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Math Expert V
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A collection of U.S. coins consists of pennies, nickels, dimes, and qu  [#permalink]

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Difficulty:   25% (medium)

Question Stats: 83% (02:18) correct 17% (02:14) wrong based on 53 sessions

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A collection of U.S. coins consists of pennies, nickels, dimes, and quarters, in the ratio 2:3:5:6, respectively. If the number of coins of one of the denominations is 30, which of the following CANNOT be the total number of coins in the collection?

(A) 80
(B) 96
(C) 112
(D) 160
(E) 240

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Bunuel wrote:
A collection of U.S. coins consists of pennies, nickels, dimes, and quarters, in the ratio 2:3:5:6, respectively. If the number of coins of one of the denominations is 30, which of the following CANNOT be the total number of coins in the collection?

(A) 80
(B) 96
(C) 112
(D) 160
(E) 240

You can't just add ratio parts and look for the answer that is NOT a multiple of 16. The answers are all multiples of 16.

Respectively, each answer, divided by 16, has a quotient of 5, 6, 7, 10, and 15

One way to find which answer is impossible:

Call the multiplier x
Find x if 6x=30
If 5x = 30
If 3x = 30
If 2x = 30
The arithmetic is not complicated. Multiply and sum.

If there are 30 of the 6x coin:
6x = 60, and x = 5
5x = 25, 3x = 15, 2x = 10
30 + 25 + 15 + 10 = 80. That's answer A

If there are 30 of the 5x coin:
5x = 30 and x = 6
6x = 36, 3x = 18, 2x = 22
30 + 36 + 18 + 12 = 96. That's answer B

If there are 30 of the 3x coin:
3x = 30 and x = 10
6x = 60, 5x = 50, 2x = 20
30 + 60 + 50 + 20 = 160 That's Answer D

If there are 30 of the 2x coin:
2x = 30 and x = 15
6x = 90, 5x = 75, 3x = 45
30 + 90 + 75 + 45 = 240. That's Answer E

112 does not work

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A collection of U.S. coins consists of pennies, nickels, dimes, and qu  [#permalink]

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The ratio is 2:3:5:6
Let the coins are 2x,3x, 5x, 6x.
Total = 16x

Since one of the coin is 30.
X can be 15, 20, 6, 5.
Hence total can be 16x = 240, 320, 96 or 80.

Hence total cannot be 112. Answer is C
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Originally posted by gmatbusters on 29 Mar 2018, 20:00.
Last edited by gmatbusters on 29 Mar 2018, 23:40, edited 1 time in total.
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Bunuel wrote:
A collection of U.S. coins consists of pennies, nickels, dimes, and quarters, in the ratio 2:3:5:6, respectively. If the number of coins of one of the denominations is 30, which of the following CANNOT be the total number of coins in the collection?
6
(A) 80
(B) 96
(C) 112
(D) 160
(E) 240

Since the ratio of the collection is 2:3:5:6,
the total coins in the collection must be 2x + 3x + 5x + 6x or 16x.

Since the number of coins of one of the denominators is 30, either 2x,3x,5x, or 6x must be 30.

If 2x = 30 -> x = 15. 16x = 240
If 3x = 30 -> x = 10. 16x = 160
If 5x = 30 -> x = 6. 16x = 96
If 6x = 30 -> x = 5. 16x = 80

Only Option C(112) CANNOT be the total number of coins in the collection.
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pushpitkc wrote:
Bunuel wrote:
A collection of U.S. coins consists of pennies, nickels, dimes, and quarters, in the ratio 2:3:5:6, respectively. If the number of coins of one of the denominations is 30, which of the following CANNOT be the total number of coins in the collection?

(A) 80
(B) 96
(C) 112
(D) 160
(E) 240

Since the ratio of the collection is 2:3:5:6,
the total coins in the collection must be 2x + 3x + 5x + 6x or 16x.

(A) 80 = 16*5
(B) 96 = 16*6
(C) 112 is not divisible by 16
(D) 160 = 16*10
(E) 240 = 16*15

Only Option C(112) CANNOT be the total number of coins in the collection.

pushpitkc and maybe gmatbusters . . .

16*7 = 112 _________________
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gmatbusters wrote:
The ratio is 2:3:5:6
Let the coins are 2x,2x 3x, 5x, 6x.
Total = 16x

Since one of the coin is 30.
X can be 15, 20, 6, 5.
Hence total can be 16x = 240, 320, 96 or 80.

Hence total cannot be 112. Answer is C

And is
Quote:
Let the coins are 2x,2x 3x, 5x, 6x

that part a typo?
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Re: A collection of U.S. coins consists of pennies, nickels, dimes, and qu  [#permalink]

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Since the ratio is given we can suppose the no of coins as 2x,3x,5x,6x.total =16x

If 2x =30
We get x = 15

Total = 15*16 = 240. Hence 240 is possible.

Similarly for other cases.

We find that x is not equal to 7. Hence 112 is not possible.

