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

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

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Re: If x and y are both positive integers, is xy >= 250? [#permalink]
Isn't zero a positive integer?
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Re: If x and y are both positive integers, is xy >= 250? [#permalink]
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Deep32470 wrote:
Isn't zero a positive integer?

No. Zero is neither positive nor negative (the only one of this kind).

ZERO:

1. Zero is an INTEGER.

2. Zero is an EVEN integer. An even number is an integer that is "evenly divisible" by 2, i.e., divisible by 2 without a remainder and as zero is evenly divisible by 2 then it must be even.

3. Zero is neither positive nor negative (the only one of this kind).

4. Zero is divisible by EVERY integer except 0 itself ($$\frac{x}{0} = 0$$, so 0 is a divisible by every number, x).

5. Zero is a multiple of EVERY integer ($$x*0 = 0$$, so 0 is a multiple of any number, x).

6. Zero is NOT a prime number (neither is 1 by the way; the smallest prime number is 2).

7. Division by zero is NOT allowed: anything/0 is undefined.

8. Any non-zero number to the power of 0 equals 1 ($$x^0 = 1$$)

9. $$0^0$$ case is NOT tested on the GMAT.

10. If the exponent n is positive (n > 0), $$0^n = 0$$.

11. If the exponent n is negative (n < 0), $$0^n$$ is undefined, because $$0^{negative}=0^n=\frac{1}{0^{(-n)}} = \frac{1}{0}$$, which is undefined. You CANNOT take 0 to the negative power.

12. $$0! = 1! = 1$$.
Re: If x and y are both positive integers, is xy >= 250? [#permalink]
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