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word problems

by Joy Shaha » Fri Apr 07, 2017 12:25 pm
Q.The cost of equities of type A and type B (in dollars) are two different integers. If 4 equities of type A & 5 equities of type B costs 27 dollars, What is the total cost of 2 equities of type A and 3 equities of type B in dollars?
A.15;
B.24;
C.35;
D.42;
E.55
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by [email protected] » Sat Apr 08, 2017 9:56 am
Hi Joy Shaha,

You would likely find it easiest to use 'brute force' on this question.

We're told that both A and B are POSITIVE INTEGERS and that 4A + 5B = 27. Since 27 is such a relatively 'small' number and there IS a definitive answer to the given question, there must be just one solution to given equation. We just have to do enough 'brute force' arithmetic to find it....

IF.... A=1, then 5B = 23... that does NOT lead to an integer value for B though, so A=1 is not possible.

IF.... A=2, then 5B = 19... that does NOT lead to an integer value for B though, so A=2 is not possible.

IF.... A=3, then 5B = 15... that DOES lead to an integer value for B (B=3), so A=3, B=3 IS correct.

The question asks for the value of 2A + 3B.... 2(3) + 3(3) = 15

Final Answer: A

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by Jay@ManhattanReview » Sun Apr 09, 2017 4:17 am
Joy Shaha wrote:Q.The cost of equities of type A and type B (in dollars) are two different integers. If 4 equities of type A & 5 equities of type B costs 27 dollars, What is the total cost of 2 equities of type A and 3 equities of type B in dollars?

A.15;
B.24;
C.35;
D.42;
E.55
Hi Joy,

May I know the source of the question? Though there is nothing wrong in the question, the options are not intelligently crafted. At the outset, we can figure out that option C, D and E cannot be an answer.

Since we have 4a + 5b = 27, and we are asked to find out the value of 2a + 3b, which is a little more than half of 4a + 5b, the answer would be a little more than 27/2 = 14.5 and certainly less than 27. The answer must be one between A and B, and most likely A.

Let's take A as an answer.

We have 4a + 5b = 27 and 2a + 3b = 15. Upon solving these, we get b = 3 and a = 3--Both are integers, qualified values!.

If you try with 2a + 3b = 24, you would not get integer values for a and b.

The correct answer: A

Hope this helps!

Relevant book: Manhattan Review GMAT Word Problems Guide

-Jay
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by Jay@ManhattanReview » Sun Apr 09, 2017 5:03 am
Joy Shaha wrote:Q.The cost of equities of type A and type B (in dollars) are two different integers. If 4 equities of type A & 5 equities of type B costs 27 dollars, What is the total cost of 2 equities of type A and 3 equities of type B in dollars?
A.15;
B.24;
C.35;
D.42;
E.55
Hi Joy,

Had the option been ranging from say from 12 to 24, the optimum approach would differ.

Let's reach the answer from the given equations.

We have 4a + 5b = 27 and we have to find out the value of 2a + 3b.

Since a and b are positive integers, we must find out their values from the linear equation: 4a + 5b = 27.

We have 4a + 5b = 27

=> 4a = 27 - 5b

Since LHS (4a) is a multiple of 4, RHS (27 - 5b) must be a multiple of 4.

Hit and trial is the most efficient way of tackling this.

Plug in positive integer values of b (1, 2, 3, 4, 5) such that you get (27 - 5b) a positive multiple of 4, thereby get the value of a.

We get b = 3 and a =3.

Thus, 2a + 3b = 2*3 + 3*3 = 15.

The correct answer: A

Hope this helps!

-Jay
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