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Erica has $460 in 5-and 10-dollar bills only. If she has [#permalink]

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28 May 2007, 22:32

6

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A

B

C

D

E

Difficulty:

25% (medium)

Question Stats:

71% (01:47) correct
29% (01:50) wrong based on 263 sessions

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Erica has $460 in 5-and 10-dollar bills only. If she has fewer 10-than 5-dollar bills, what is the least possible number of 5-dollar bills she could have?

also, C and E won't work b/c when multiplied by 5 they give integer 5 in the units digit. subtracting xx5 from 460 will give you xx5. xx5/10 = integer.5.

Erica has $460 in 5-and 10-dollar bills only. If she has fewer 10-than 5-dollar bills, what is the least possible number of 5-dollar bills she could have? (A) 32 (B) 30 (C) 29 (D) 28 (E) 27

If she had an equal number of each, , she could have 30 of each for a total of $450, and another 2 fivers to make $460. TOTAL = 32. Note that all other choices would give less than $450.

Erica has $460 in 5-and 10-dollar bills only. If she has fewer 10-than 5-dollar bills, what is the least possible number of 5-dollar bills she could have?

(A) 32 (B) 30 (C) 29 (D) 28 (E) 27

Given that: 5x+10y=460 --> 10y=460-5x; x>y --> 10x>10y.

Re: Erica has $460 in 5-and 10-dollar bills only. If she has [#permalink]

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04 Dec 2013, 15:44

OK so there is a 2:1 ratio between 5 and 10 dollar notes. This means that the answer choice can only be even. so that's A, B or D.

Test b: number of 5 dollar notes equal 30. total revenue=150. To make up to 460 total, you need 31 ten dollar notes. Since there is a greater number of $10 dollar notes than $5 dollar notes. Requirement not met. We also know that D is wrong now...as it would give more $10 dollar notes than $5. Therefore A must be the right choice.

Erica has $460 in 5-and 10-dollar bills only. If she has [#permalink]

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10 Aug 2017, 13:59

bmwhype2 wrote:

Erica has $460 in 5-and 10-dollar bills only. If she has fewer 10-than 5-dollar bills, what is the least possible number of 5-dollar bills she could have?

(A) 32 (B) 30 (C) 29 (D) 28 (E) 27

let x=least possible number of fives 5x+10(x-1)=460 x=31.3 5x+10(x-2)=460 x=32 A

Erica has $460 in 5-and 10-dollar bills only. If she has fewer 10-than 5-dollar bills, what is the least possible number of 5-dollar bills she could have?

(A) 32 (B) 30 (C) 29 (D) 28 (E) 27

We can create the following equation in which f = the number of 5-dollar bills and t = the number of 10-dollar bills.

5f + 10t = 460

f + 2t = 92

If the number of 5-dollar bills and the number of 10-dollar bills are equal, i.e., f = t, then we have:

f + 2f = 92

3f = 92

f = 30⅔

Since f, the number of 5-dollar bills, must be a whole number, and f > t, f should be at least 31. Let’s check whether f can be 31t:

If f = 31, then 31 + 2t = 92 → 2t = 61 → t = 30.5. However, t must be whole number also, so f can’t be 31.

Now let’s check if f can be 32:

If f = 32, then 32 + 2t = 92 → 2t = 60 → t = 30. We see that t is a whole number and f > t. So, the least possible value of f is 32.

Answer: A
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