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Bonds problem

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srichaks
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Bonds problem [#permalink] New post   12 May 2010, 18:49
00:00
A
B
C
D
E

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Q:Robert purchased $2000 worth of US saving bonds. If bonds are sold in $50 or $100 denominations only, which of the following CANNOT be the number of US saving bonds that Robert purchased?
A:20
B:27
C:30
D:40
E:50

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OA: E


Please explain the problem and also why other answer choices are incorrect?

Thanks in advance.



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Re: Bonds problem [#permalink] New post   12 May 2010, 18:53
I started off with looking at the answer choices... 20-27-30 are in a tight range, so my guess was to look and rule out the bigger numbers.

The total amount is $2000. So with 50 bonds, each $50 = $2500 , we already exceed the $2000 limit. Hence E is the answer.

40bonds could be correct too but it works out to $2000 right away so it is also ruled out.

E remains.
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Re: Bonds problem [#permalink] New post   12 May 2010, 22:15
The question is basically asking if you have $2000 in some combination of $50s and $100s, how many bills (bonds) are there? Or in this case, which is not a possibility.

Glancing over the options, I knew 50 bills was too high to work. The maximum number of bonds has to be 40 (all $50s), so E has to be the answer. Don't worry about why the others are incorrect.

In questions like this, I usually try to narrow down the choices by determining the range of answers. In this case, the number of bills would have to range from 20 (all $100) to 40. Anything outside that range would not work in the formula.
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Re: Bonds problem [#permalink] New post   14 May 2010, 00:51
T = 2000 (total value of bonds)
we know that the only denominations he bought the bonds are 50 and 100 so we can write this as an algerbraic equation

50a + 100b = 2000

--> a + 2b = 40 --(a)

now lets look at choices and see which one fits

A) a + b = 20
so a = 20 -b

putting this into equation

20 - b + 2b = 40
b = 20 ...so it is possible


B) 27 - b + 2b = 40
b = 13

Moving on to D

D) 40 + b = 40
b = 0
so possible because a = 40 in this case

E) 50 + b = 40
b = -10
ok this is not possible and that shows that this is our answer
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Re: Bonds problem [#permalink] New post   14 May 2010, 11:35
this question need a logic rather than math skills, the maximum no. of bond which is be purchased is 40 ( 2000/50) hence any no. greater than 40 is not posssible hence ans E



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Re: Bonds problem [#permalink]
14 May 2010, 11:35
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