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A man purchased $510 worth savings bonds in denominations of
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07 Aug 2020, 10:05
07 Aug 2020, 10:05
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39% (02:45) correct
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A man purchased $510 worth savings bonds in denominations of $15 and $30, including at least 1 of each denomination. He gave away 8 of the bonds as gifts but then lost all the rest of the bonds he had purchased. If the number of $30 bonds he gave away was a multiple of the number of $15 bonds he gave away, what was maximum possible value of the bonds that he lost?
A. 180
B. 225
C. 285
D. 300
E. 330
Kudos for the right solution and explanation
A. 180
B. 225
C. 285
D. 300
E. 330
Kudos for the right solution and explanation
Re: A man purchased $510 worth savings bonds in denominations of
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11 Aug 2020, 05:56
11 Aug 2020, 05:56
1
Man gave away 8 bonds and lost the rest.
So the maximum value of bonds will be lost only if the value of bonds given away would be the minimum.
Now, the bonds given away would be minimum if the $30 value bonds is the least.
Condition : Number of $30 bonds is a multiple of $15 bonds given.
the only number that give the least $30 bonds and also satisfy the question is 4.
8 bonds := 4($30 bonds) which is a multiple of 4 ($15 bonds)
So the value of bonds lost = 510 - [ 4 * 30 + 4 * 15 ] = 330
So the maximum value of bonds will be lost only if the value of bonds given away would be the minimum.
Now, the bonds given away would be minimum if the $30 value bonds is the least.
Condition : Number of $30 bonds is a multiple of $15 bonds given.
the only number that give the least $30 bonds and also satisfy the question is 4.
8 bonds := 4($30 bonds) which is a multiple of 4 ($15 bonds)
So the value of bonds lost = 510 - [ 4 * 30 + 4 * 15 ] = 330
Re: A man purchased $510 worth savings bonds in denominations of
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19 Sep 2020, 12:01
19 Sep 2020, 12:01
2
Aaka wrote:
Man gave away 8 bonds and lost the rest.
So the maximum value of bonds will be lost only if the value of bonds given away would be the minimum.
Now, the bonds given away would be minimum if the $30 value bonds is the least.
Condition : Number of $30 bonds is a multiple of $15 bonds given.
the only number that give the least $30 bonds and also satisfy the question is 4.
8 bonds := 4($30 bonds) which is a multiple of 4 ($15 bonds)
So the value of bonds lost = 510 - [ 4 * 30 + 4 * 15 ] = 330
So the maximum value of bonds will be lost only if the value of bonds given away would be the minimum.
Now, the bonds given away would be minimum if the $30 value bonds is the least.
Condition : Number of $30 bonds is a multiple of $15 bonds given.
the only number that give the least $30 bonds and also satisfy the question is 4.
8 bonds := 4($30 bonds) which is a multiple of 4 ($15 bonds)
So the value of bonds lost = 510 - [ 4 * 30 + 4 * 15 ] = 330
Why can't the number of $15 denomination bonds given away be 8 and the number of $30 denomination bonds given away be 0?
0 is a multiple of 8 since 0=0*8. There is no restriction on the number of bonds of each denomination that were given away, only a restriction of at least one of each when purchased.
So the total purchased would be 13 $30 bonds, and 8 $15 bonds....giving a total of $510 worth in value
In this case the max value lost would be ($15)*0+($30)*13=$390
