Robert purchased $2000 worth of US saving bonds

Basically it means that I gave you $2000 in currency notes of $100 and $50. No other notes are allowed.

Now of I give you only $50s then I will need to give you 40 notes to make it $2000 (as 2000=50*40).

If I give you only $100, then I need to give you 20 notes to make it $2000.

If I use a combination of 50s and 100s, then I will give you between 40 and 20 notes.

But I cannot give you 50 notes. Because even if I use only $50, 50 notes will make the total $2500 (50*50) which is not the amount we want.

So, 50 is the answer we are looking for.

Hence, E!

vinni.k wrote:source "kaplan"

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

OA: E

Please explain the problem.

Thanks & Regards
Vinni

Let x = the number of $50 bonds and y = the number of $100 bonds.
Since $2000 worth of bonds were purchased, we get:
50x + 100y = 2000
50(x+2y) = 2000
x+2y = 40.

Looking at the answer choices:
Since x+2y = 40, it is not possible that the total number of bonds -- in other words, the value of x+y -- is equal to 50.

The correct answer is E.

We can assume $50 bonds = x
$100 bonds = y

50x+100y = 2000
x+2y = 40

So if you look at it many other values are there which are not possible
For example you can even have 40 bonds because lets say if y = 1 x = 38 --> 39 bonds

Please explain the confusion

GMATGuruNY wrote::
Since x+2y = 40, it is not possible that the total number of bonds -- in other words, the value of x+y -- is equal to 50.

The correct answer is E.

Thanks for your replies.
Even I am also not able to relate this x + 2y = 40 with the answer. I am bit confused after this.


Vinni

vinni.k wrote:

GMATGuruNY wrote::
Since x+2y = 40, it is not possible that the total number of bonds -- in other words, the value of x+y -- is equal to 50.

The correct answer is E.

Thanks for your replies.
Even I am also not able to relate this x + 2y = 40 with the answer. I am bit confused after this.


Vinni

From my post above:
x+2y = 40.

Answer choice E implies that the number of bonds purchased is equal to 50:
x+y = 50.

Subtracting the second equation from the first, we get:
(x+2y) - (x+y) = 40-50
y = -10.
Doesn't work: it is not possible that the number of $100 bonds purchased is equal to a negative value.

We also can reason our way to the correct answer.
The greatest answer choice is 50.
If 50 of the $50 bonds are purchased, the total amount purchased = 50*50 = 2500.
Too much: the total amount purchased must be equal to 2000.
Since purchasing 50 of the cheaper of the two bonds yields a total greater than 2000, it is not possible to purchase 50 bonds.

Thanks Mitch. I have understood your explanation.

Regards
vinni

GMATGuruNY wrote: From my post above:
x+2y = 40.

Answer choice E implies that the number of bonds purchased is equal to 50:
x+y = 50.

Subtracting the second equation from the first, we get:
(x+2y) - (x+y) = 40-50
y = -10.
Doesn't work: it is not possible that the number of $100 bonds purchased is equal to a negative value.

We also can reason our way to the correct answer.
The greatest answer choice is 50.
If 50 of the $50 bonds are purchased, the total amount purchased = 50*50 = 2500.
Too much: the total amount purchased must be equal to 2000.
Since purchasing 50 of the cheaper of the two bonds yields a total greater than 2000, it is not possible to purchase 50 bonds.