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Is xy > 5?

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Joined: 02 Sep 2009
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23 Jan 2014, 03:26
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The Official Guide For GMAT® Quantitative Review, 2ND Edition

Is xy > 5?

(1) $$1\leq{x}\leq{3}$$ and $$2\leq{y}\leq{4}$$
(2) x + y = 5

Data Sufficiency
Question: 52
Category: Algebra Inequalities
Page: 156
Difficulty: 650

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Re: Is xy > 5?  [#permalink]

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23 Jan 2014, 03:26
SOLUTION

Is xy > 5?

(1) $$1\leq{x}\leq{3}$$ and $$2\leq{y}\leq{4}$$
(2) x + y = 5

Probably the easiest way to tackle this problem is to pick numbers. Quite easy to get both an YES and a NO answers:

x = 1 and y = 4 --> xy = 4 < 5;
x = 3 and y = 2 --> xy = 6 > 5.

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Re: Is xy > 5?  [#permalink]

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23 Jan 2014, 04:06
2
Bunuel wrote:

Is xy > 5?

(1) $$1\leq{x}\leq{3}$$ and $$2\leq{y}\leq{4}$$
(2) x + y = 5

Sol:St 1: Given $$1\leq{x}\leq{3}$$ and $$2\leq{y}\leq{4}$$

Note x and y can have any values (not only integer) in this range.

So x =1 , y=4 the answer to the question is NO
But if x=2, y=3 then answer is YES.

So A and D ruled out
St 2: x+y=5 the above values can be used.
So not enough
B ruled out

Let x=1.1, y=3.9 then xy is less than 5
but if x=2 and y=3 then xy is greater then 5.

Ans is E

Difficulty level of 650 is okay.
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Re: Is xy > 5?  [#permalink]

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23 Jan 2014, 04:27
Not necessary to pick decimals, lets pick simpler numbers

1+2

x=1 and y=4
is xy>5?

x=3 y=2
is xy>5?

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Re: Is xy > 5?  [#permalink]

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23 Jan 2014, 11:00
1
x can take any values between 1 and 3 ( both included), y can take any values between 2 and 4 ( both included).

Please note x and y can even take decimal values.

For simplification lets work with integer values only

Statement 1 3 * 2 =6 [yes, xy > 5]
But, 2 * 2 = 4 [ No, xy is not greater than 5]

We have two answers to the questions from statement 1. Hence statement 1 is not sufficient.
Options A and D are eliminated.

Statement 2 says x + y = 5

When x = 1, y = 4 xy <5
When x = 2, y = 3 xy >5

Here, again we have two answers to our question. Hence, statement two alone is not sufficient.

Option B is eliminated.

Now, lets combine both the statements and check.

x = 1, y = 4 xy < 5
x = 3, y = 2 xy > 5

We do not have an definite answer. Both the statements together are also not sufficient.

Hence, option E

Regards,
Harish
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Re: Is xy > 5?  [#permalink]

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23 Jan 2014, 22:24
1
Here, the question does not specify that the numbers are restricted only to integers. So, it can include even decimals but it is enough to consider integers in the first place.

Is xy>5?
Here, just to understand, so far from the question, we can infer that either both x & y are positive or both x & y are negative.

Statement 1:
From the range, if we assume x=2 and y=3; xy=6; we get the answer YES.
If we assume x=1 and y=2; xy=2; we get the answer NO.
Insufficient.

Statement 2:
Here, x and y can take multiple values:
x=2 and y=3; we get the answer YES.
x=1 and y=4; we get the answer NO.
There are more values possible, of course, including decimals.
Insufficient.

Combined, we have a specific range of values and still it is insufficient, as in Statement 2 example.

Ans is (E).
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Re: Is xy > 5?  [#permalink]

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24 Jan 2014, 02:14
1
Is $$xy > 5?$$

(1) $$1\leq{x}\leq{3}$$ and $$2\leq{y}\leq{4}$$
(2) $$x + y = 5$$

Statement 1
Given the range of values of x and y : $$1\leq{x}\leq{3}$$ and $$2\leq{y}\leq{4}$$

for $$x = 3$$ and $$y =4$$, $$xy = 12$$ or, $$xy > 5$$
for $$x = 1$$ and $$y= 2$$, $$xy = 2$$ or, $$xy < 5$$

So, statement (1) is not sufficient.................(A)(D)

Statement 2

Given that, $$x + y = 5$$ is satisfied by $$(x= 1$$ and $$y = 4)$$ & $$( x= 2$$ and $$y = 3)$$

for $$x= 1$$ and $$y = 4$$, $$xy = 4$$ or $$xy < 5$$
for $$x= 2$$ and $$y = 3$$, $$xy = 6$$ or $$xy > 5$$

So,statement (2) is not sufficient.................(B)

Since, the set of values in statement (2) also satisfies condition in statement (1), both statements (1) and (2) are insufficient to evaluate $$xy > 5$$.

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Re: Is xy > 5?  [#permalink]

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