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# The product of 2 positive integers is 720. If one of the numbers is in

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The product of 2 positive integers is 720. If one of the numbers is in [#permalink]

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Updated on: 04 Dec 2014, 04:18
1
6
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Difficulty:

45% (medium)

Question Stats:

73% (01:58) correct 27% (01:47) wrong based on 125 sessions

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The product of 2 positive integers is 720. If one of the numbers is increased by 10 and the other reduced by 1, the product remains unaltered. What is the value of the smaller of the two integers?

A) 6
B) 7
C) 8
D) 9
E) 10

Originally posted by desaichinmay22 on 04 Dec 2014, 04:05.
Last edited by Bunuel on 04 Dec 2014, 04:18, edited 1 time in total.
Renamed the topic and edited the question.
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Posts: 47037
Re: The product of 2 positive integers is 720. If one of the numbers is in [#permalink]

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04 Dec 2014, 04:27
1
1
desaichinmay22 wrote:
The product of 2 positive integers is 720. If one of the numbers is increased by 10 and the other reduced by 1, the product remains unaltered. What is the value of the smaller of the two integers?

A) 6
B) 7
C) 8
D) 9
E) 10

$$ab = 720$$;
$$(a + 10)(b - 1) = 720$$ --> $$ab +10b - a - 10 = 720$$ --> $$720 + 10b - a - 10 = 720$$ --> $$10b - a - 10 = 0$$.

$$10b - a - 10 = 0$$ --> $$10b - \frac{720}{b} - 10 = 0$$ --> multiply by b: $$10b^2 - 10b - 720 = 0$$ --> $$b^2 - b - 72 = 0$$ --> $$(b + 8)(b - 9) = 0$$ --> $$b = 9$$ (discard negative root since we know that a and b must be positive) --> $$a=80$$ --> smaller number is 9.

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Re: The product of 2 positive integers is 720. If one of the numbers is in [#permalink]

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04 Dec 2014, 05:04
desaichinmay22 wrote:
The product of 2 positive integers is 720. If one of the numbers is increased by 10 and the other reduced by 1, the product remains unaltered. What is the value of the smaller of the two integers?

A) 6
B) 7
C) 8
D) 9
E) 10

let two numbers be x an y
thus, xy=720.------------1)
also, (x+10)(y-1)=720
from 1, we have (x+10)(y-1)=xy
xy-x+10y-10=xy
10y=10+x
or y=1+x/10

now for x=80 y becomes 9. and product becomes 720. thus value of smaller integer =9
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Re: The product of 2 positive integers is 720. If one of the numbers is in [#permalink]

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04 Dec 2014, 19:06
1

Say one of the number = x, other would be $$\frac{720}{x}$$

$$x * \frac{720}{x} = 720$$

x is increased by 10, $$\frac{720}{x}$$ is decreased by 1

Setting up the equation

$$(x+10)(\frac{720}{x} - 1) = 720$$

$$x^2 + 10x - 7200 = 0$$

x = 80

$$Smaller = \frac{720}{80} = 9$$
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Re: The product of 2 positive integers is 720. If one of the numbers is in [#permalink]

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25 Jan 2016, 10:35
1
Hi All,

This question can be solved by TESTing THE ANSWERS.

We're told that the product of 2 positive integers is 720. Next, we're told that If one of the numbers is increased by 10 and the other reduced by 1, the product remains the SAME. We're asked for the value of the smaller of the two integers.

Since the number 7 does NOT divide evenly into 720, Answer B CANNOT be correct. So...

IF....
Smaller number = 9
Larger number = 720/9 = 80

Decreasing the smaller number = 9-1 = 8
Increasing the larger number = 80+10 = 90
(8)(90) = 720
This is an exact MATCH for what we were told, so this MUST be the answer.

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Re: The product of 2 positive integers is 720. If one of the numbers is in [#permalink]

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15 Jan 2018, 05:12
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Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: The product of 2 positive integers is 720. If one of the numbers is in   [#permalink] 15 Jan 2018, 05:12
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