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# What is the value of the positive integer x ?

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Math Expert
Joined: 02 Sep 2009
Posts: 59573
What is the value of the positive integer x ?  [#permalink]

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21 Nov 2019, 03:25
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Difficulty:

55% (hard)

Question Stats:

61% (01:50) correct 39% (01:34) wrong based on 17 sessions

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What is the value of the positive integer x ?

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

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Re: What is the value of the positive integer x ?  [#permalink]

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21 Nov 2019, 03:52
(1) x leaves a remainder of 2 when divided by 3, 7, or 11.
Hence, x = N*(LCM of 3, 7, 11) +2
0r, x = 231N +2
Not sufficient to find the exact value of x.
Hence INSUFFICIENT.

(2) 200 < x < 500
Not sufficient to find the exact value of x.
Hence INSUFFICIENT.

Even after combining St1 & 2,
x = = 231N +2
x can be 233 (for N =1) or 464 (for N=2)
Not sufficient to find the exact value of x.
Hence INSUFFICIENT.

Bunuel wrote:
What is the value of the positive integer x ?

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

Are You Up For the Challenge: 700 Level Questions

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Concentration: Sustainability, Marketing
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WE: Marketing (Energy and Utilities)
What is the value of the positive integer x ?  [#permalink]

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21 Nov 2019, 03:55
Bunuel wrote:
What is the value of the positive integer x ?

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

Are You Up For the Challenge: 700 Level Questions

#1x leaves a remainder of 2 when divided by 3, 7, or 11.
LCM = 231 ; so factor of 231*x+2 values
insufficient
#2
200 < x < 500
many possible values
insufficient
from 1 &2
we get 229, 460 ... so on
insufficient
IMO E
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What is the value of the positive integer x ?  [#permalink]

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22 Nov 2019, 07:12
Bunuel wrote:
What is the value of the positive integer x ?

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

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

$$x=3a+2=7b+2=11c+2…x=(2*7*11)d+2$$
$$x=231d+2=(231+2=233,462+2=464…)$$

(2) 200 < x < 500 insufic

(1&2) insufic

$$x=233,464$$

Ans (E)
What is the value of the positive integer x ?   [#permalink] 22 Nov 2019, 07:12
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