GMAT:Punch of the Week(09-March-09)

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Sureshbala

GMAT:Punch of the Week(09-March-09)

Author: Sureshbala

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What is "Punch Of The Week"?

Every week Learnhub's team will post one question each on Verbal Ability and Quantitative Ability of the GMAT Test Preparation
Members can post their answers along with explanations for the next one week.
After one week, Learnhub's team will post the official answer along with the explanation.Besides answering the previous week's questions, Learnhub's Team will come up with the next set of questions for that week as well.

What are the rules of "Punch Of The Week"?

	Every user must refrain from posting sarcastic comments on the answers posted by others.
	Once the Learnhub's team posts the official answer along with the explanation, no comments must be made regarding those questions. In case of further clarification please send a personal message to the respective team member
	If you think that there is something wrong with the explanation of the Learnhub's Team, which seldom happens, please send a personal message to the respective team member informing him/her the same. Posting the same here will not be considered and will be deleted.
	Please bear in mind that only Learnhub's Team members have the privilege of posting questions here. Questions posted by other members will not be entertained and hence will be deleted immediately.

"Punch Of The Week" Team Members

This Week's Punches

Sentence Correction

A career in the medical profession,which requires an enormous investment of time and money, do not guarantee success as there is so much competition.

(A) which requires an enormous investment of time and money, do not guarantee success as there is so much competition.
(B) which requires an enormous investment of time and money, does not guarantee success since there is so much competition.
(C) requiring an enormous investment of time and money, without guarantee because there is so much competition.
(D) requires an enormous investment of time and money, and it cannot guarantee success because there is so much competition.
(E) requires that an enormous investment of time and money be made and success cannot be guaranteed due to the competition.

Problem Solving

If a,b and c are real numbers such that a^2+2b=7,b^2+4c=-7,c^2+6a=-14,

then find the value of a^2+b^2+c^2

(A)14
(B)21
(C)28
(D)35
(E)49

Posted on 16-March-09

So, folks here are the correct answers

Sentence Correction

The correct answer is (B).
The original sentence is incorrect because the subject and verb do not agree.
Further, it is incorrect to use as to mean because.
(C) is incorrect because the resulting sentence lacks a main verb.
(D) is incorrect because the "it" has no antecedent.
(E) is not technically wrong, but it is too wordy.

Problem Solving

The correct answer is (A).
Adding the three equations, we get
(a^2+6a)+(b^2+2b)+(c^2+4c)=-14

$\Rightarrow (a^2 + 6a + 9)+(b^2 + 2b + 1)$ + (c^2 + 4c + 4) =-14+14

$\Rightarrow (a+3)^2 + (b+1)^2 + (c+2)^2 = 0$
$\Rightarrow a=-3, b=-1 \text{ and }c=-2$
$\Rightarrow a^2+b^2+c^2 = 9+1+4 = 14$

Click here for the next week's Punch

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20 Comments

omshanker said – Wed, 11 Mar 2009 18:17:34 -0000 ( Flag Edit Link )

The Answer for the verbal is B and for the problem solving it is C
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Sandeep Dosanjh said – Wed, 11 Mar 2009 21:48:11 -0000 ( Flag Edit Link )

The answer for verbal is B
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neetu111 said – Wed, 11 Mar 2009 21:59:29 -0000 ( Flag Edit Link )

vebal’s B..

but i cant crack ques 2…

mind sharing the explanation,anyone??
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1. sanju09 said – Sat, 14 Mar 2009 10:36:25 -0000 ( Flag Edit Link )
  
  Add the three equations to get
  
  a ^ 2 + 6 a + b ^ 2 + 2 b + c ^ 2 + 4 c = -14
  
  there is a chance of framing perfect square expressions just by supplying (in fact adding) 9, 1, and 4 at their suitable places, like
  
  a ^ 2 + 6 a + 9 + b ^ 2 + 2 b + 1 + c ^ 2 + 4 c + 4 = -14 + 14
  
  or, (a + 3) ^ 2 + (b + 1) ^ 2 + (c + 2) ^ 2 = 0
  
  which is possible only when a = -3, b = -1, and c = -2;
  
  and hence a ^ 2 + b ^ 2 + c ^ 2 = (-3) ^ 2 + (-1) ^ 2 + (-2) ^ 2 = 14; go with A.
  
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manisha sachdeva said – Thu, 12 Mar 2009 04:55:15 -0000 ( Flag Edit Link )

verbal’s B
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manisha sachdeva said – Thu, 12 Mar 2009 05:04:29 -0000 ( Flag Edit Link )

For answer 2, If we do backsolving, (putting answer choices in question) then only 28 gives real value and 14 gives 0 whereas all other give fraction (which is not possible).

so logically answer seems to be c…...but not sure how to solve it…
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mahatma_rohit said – Thu, 12 Mar 2009 05:53:36 -0000 ( Flag Edit Link )

Ans for SC – B
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mholey said – Thu, 12 Mar 2009 09:14:06 -0000 ( Flag Edit Link )

For SC Answer is B
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sararna said – Thu, 12 Mar 2009 09:24:54 -0000 ( Flag Edit Link )

