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Mary has $4.6 in nickels and dimes only. If she has fewer dimes than

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Mary has $4.6 in nickels and dimes only. If she has fewer dimes than  [#permalink]

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New post 09 Dec 2018, 05:11
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A
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C
D
E

Difficulty:

  55% (hard)

Question Stats:

54% (01:37) correct 46% (01:15) wrong based on 56 sessions

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Mary has $4.6 in nickels and dimes only. If she has fewer dimes than nickels, what is the least possible number of nickels she could have?

(A) 24

(B) 27

(C) 30

(D) 32

(E) 36

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Mary has $4.6 in nickels and dimes only. If she has fewer dimes than  [#permalink]

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New post 09 Dec 2018, 07:36
rohan2345, is the question complete?. The price of nickle and dime is not given.

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Re: Mary has $4.6 in nickels and dimes only. If she has fewer dimes than  [#permalink]

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New post 14 Dec 2018, 00:02
Afc0892 wrote:
rohan2345, is the question complete?. The price of nickle and dime is not given.

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Hi Afc0892,

A Nickel is 5 cents and a Dime is 10 Cents , so 10x+5y=460 cents , where x is number of dimes and y is number of Nickels. Now please try to solve.

Hope this helps!
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Re: Mary has $4.6 in nickels and dimes only. If she has fewer dimes than  [#permalink]

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New post 15 Dec 2018, 08:37
rohan2345 wrote:
Mary has $4.6 in nickels and dimes only. If she has fewer dimes than nickels, what is the least possible number of nickels she could have?

(A) 24

(B) 27

(C) 30

(D) 32

(E) 36



We need to find the min value of nickels.

So let no of nickels = x
no of dimes = y

So the equation will be 5x+10y=460

First 3 answer choice will make the dimes more than nickels . So A,B,C are eliminated

D) 32*5 = 160

Nickel = 32 Dime = 30


E) 36*5=180
So Nickel = 36 and Dimes = 28

But we need to calculate min value of Nickel

So D is the correct choice.
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Re: Mary has $4.6 in nickels and dimes only. If she has fewer dimes than  [#permalink]

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New post 17 Dec 2018, 04:23
1 Nickel = 5 cents, Let Mary have x nickels
1 Dime = 10 cents, let Mary have y dimes
Total amount = 460 cents

We get the equation 5x + 10y = 460

x + 2y = 92
Note that the coefficients are co-prime
First value that satisfies is x = 2, y= 45
After these the subsequent values of x are obtained by adding 2(coefficient of y in the equation) to the previous value
So, x = 2,4,6,8,.... which is an A.P
Similarly the subsequent values of y are obtained by subtracting 1(coefficient of x in the equation) to the previous value
So, y= 45,44,43,42,.... which is an A.P
Now it is given that x > y

Let it happen for the nth term of each A.P
2n > 45 - (n - 1 )

3n > 46

n > 15.33
i.e 16th term
number of nickels = 32 ; number of dimes = 30
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Re: Mary has $4.6 in nickels and dimes only. If she has fewer dimes than &nbs [#permalink] 17 Dec 2018, 04:23
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