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A steel bar 135 inches long will be cut into a num

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A steel bar 135 inches long will be cut into a num [#permalink] New post 15 Aug 2017, 01:28
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A steel bar 135 inches long will be cut into a number of 5-inch and 7-inch seg­ments, with no part of the original steel bar left over.

Quantity A
Quantity B
The minimum possible number of 5-inch pieces
5


A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
[Reveal] Spoiler: OA

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Re: A steel bar 135 inches long will be cut into a num [#permalink] New post 28 Sep 2017, 08:55
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Not the fastest way to solve it but it's a try.

We can rewrite the statement as an equation \(135 = 7x + 5y\). Then, we can solve for x, the number of 7-long pieces as \(x = \frac{5}{7}(27-y)\). Then, we can try to substitute various values of y in order to get the smallest value for y so that x is an integer. This will lead to getting that with y = 6, x = 15. Thus, the minimal value of 5-long pieces is 6. Answer A!
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Re: A steel bar 135 inches long will be cut into a num [#permalink] New post 28 Sep 2017, 09:23
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Carcass wrote:
A steel bar 135 inches long will be cut into a number of 5-inch and 7-inch seg­ments, with no part of the original steel bar left over.

Quantity A
Quantity B
The minimum possible number of 5-inch pieces
5


A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.


If we can divide 135 by 5 and 7 and the result sum up to 135

1. when 7*0 then 5*27 i.e 0+135 =135

2. when 7*5 then 5*20 i.e 35+100 = 135

3. when 7*10 then 5*13 i.e 70+65 =135

4. when 7*15 then 5*6 i.e 105+30 =135

No other possible option available so QTY A is 6, which is > QTY B
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Re: A steel bar 135 inches long will be cut into a num [#permalink] New post 19 Feb 2018, 06:09
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We can simply form an equation like:
5*x+7*y=135 or, 5*x+7*15=135 or, 5*x=30 or, x=6 [Here, we count for the largest value of 7-inch seg­ments so that we can get the minimum number of 5-inch segments]
So A is the answer.
Re: A steel bar 135 inches long will be cut into a num   [#permalink] 19 Feb 2018, 06:09
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