Hope it is clear now.

generis wrote:
gmatbusters wrote:
The ratio is 2:3:5:6
Let the coins are 2x,3x, 5x, 6x.
Total = 16x

Since one of the coin is 30.
X can be 15, 20, 6, 5.
Hence total can be 16x = 240, 320, 96 or 80.

Hence total cannot be 112. Answer is C

And is
Quote:
Let the coins are 2x,2x 3x, 5x, 6x

that part a typo?

Posted from my mobile device
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Re: A collection of U.S. coins consists of pennies, nickels, dimes, and qu  [#permalink]

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Yes you are right.2x has been written twice inadvertently. it is a typo. Tganks for pointing out.

I revised it.

generis wrote:
gmatbusters wrote:
The ratio is 2:3:5:6
Let the coins are 2x,2x 3x, 5x, 6x.
Total = 16x

Since one of the coin is 30.
X can be 15, 20, 6, 5.
Hence total can be 16x = 240, 320, 96 or 80.

Hence total cannot be 112. Answer is C

And is
Quote:
Let the coins are 2x,2x 3x, 5x, 6x

that part a typo?

Posted from my mobile device
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Re: A collection of U.S. coins consists of pennies, nickels, dimes, and qu  [#permalink]

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We find that if total is 112,which is 16*7 doesnt gives any number of coin as 30.

If we take 112 as total, and ratio as 2:3:5:6.
Then the coins will be
2*112/(2+3+5+6) =14,
3*112/(2+3+5+6) =21,
5*112/(2+3+5+6) =35,
6*112/(2+3+5+6) =42.

No denomination is present as 30 numbers. which is against the question.

Hence 112 is not the total number of coins.

generis wrote:
pushpitkc wrote:
Bunuel wrote:
A collection of U.S. coins consists of pennies, nickels, dimes, and quarters, in the ratio 2:3:5:6, respectively. If the number of coins of one of the denominations is 30, which of the following CANNOT be the total number of coins in the collection?

(A) 80
(B) 96
(C) 112
(D) 160
(E) 240

Since the ratio of the collection is 2:3:5:6,
the total coins in the collection must be 2x + 3x + 5x + 6x or 16x.

(A) 80 = 16*5
(B) 96 = 16*6
(C) 112 is not divisible by 16
(D) 160 = 16*10
(E) 240 = 16*15

Only Option C(112) CANNOT be the total number of coins in the collection.

pushpitkc and maybe gmatbusters . . .

16*7 = 112 Posted from my mobile device
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Re: A collection of U.S. coins consists of pennies, nickels, dimes, and qu  [#permalink]

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This approach is not applicable to this question, as all the options are multiple od 16.

pushpitkc wrote:
Bunuel wrote:
A collection of U.S. coins consists of pennies, nickels, dimes, and quarters, in the ratio 2:3:5:6, respectively. If the number of coins of one of the denominations is 30, which of the following CANNOT be the total number of coins in the collection?

(A) 80
(B) 96
(C) 112
(D) 160
(E) 240

Since the ratio of the collection is 2:3:5:6,
the total coins in the collection must be 2x + 3x + 5x + 6x or 16x.

(A) 80 = 16*5
(B) 96 = 16*6
(C) 112 is not divisible by 16
(D) 160 = 16*10
(E) 240 = 16*15

Only Option C(112) CANNOT be the total number of coins in the collection.

Posted from my mobile device
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A collection of U.S. coins consists of pennies, nickels, dimes, and qu  [#permalink]

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generis wrote:
pushpitkc wrote:
Bunuel wrote:
A collection of U.S. coins consists of pennies, nickels, dimes, and quarters, in the ratio 2:3:5:6, respectively. If the number of coins of one of the denominations is 30, which of the following CANNOT be the total number of coins in the collection?

(A) 80
(B) 96
(C) 112
(D) 160
(E) 240

Since the ratio of the collection is 2:3:5:6,
the total coins in the collection must be 2x + 3x + 5x + 6x or 16x.

(A) 80 = 16*5
(B) 96 = 16*6
(C) 112 is not divisible by 16
(D) 160 = 16*10
(E) 240 = 16*15

Only Option C(112) CANNOT be the total number of coins in the collection.

pushpitkc and maybe gmatbusters . . .

16*7 = 112 Thanks for informing generis - Corrected my solution!
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Re: A collection of U.S. coins consists of pennies, nickels, dimes, and qu  [#permalink]

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Bunuel wrote:
A collection of U.S. coins consists of pennies, nickels, dimes, and quarters, in the ratio 2:3:5:6, respectively. If the number of coins of one of the denominations is 30, which of the following CANNOT be the total number of coins in the collection?

(A) 80
(B) 96
(C) 112
(D) 160
(E) 240

We can create the ratio of pennies : nickels : dimes : quarters = 2x : 3x : 5x : 6x

So the total number of coins is 16x.

If there are 30 pennies, then x = 15 and 16x = 240.

If there are 30 nickels, then x = 10 and 16x = 160.

If there are 30 dimes, then x = 6 and 16x = 96.

If there are 30 quarters, then x = 5 and 16x = 80.

Thus, 112 cannot be the total number of coins.

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