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# If x and y are both positive integers, is xy >= 250?

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Math Expert
Joined: 02 Sep 2009
Posts: 58434
If x and y are both positive integers, is xy >= 250?  [#permalink]

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20 Mar 2018, 06:39
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15% (low)

Question Stats:

85% (00:41) correct 15% (00:45) wrong based on 48 sessions

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If x and y are both positive integers, is xy >= 250?

(1) x = 300
(2) 50 < y < 100

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Math Expert
Joined: 02 Sep 2009
Posts: 58434
Re: If x and y are both positive integers, is xy >= 250?  [#permalink]

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20 Mar 2018, 06:44
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Joined: 31 Oct 2013
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Concentration: Accounting, Finance
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Re: If x and y are both positive integers, is xy >= 250?  [#permalink]

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20 Mar 2018, 07:23
Bunuel wrote:
If x and y are both positive integers, is xy >= 250?

(1) x = 300
(2) 50 < y < 100

we are asked to find out whether xy>=250.

Important Note:
1. both x and y are positive.
2. both x and y are integers.

statement 1: x=300. if we consider the value of y in minimum range just 1 total value of xy will be greater than 250. but we have have to keep in mind that we are looking for greater that + equal. so, not sufficient.
statement 2: the range value is given here. and we don't know anything about x. so not sufficient.

so, correct answer will be E.
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Re: If x and y are both positive integers, is xy >= 250?  [#permalink]

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20 Mar 2018, 08:18
2
If x and y are both positive integers, is xy >= 250?

(1) x = 300
Min value of positive integer = 1, hence min value of xy = 300. hence xy>= 250. Sufficient.

(2) 50 < y < 100.
(x,y) can be (1,60) or (4,90) . Hence xy =60 or 360. not sufficient.

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Re: If x and y are both positive integers, is xy >= 250?  [#permalink]

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20 Mar 2018, 08:26
Bunuel wrote:
If x and y are both positive integers, is xy >= 250?

(1) x = 300
(2) 50 < y < 100

St1 : X=300
Since x and y both are positive, this implies that the min value for both X and Y is 1
So any positive multiple of X (= 300), will be >=300

Hence Yes to the question, and sufficient.

St2: 50<y<100
X can be anything from 1 to +infinity, and the range of XY is 50<XY<+infinity...so for the range 50<XY<249 the answer to question is NO, but XY>=250 the answer is YES

Hence insufficient.

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Re: If x and y are both positive integers, is xy >= 250?  [#permalink]

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20 Mar 2018, 09:22
Bunuel wrote:
If x and y are both positive integers, is xy >= 250?

(1) x = 300
(2) 50 < y < 100

x and y are both positive integers

(1) if x = 300, then x * y will be >= 300 (y is positive integer => y minimum = 1). Sufficient
(2) if y = 99 and x = 10, then xy > 250, but if y = 99 and x = 1 then xy < 250. Insufficient

Re: If x and y are both positive integers, is xy >= 250?   [#permalink] 20 Mar 2018, 09:22
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