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# x = ? (1) x leaves a remainder of 2 when divided by 3, 7, or 11

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Manager
Joined: 07 Jun 2017
Posts: 175
Location: India
Concentration: Technology, General Management
GMAT 1: 660 Q46 V38
GPA: 3.6
WE: Information Technology (Computer Software)
x = ? (1) x leaves a remainder of 2 when divided by 3, 7, or 11  [#permalink]

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03 Nov 2017, 04:41
00:00

Difficulty:

75% (hard)

Question Stats:

52% (01:44) correct 48% (02:05) wrong based on 83 sessions

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x = ?

(1) x leaves a remainder of 2 when divided by 3, 7, or 11.
(2) 200 < x < 500

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Naveen
email: nkmungila@gmail.com
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Posts: 7098
Re: x = ? (1) x leaves a remainder of 2 when divided by 3, 7, or 11  [#permalink]

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03 Nov 2017, 05:11
x = ?

(1) x leaves a remainder of 2 when divided by 3, 7, or 11.
This tells us that x =n*LCM of 3,7,11 + 2
And n can be any non NEGATIVE INTEGER..
So x can be smallest 2..
Or LCM of 3,7,11=223...
So 223+2=225 or 2*223+2=448..
Insufficient

(2) 200 < x < 500
Can be any value between 200 and 500
Insufficient

Combined..
It can be 225 or 448
Insufficient

E
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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Manager
Joined: 08 Sep 2017
Posts: 78
GMAT 1: 710 Q49 V39
x = ? (1) x leaves a remainder of 2 when divided by 3, 7, or 11  [#permalink]

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07 Nov 2017, 17:57
chetan2u wrote:
x = ?

(1) x leaves a remainder of 2 when divided by 3, 7, or 11.
This tells us that x =n*LCM of 3,7,11 + 2
And n can be any non NEGATIVE INTEGER..
So x can be smallest 2..
Or LCM of 3,7,11=223...
So 223+2=225 or 2*223+2=448..
Insufficient

(2) 200 < x < 500
Can be any value between 200 and 500
Insufficient

Combined..
It can be 225 or 448
Insufficient

E

LCM of 3,7,11=223...?? LCM=231---> x= 231 +2=233

If we take x=231*k +2 (where k is any number) we have infinite solutions; for example with k=2; x= 462 +2= 464 --> 464/3=>R=2 // 464/7=>R=2 // 464/11=>R=2 ...and so on

So if combined, x can be 233 or 464 ---> NS ----> Answer E
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x = ? (1) x leaves a remainder of 2 when divided by 3, 7, or 11 &nbs [#permalink] 07 Nov 2017, 17:57
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