also use the property of perfect squares: prime factors must have even number exponents
450x=(3^2)(5^2)(2)(x)
therefore: minimum value of x must be 2
next possible value is 2*2^2=8, which is greater than 5
if x is not an integer, which is the case since not mentioned
1) when x>0
if x=2
450(2)=900=30^2
if x=8
450(8)=3600=60^2
At least 2 possible answers: INSUFFICIENT
2) x<5
x=1/2, x=2, x=961/450...
multiple possible answers
INSUFFICIENT
IMO CORRECT ANSWER IS E
Archit3110
21 Oct 2020, 07:52
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GMATinsight
factor of 450 ; 3^2*5^2*2
#1
x is +ve
x can be 450 , 2, 1/2 , or any even powered value of 3 & 5 and odd power factor value of 2
insufficient
#2
x<5
x =2,1/2
insufficient
from 1 &2
we done get one unique value of x ;
insufficient
option E is correct
