Find all School-related info fast with the new School-Specific MBA Forum

 It is currently 19 May 2013, 20:14

# If square roots of numbers are positive.. Is a<c?

Author Message
TAGS:
Manager
Joined: 23 Aug 2011
Posts: 83
Followers: 3

Kudos [?]: 19 [0], given: 13

If square roots of numbers are positive.. Is a<c? [#permalink]  27 Aug 2012, 11:41
00:00

Question Stats:

50% (02:36) correct 50% (01:31) wrong based on 1 sessions
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}
[Reveal] Spoiler: OA

_________________

Whatever one does in life is a repetition of what one has done several times in one's life!
If my post was worth it, then i deserve kudos

Director
Joined: 22 Mar 2011
Posts: 608
WE: Science (Education)
Followers: 43

Kudos [?]: 267 [0], given: 43

Re: If square roots of numbers are positive.. Is a<c? [#permalink]  27 Aug 2012, 14:39
conty911 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}

Since all the numbers are positive and the square roots are also positive, the question can be restated as is \sqrt{a}<\sqrt{c}?
Also, (1) can be replaced by \sqrt{c}=\sqrt{d}.

(1) Obviously not sufficient. Too many degrees of freedom to choose values for the five variables.

(2) Since \sqrt{b}+\sqrt{d}<\sqrt{e} necessarily \sqrt{b}<\sqrt{e} and then, using the equality in the question stem, we can deduce that \sqrt{a}>\sqrt{c}+\sqrt{d}>\sqrt{c}. In conclusion, \sqrt{a}>\sqrt{c}.
Sufficient.

_________________

PhD in Applied Mathematics
Love GMAT Quant questions and running.

Manager
Joined: 23 Aug 2011
Posts: 83
Followers: 3

Kudos [?]: 19 [0], given: 13

Re: If square roots of numbers are positive.. Is a<c? [#permalink]  27 Aug 2012, 17:23
EvaJager wrote:
conty911 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}

Since all the numbers are positive and the square roots are also positive, the question can be restated as is \sqrt{a}<\sqrt{c}?
Also, (1) can be replaced by \sqrt{c}=\sqrt{d}.

(1) Obviously not sufficient. Too many degrees of freedom to choose values for the five variables.

(2) Since \sqrt{b}+\sqrt{d}<\sqrt{e} necessarily \sqrt{b}<\sqrt{e} and then, using the equality in the question stem, we can deduce that \sqrt{a}>\sqrt{c}+\sqrt{d}>\sqrt{c}. In conclusion, \sqrt{a}>\sqrt{c}.
Sufficient.

Thanks for the reply , also can you elaborate more on how you deduced this inequality \sqrt{a}>\sqrt{c}+\sqrt{d}>\sqrt{c}. I didn't quite understood that
_________________

Whatever one does in life is a repetition of what one has done several times in one's life!
If my post was worth it, then i deserve kudos

Director
Joined: 22 Mar 2011
Posts: 608
WE: Science (Education)
Followers: 43

Kudos [?]: 267 [1] , given: 43

Re: If square roots of numbers are positive.. Is a<c? [#permalink]  28 Aug 2012, 05:04
1
KUDOS
conty911 wrote:
EvaJager wrote:
conty911 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}

Since all the numbers are positive and the square roots are also positive, the question can be restated as is \sqrt{a}<\sqrt{c}?
Also, (1) can be replaced by \sqrt{c}=\sqrt{d}.

(1) Obviously not sufficient. Too many degrees of freedom to choose values for the five variables.

(2) Since \sqrt{b}+\sqrt{d}<\sqrt{e} necessarily \sqrt{b}<\sqrt{e} and then, using the equality in the question stem, we can deduce that \sqrt{a}>\sqrt{c}+\sqrt{d}>\sqrt{c}. In conclusion, \sqrt{a}>\sqrt{c}.
Sufficient.

Thanks for the reply , also can you elaborate more on how you deduced this inequality \sqrt{a}>\sqrt{c}+\sqrt{d}>\sqrt{c}. I didn't quite understood that

(2) Since \sqrt{b}+\sqrt{d}<\sqrt{e} necessarily \sqrt{b}<\sqrt{e} if the sum of two positive numbers is less than another positive number, then each term of the sum is less than that number and then, using the equality in the question stem, we can deduce that \sqrt{a}>\sqrt{c}+\sqrt{d}>\sqrt{c} - if \sqrt{a}\leq\sqrt{c}+\sqrt{d} then the equality in the stem would not hold; if 2 < 3 and 4 < 7, 2 + 4 cannot be equal to 3 + 7. In addition, \sqrt{c}+\sqrt{d}>\sqrt{c} because \sqrt{d} is positive.
In conclusion, \sqrt{a}>\sqrt{c}.

_________________

PhD in Applied Mathematics
Love GMAT Quant questions and running.

Re: If square roots of numbers are positive.. Is a<c?   [#permalink] 28 Aug 2012, 05:04
Similar topics Replies Last post
Similar
Topics:
The number q is a positive integer. Is the square root of q 5 09 Jul 2006, 04:21
1 If x is a positive number and 1/2 the square root of x is 2 09 Jun 2007, 16:33
2 Numbers-Squares root 13 04 Nov 2009, 00:22
1 Square Root = Always Positive? 11 23 May 2011, 15:34
2 Positive square root 2 28 Nov 2011, 10:31
Display posts from previous: Sort by