Data Sufficiency Challenge Question: Try Your Hand!
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Take two minutes to solve this data sufficiency question:
In a certain store, the price of five pens is equal to the price of a notebook. What is the cost of a ruler in this store?
- The cost of four pens and two notebooks is 10 dollars more than the cost of six rulers.
- The cost of seven notebooks is 25 dollars more than the cost of 15 rulers.
Have your answer? Great! Let’s go ahead and walk through it.
My first step is to assign variables and translate the prompt into math – I let p represent the number of pens, n represent the number of notebooks, and r represent the number of rulers. From the prompt, then, I can get the equation 5p = n, and I want to find the value of r.
Translating statement 1, I can say that 4p + 2n = 10 + 6r. Three variables in one equation doesn’t help me, but I can substitute 5p for n to get 4p + 2(5p) = 10 + 6r, or 14p = 10 + 6r. Uh-oh – I have two variables, but only one linear equation! I can’t solve for r, so statement 1 must be insufficient.
Moving on to statement 2, I can translate to get the equation 7n = 25 + 15r. I’m already suspicious, because again I have two variables and only one linear equation, but I’ll try substituting 5p from the prompt anyway. This gives me 7(5p) = 25 + 15r, or 35p = 25 + 15r. Well, that didn’t really help me – I still have two variables and only one equation, so I can’t solve for r. Statement 2 must be insufficient.
Now I consider the statements together. I can see from statement 1 that I have a linear equation with the variables r and p. In statement 2, I have another equation with the same two variables. Two variables and two linear equations? Great! I’m a good data sufficiency strategist, so I know that I shouldn’t waste time to actually do the math here – I know that I can solve for both variables in the system, so I’ll be able to find the value of r. The answer here is C.
Right?
14 comments
ralf on April 10th, 2012 at 12:26 am
oh,good!!
ronnie1985 on April 17th, 2012 at 10:38 pm
Both the equations are same and hence do not yield any solution.
(D) is answer.
Nav on April 10th, 2012 at 3:14 am
Not sure if C is the right answer - I would go for E as both equations created aren't actually different. Multiplying 14p = 10 + 6r by (5/2) gives us 35p = 25 + 15r so we still can't solve the equations and get a value of r.
suresh on April 10th, 2012 at 3:52 am
yeah agree,,with NAV... c is not the correct answer..correct answer is E.. as both the linear equation is same....35p=25+15r
Andy R on April 10th, 2012 at 4:44 am
agree with the above, since both equations are the same and you cannot solve this. from (1) 14x-6y=10 from (2) 7x-3y=5 which is the same as (1). E for me too
Rahul Dudheria on April 10th, 2012 at 9:06 am
Agree! with others on this. Answer should be E.
Meesum on April 10th, 2012 at 12:27 pm
It should be 'E' as explained by others, the two equations are the same
Seetharaman on April 10th, 2012 at 6:18 pm
True. The actual proce of any one of the item should be given to find the price. IMO its E.
MomentsOfReflection on April 10th, 2012 at 8:12 pm
This is a typical trick gmat question where they provide seemingly different equations which later turn out to be the same.
P==> Pencil
n==>NoteBook
R==>Ruler
Equation 1 ==> 5P = N (from Question Stem)
As per statement A==> 4P + 2N - 6R = 10
Using 1 ==> 7N-15R = 25
As per statement B ===> 4P + 10P -6R = 10
Using 1 ==> 35 P - 15 R = 25
Look at the RHS of the equations, one is 10 and the other is 25
Multiply 1 by 2.5 and you will get the exact same equation as 1
Every one knows that one needs 'n' equations to solve for 'n' variables. The GMAT knows that everyone knows this. Be Warned !
Suresh on April 10th, 2012 at 11:33 pm
Yes, the answer should be E, as combining two equations would give us back the same equation 5pens = book, so we cannot find a solution with the given 2 options
iwillsurvive101 on April 11th, 2012 at 8:19 am
I solved it, and, I got C @ my first take as well.
Then I read the explanation, went back and solved it again, got E.
The thing we all need to learn(and develop so that it comes quickly) is when to trust the gut, and when not to. I've gone about trusting my inner gut and leave many DS problems unsolved(when it starts to mean something) and got it right. But, questions like the above leads to a wrong conclusion if you try to trust your gut.
Suggestions on when not to and examples would help.
Thanks for this wonderful problem.
rao on April 13th, 2012 at 9:54 am
The Answer must be E. becuase can not be solved for those variables.
abhi.iitb on April 20th, 2012 at 11:57 pm
Since here we have two equations of parallel lines. but, parallel lines do not intersect so no solution exist for two variables. Hence, Ans is E
Ken on June 25th, 2012 at 2:31 pm
Someone should remove or edit this article - makes Veritas look bad (now I know why my iPhone app has so many spelling errors)! Answer is E, not C.