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Is positive integer x greater than 1000? (1) x is a positive multiple

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Is positive integer x greater than 1000? (1) x is a positive multiple  [#permalink]

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New post 15 Oct 2019, 23:04
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

76% (00:56) correct 24% (00:52) wrong based on 21 sessions

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Re: Is positive integer x greater than 1000? (1) x is a positive multiple  [#permalink]

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New post 15 Oct 2019, 23:34
Bunuel wrote:
Is positive integer x greater than 1000?

(1) x is a positive multiple of 49

(2) x is a positive multiple of 21

(1) x is a positive multiple of 49

x>0 and x can be any multiple of 49. Obviously insufficient

(2) x is a positive multiple of 21

x>0 and x can be any multiple of 21. Obviously insufficient

(1)+(2) x is a positive multiple of 21 (21=7*3) and 49 (49=7*7)

x is at least 7*7*3=147

x can be any positive multiple of 147

(1)+(2) is insufficient

Answer is (E)
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Re: Is positive integer x greater than 1000? (1) x is a positive multiple  [#permalink]

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New post 16 Oct 2019, 00:16
Bunuel wrote:
Is positive integer x greater than 1000?

(1) x is a positive multiple of 49

(2) x is a positive multiple of 21


(1) x is a positive multiple of 49
—> x/49 = p, for any positive integer p
—> x = 7^2*p
—> x = 49, 98, . . . . 4900 . . . 9800 —> Insufficient

(2) x is a positive multiple of 21
—> x/21 = q, for any positive integer q
—> x = 7*3*q
—> x = 21, 42, 63, 84, 105, . . . . . 2100, . . . —> Insufficient

Combining (1) & (2),
x will take values 7^2*3*r, for any positive integer r
—> x = 147, 294, . . . . 1470 . . .
—> x can be less than 1000 or greater than 1000 —> Insufficient

IMO Option E

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Re: Is positive integer x greater than 1000? (1) x is a positive multiple   [#permalink] 16 Oct 2019, 00:16
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