Martha bought several pencils

[guest]

Can someone please help explain the steps involved in solving the problem below:

Martha bought several pencils. If each pencil was either 23 cents or 21 cents. How many pencils did martha buy?

1. Martha bought a total of 6 pencils

2. The total value of pencils bought by martha was 130 cents.

OA is B

[Nov1907]

Aaah. Just got this question on my second Gprep and clicked C as the answer and realised after the test that the solutions can only be integers and so B was sufficient. Let me explain.

Let the number of 23 cent pencils be x. Let the number of 21 cent pencils be y. (1) states that x+y=6. That is clearly insufficient. Let us consider (2): 23x+ 21y = 130. Now x and y are integers greater than 0.

23x = 130-21y. So the RHS needs to be greater than zero and a multiple of 23. Since 130-21y >=23 we have y<=(107/21) y<= 5.abc. So only possible values for y according to this inequality 1,2,3,4,5. Now x also needs to be an integer. So for x to be an integer only solution is y = 4. In this case x = 2 (In fact the first statement gives you a hint of what to look for because it says x+y = 6.). Hence Sufficient - B is the answer. This is the best solution I could think of.If there is something more intuitive I would like to know. Thanks!

[Guest]

Guys, I am not sure whether I understand why 1st choice is not sufficient as well?

The question is: How many pencils did Martha buy?

The first answer choice: Martha bought a total of 6 pencils

Why this choice is not sufficient? The question doesn’t ask how many pencils which cost 23 cents and how many pencils which cost 21 cents Martha bought...

[guest - who posted the Q]

Sorry - I made a typo - The question is how many 23 cent pencils did martha buy?

I made the same mistake - chose C. Need to slow down a little...

[guest - who posted the Q]

Thanks nov1907. Makes sense now...

[StaceyKoprince]

To clarify - the original question should read "how many 23 cent pencils did Martha buy?" If so, original poster, please edit your first post to correct the problem. Thanks!

[Guest]

Can someone please help explain the steps involved in solving the problem below:

Martha bought several pencils. If each pencil was either 23 cents or 21 cents. how many 23 cent pencils did Martha buy?

1. Martha bought a total of 6 pencils

2. The total value of pencils bought by martha was 130 cents.

OA is B

[RonPurewal]

http://www.manhattangmat.com/forums/mar ... t2426.html