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Robert purchased $2000 worth of US saving bonds. If bonds are sold in

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Robert purchased $2000 worth of US saving bonds. If bonds are sold in  [#permalink]

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New post 23 Dec 2018, 10:43
1
1
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

59% (02:00) correct 41% (01:16) wrong based on 38 sessions

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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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Re: Robert purchased $2000 worth of US saving bonds. If bonds are sold in  [#permalink]

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New post 23 Dec 2018, 13:58
1
SajjadAhmad - Thank you for this high quality question.

Beware of questions such as this one because these are very time consuming. Many test takers would mistakenly choose Option B. 27 since most of the number ending with zero, and answer option B pops out as the only odd number. However, answer option B is not correct.

Solution

First, let us form the equation.

Since bonds are sold in $50 or $100 denominations only, and the total value of bonds purchased is purchased $2000, the equation is as follows:
50 A + 100 B = 2000
A + 2B = 40
Where A = number of $50 bonds
& B = number of $100 bonds
Note: A and B could be zero as well

Now we have to find A + B

A. 20: A = 0 & B = 20 (Satisfies A + 2B = 40)
B. 27: A = 14 & B = 13 (Satisfies A + 2B = 40)
C. 30: A = 20 & B = 10 (Satisfies A + 2B = 40)
D. 40: A = 40 & B = 0 (Satisfies A + 2B = 40)

E. 50: Cannot be solved for non negatives values of both A & B

Short cut: Can be solved in 30 seconds
Since A + 2B = 40, then A + B cannot be greater than 40, since A & B cannot be negative values (number of bonds cannot be negative)
The only option in which A + B is greater than 40 is Option E. 50. Quickly eliminate
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Re: Robert purchased $2000 worth of US saving bonds. If bonds are sold in   [#permalink] 23 Dec 2018, 13:58
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