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Alice bought a certain number of 30 cent stamps, 35 cent stamps and 40

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Alice bought a certain number of 30 cent stamps, 35 cent stamps and 40  [#permalink]

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New post 14 Jul 2018, 02:04
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Question Stats:

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Alice bought a certain number of 30 cent stamps, 35 cent stamps and 40 cent stamps. She spent a total of $4.20 in buying these stamps. Did she buy more than 5 stamps of any of the three values?

(1) The number of 35 cent stamps and 40 cent stamps that Alice bought are equal.
(2) The number of 30 cent stamps and 40 cent stamps that Alice bought are equal. The number of 35 cent stamps that she bought was not more than the number of 40 cent stamps that she bought.
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Alice bought a certain number of 30 cent stamps, 35 cent stamps and 40  [#permalink]

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New post 14 Jul 2018, 04:00
1
PKN wrote:
Alice bought a certain number of 30 cent stamps, 35 cent stamps and 40 cent stamps. She spent a total of $4.20 in buying these stamps. Did she buy more than 5 stamps of any of the three values?

(1) The number of 35 cent stamps and 40 cent stamps that Alice bought are equal.
(2) The number of 30 cent stamps and 40 cent stamps that Alice bought are equal. The number of 35 cent stamps that she bought was not more than the number of 40 cent stamps that she bought.


30a+35b+40c=420

(1) b=c
So 30a+75b=420
If b=2, 30a=420-150=270.....a=9 so >5
If b=4, 30a=420-300=120....a=4 and b=c=2 so none is greater than 5
Insufficient


(2) The number of 30 cent stamps and 40 cent stamps that Alice bought are equal. The number of 35 cent stamps that she bought was not more than the number of 40 cent stamps that she bought.

So a=c and \(b\leq{c}\)
So 30a+35b+40c=420......70a+35b=420.....you can divide entire equation by 35
2a+b=12.....
Max value of a is 5 and therefore max value of c is 5 and b cannot be greater than c
No combination of a,b,c greater than 5 is possible..
So sufficient

B
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Re: Alice bought a certain number of 30 cent stamps, 35 cent stamps and 40  [#permalink]

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New post 14 Jul 2018, 04:10
To find if Alice bought more than 5 stamps of any of the three values

Let x be the number of 30 stamps and x > 0
Let y be the number of 35 stamps and y > 0
Let z be the number of 40 stamps and z > 0

Alice spent a total of $4.20 in buying these stamps

=> 30x + 35y + 40z = $4.20 = 420 cents ------- (1)

Statement 1

The number of 35 cent stamps and 40 cent stamps that Alice bought are equal.

=> y = z

=> From equation 1, 30x + y(35 + 40) = 420

=> 30x + 75y = 420

Case 1)

x = 9, y = 2 satisfies the equation. So might have bought more than 5 30 cent stamps.

case 2)

x = 4, y = 4 satisfies the equation. So might have bought less than 5 30 cent stamps.

Since we don't get an unique answer, statement 1 is not sufficient.

Statement 2

The number of 30 cent stamps and 40 cent stamps that Alice bought are equal. The number of 35 cent stamps that she bought was not more than the number of 40 cent stamps that she bought.

=> x = z and y \(\leq\) z = x

From equation 1, we get 30x + 40x + 35y = 420

=> 70x + 35y = 420 ---------- (2)

Since y \(\geq\) 0 and y \(\leq\) x lets start figuring out the minimum possible value for y

If y \(\geq\)0 and y is an integer lets start at y=1

=> 70x + 35 = 420

=> 70x = 385

=> x is not an integer which is false => y > 1

Lets see if y = 2

From equation 2, => 70x + 70 = 420

=> 70x = 350

=> x = 5

Since the minimum possible value for y is 2 and if y=2 => x = z = 5

=> x, z \(\leq\) 5

Statement 2 is sufficient

Hence option B
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Re: Alice bought a certain number of 30 cent stamps, 35 cent stamps and 40  [#permalink]

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New post 14 Jul 2018, 04:12
chetan2u wrote:
PKN wrote:
Alice bought a certain number of 30 cent stamps, 35 cent stamps and 40 cent stamps. She spent a total of $4.20 in buying these stamps. Did she buy more than 5 stamps of any of the three values?

(1) The number of 35 cent stamps and 40 cent stamps that Alice bought are equal.
(2) The number of 30 cent stamps and 40 cent stamps that Alice bought are equal. The number of 35 cent stamps that she bought was not more than the number of 40 cent stamps that she bought.


30a+35b+40c=420

(1) b=c
So 30a+75b=420
If b=2, 30a=420-150=270.....a=9 so >5
If b=4, 30a=420-300=120....a=4 and b=c=2 so none is greater than 5
Insufficient


(2) The number of 30 cent stamps and 40 cent stamps that Alice bought are equal. The number of 35 cent stamps that she bought was not more than the number of 40 cent stamps that she bought.
So a=c and b>c
So 30a+35b+40c=420......70a+35b=420.....you can divide entire equation by 35
2a+b=12.....
Max value of a is 5 and therefore max value of c is 5 and b cannot be greater than c
No combination of a,b,c greater than 5 is possible..
So sufficient

B


Hi chetan2u,
Could you please correct me? I think it's \(b\leq{c}\).
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Re: Alice bought a certain number of 30 cent stamps, 35 cent stamps and 40  [#permalink]

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New post 14 Jul 2018, 04:17
1
PKN wrote:
Alice bought a certain number of 30 cent stamps, 35 cent stamps and 40 cent stamps. She spent a total of $4.20 in buying these stamps. Did she buy more than 5 stamps of any of the three values?

(1) The number of 35 cent stamps and 40 cent stamps that Alice bought are equal.
(2) The number of 30 cent stamps and 40 cent stamps that Alice bought are equal. The number of 35 cent stamps that she bought was not more than the number of 40 cent stamps that she bought.


PKN wrote:
Alice bought a certain number of 30 cent stamps, 35 cent stamps and 40 cent stamps. She spent a total of $4.20 in buying these stamps. Did she buy more than 5 stamps of any of the three values?

(1) The number of 35 cent stamps and 40 cent stamps that Alice bought are equal.
(2) The number of 30 cent stamps and 40 cent stamps that Alice bought are equal. The number of 35 cent stamps that she bought was not more than the number of 40 cent stamps that she bought.


B.

let x,y,and z be # of 30,35,and 40 cent stamps respectively
so, 30x+35y+40z = 420

1) y=z
=> 30x+75k = 420
(k,x) = (2,9) & (4,4)
or (x,y,z) = (9,1,1) & (4,2,2)
insufficient.

2) x=z
=> 35y+70k = 420
(k,y) = (2,8) , (4,4) & (6,0)
or (x,y,z) = (1,8,1) , (2,4,2) & (3,0,3)
(1,8,1) is discarded since y =< z
so Alice did not purchase any value stamp in a quantity more than 5. sufficient.
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Re: Alice bought a certain number of 30 cent stamps, 35 cent stamps and 40 &nbs [#permalink] 14 Jul 2018, 04:17
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Alice bought a certain number of 30 cent stamps, 35 cent stamps and 40

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