Ans to SC is B

Ans to PS is 14 solution: a ^{2 = 9;
b ^2 = 1;
c ^2 = 4
implies a}2 + b^{2 + c}2 =14 while substituting in the eqns there is always two possibilities for each value, means a=+or-3; b=+or-1; c=+or-2. for the first eqn, a^{2 + 2b = 7,
sub a=+or-3 and b=-1
for the second eqn, b}2 + 4c=-7, sub b=+or-1 and c=-2 for the third eqn, c^2 + 6a=-14, sub c=+or-2 abd a=-3

With these substitutions all the eqns are solved Hence ans is 14
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brar4318 said – Thu, 12 Mar 2009 12:23:40 -0000 ( Flag Edit Link )

I WANT TO ASK THAT WHICH COURSE IS BETTER IF YOU ARE GIVEN AN OPTION TO CHOOSE ONE AMONG TWO COURSES.GIVE THE MERITS FOR YOUR DECISION
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mits83 said – Thu, 12 Mar 2009 13:54:06 -0000 ( Flag Edit Link )

Ans to SC is B and PS is A (14). a=-3, b=-1, c=-2
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ab4sap said – Thu, 12 Mar 2009 14:52:19 -0000 ( Flag Edit Link )

For Problem Solving it answer is A means 14. if i am taking ab,b & c values as integers, then a^{2 + b}2 + c^{2 can be only 14.
not any integer can fulfill the value of a}2 + b^{2 + c}2 as 21,28,35,49. and in answer its really not needed to go to individual values. but if you go to such level then a =-3, b= -1 and c= -2 will fulfill the equations. So answer for PS is A.

For SC answer is B.

correct me if i m wrong.
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mini_india said – Thu, 12 Mar 2009 15:03:18 -0000 ( Flag Edit Link )

Everyone has concurred on the verbal question’s answer.

here’s my approach to the quant question :

Add up all the equations. You have sum of the squares of a, b and c AND 2(b+2c+3a) = -14. What you can conclude from this equation is : a^{2, b}2 and c^2 are integers (from the given ansa choices) and their sum is even because -14 is even and 2(b+2c+3a) will be even. E+E=E

From the answer choices, only two possibilities arise – 14 / 28.

If I try to fit in 14, 2(b+2c+3a) = -42. If I substitute the expression with b= -1, c= -2 and a = -3, the equation is satisfied and eureka! I have my answer.

Cheers,
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jewel said – Fri, 13 Mar 2009 06:38:06 -0000 ( Flag Edit Link )

answer for verbal is – B
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invinseble said – Fri, 13 Mar 2009 11:42:19 -0000 ( Flag Edit Link )

Although B seems convincing can somebody give the explanation please?
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1. dku12 said – Fri, 13 Mar 2009 15:46:27 -0000 ( Flag Edit Link )
  
  the, correct answer is C
  
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jaskyac said – Sat, 14 Mar 2009 08:34:33 -0000 ( Flag Edit Link )

a^2+2b=7,b2+4c=-7,c^2+6a=-14.

SUM all: a2+6a+b^2+2b+c2+4c=-14

<=>a^2+6a+9-9+b2+2b+1-1+c^2+4c+4-4=-14

<=>(a+3)2+(b+1)^2+(c+2)2-14=-14

<=>(a+3)^2+(b+1)2+(c+2)²⁼⁰

=>a=-3,b=-1,c=-2

=>a2+b^2+c2=14
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neetu111 said – Sun, 15 Mar 2009 03:24:45 -0000 ( Flag Edit Link )

thanks for this..truly helped..

Cheers,
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iikarthik said – Sun, 15 Mar 2009 18:05:19 -0000 ( Flag Edit Link )

Sc—Answer is d
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Sureshbala said – Mon, 16 Mar 2009 07:24:18 -0000 ( Flag Edit Link )

So, folks here are the correct answers

Sentence Correction

The correct answer is (B).
The original sentence is incorrect because the subject and verb do not agree.
Further, it is incorrect to use as to mean because.
(C) is incorrect because the resulting sentence lacks a main verb.
(D) is incorrect because the “it” has no antecedent.
(E) is not technically wrong, but it is too wordy.

Problem Solving

The correct answer is (A).
Adding the three equations, we get
(a^2+6a)+(b^2+2b)+(c^2+4c)=-14

$\Rightarrow (a^2 + 6a + 9)+(b^2 + 2b + 1)$ + (c^2 + 4c + 4) =-14+14

$\Rightarrow (a+3)^2 + (b+1)^2 + (c+2)^2 = 0$
$\Rightarrow a=-3, b=-1 \text{ and }c=-2$
$\Rightarrow a^2+b^2+c^2 = 9+1+4 = 14$

Click here for the next week’s Punch

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khush24 said – Tue, 17 Mar 2009 15:34:54 -0000 ( Flag Edit Link )

so ans for sc is C and ans for ps is A
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angeldebi said – Wed, 29 Apr 2009 06:52:13 -0000 ( Flag Edit Link )

verbal ans is (B)
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