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Inequality Prob

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by vishwas.arora » Mon Aug 01, 2011 12:35 am
If square roots of numbers are considered positive and sqrt (a) + sqrt (b) = sqrt (c) + sqrt (d) + sqrt (e) , then is a < c?

(1) c = d
(2) sqrt (b) + sqrt (d) < sqrt (e)

Pl read sqrt (x) as positive square root of x

Can anyone please explain the arithmetic approach..

Thanks in advance.

OA B
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Source: — Data Sufficiency |
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by GMATGuruNY » Mon Aug 01, 2011 3:08 am
vishwas.arora wrote:If square roots of numbers are considered positive and sqrt (a) + sqrt (b) = sqrt (c) + sqrt (d) + sqrt (e) , then is a < c?

(1) c = d
(2) sqrt (b) + sqrt (d) < sqrt (e)

Pl read sqrt (x) as positive square root of x

Can anyone please explain the arithmetic approach..

Thanks in advance.

OA B
Stem equation rephrased:
√c = √a + (√b - √d - √e).

If (√b - √d - √e) > 0, then √c > √a and c>a.

Question rephrased: Is √b - √d - √e > 0?

Statement 1: c = d.
No way to determine whether √b - √d - √e > 0.
Insufficient.

Statement 2: √b + √d < √e.
√b + √d - √e < 0.
√b + √d - 2√d - √e < -2√d.
√b - √d - √e < -2√d.
Since -2√d < 0, we know that √b - √d - √e < 0.
Sufficient.

The correct answer is B.
Last edited by GMATGuruNY on Mon Aug 01, 2011 7:10 am, edited 1 time in total.
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by vishwas.arora » Mon Aug 01, 2011 6:22 am
Thanks a lot Mitch.
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by Ozlemg » Mon Aug 01, 2011 6:43 am
GMATGuruNY wrote:
vishwas.arora wrote:If square roots of numbers are considered positive and sqrt (a) + sqrt (b) = sqrt (c) + sqrt (d) + sqrt (e) , then is a < c?

(1) c = d
(2) sqrt (b) + sqrt (d) < sqrt (e)

Pl read sqrt (x) as positive square root of x

Can anyone please explain the arithmetic approach..

Thanks in advance.

OA B
Stem equation rephrased:
√c = √a + (√b - √d - √e).

If (√b - √d - √e) > 0, then √c < √a and c<a.
Question rephrased: Is √b - √d - √e > 0?

Statement 1: c = d.
No way to determine whether √b - √d - √e > 0.
Insufficient.

Statement 2: √b + √d < √e.
√b + √d - √e < 0.
√b + √d - 2√d - √e < -2√d.
√b - √d - √e < -2√d.
Since -2√d < 0, we know that √b - √d - √e < 0.
Sufficient.

The correct answer is B.
Hi
What do you think about the red part? Isnt it vice versa?
The more you suffer before the test, the less you will do so in the test! :)
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by GMATGuruNY » Mon Aug 01, 2011 7:11 am
Ozlemg wrote:
GMATGuruNY wrote:
vishwas.arora wrote:If square roots of numbers are considered positive and sqrt (a) + sqrt (b) = sqrt (c) + sqrt (d) + sqrt (e) , then is a < c?

(1) c = d
(2) sqrt (b) + sqrt (d) < sqrt (e)

Pl read sqrt (x) as positive square root of x

Can anyone please explain the arithmetic approach..

Thanks in advance.

OA B
Stem equation rephrased:
√c = √a + (√b - √d - √e).

If (√b - √d - √e) > 0, then √c < √a and c<a.
Question rephrased: Is √b - √d - √e > 0?

Statement 1: c = d.
No way to determine whether √b - √d - √e > 0.
Insufficient.

Statement 2: √b + √d < √e.
√b + √d - √e < 0.
√b + √d - 2√d - √e < -2√d.
√b - √d - √e < -2√d.
Since -2√d < 0, we know that √b - √d - √e < 0.
Sufficient.

The correct answer is B.
Hi
What do you think about the red part? Isnt it vice versa?
Yes, indeed! I've corrected the typo in my original post. Thanks.
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I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
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by ArpanaAmishi » Mon Aug 01, 2011 10:42 pm
Hi GMATGuru,
Since -2√d < 0, we know that √b - √d - √e < 0.

Could you please elaborate on bold part ...I couldn't get from where we got this relationship.
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