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# If xy = -18, is x less than y? (1) x < 0 (2) y < 10

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Re: If xy = -18, is x less than y? (1) x < 0 (2) y < 10 [#permalink]
xy is -ve --> one number is +ve and the other one is -ve.

1) x<0 --> y must be +ve --> x<y. Sufficient.
2) y<10 --> y may take a +ve or a -ve sign. Insufficient.

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Re: If xy = -18, is x less than y? (1) x < 0 (2) y < 10 [#permalink]
Condition (1) provides x < 0 . So, y must be positive (y > 0) . This condition gives x < y which is sufficient.

Condition (2) provides that y can have all negative values and positive values less than 10. So,
if y is positive, x will be negative. We'll get x < y.
if y is negative, x will be positive.We'll get x > y.
Hence, this condition is not sufficient.

Ans : option A.
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Re: If xy = -18, is x less than y? (1) x < 0 (2) y < 10 [#permalink]
If x<0 then y>0 . Hence, x<y. A is sufficient.
However, for B if y<10 could mean y=9 or -9. In which case x could be -2 or +2. Inconclusive.

Hence, A alone is sufficient to answer
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Re: If xy = -18, is x less than y? (1) x < 0 (2) y < 10 [#permalink]
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Step 1: Analyse Question Stem

It is given that xy = -18.
Since the product of x and y is a negative number, x and y bear opposite signs and none of them are equal to zero

We have to find out if x is less than y.

Step 2: Analyse Statements Independently (And eliminate options) – AD / BCE

Statement 1: x < 0

Since x is negative, y has to be positive.

Is x less than y? YES, because a negative number is always less than a positive number.
Note that we do not have to find the exact values of x and y to answer the question. Knowing the signs is enough to say one is smaller than the other.

The data in statement 1 is sufficient to answer the question with a definite YES.
Statement 1 alone is sufficient. Answer options B, C and E can be eliminated.

Statement 2: y < 10

We also know that xy = -18

If y = 9, x = -2. Here, x is less than y.
If y = -2, x = 9. Here, x is NOT less than y.

Just a couple of cases were enough to expose the inadequacy of statement 2.

The data in statement 2 is insufficient to answer the question with a definite YES or NO.
Statement 2 alone is insufficient. Answer option D can be eliminated.

The correct answer option is A.
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Re: If xy = -18, is x less than y? (1) x < 0 (2) y < 10 [#permalink]
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Re: If xy = -18, is x less than y? (1) x < 0 (2) y < 10 [#permalink]
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