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# Is the product of two numbers greater than 100?

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Senior RC Moderator
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Is the product of two numbers greater than 100?  [#permalink]

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26 Aug 2017, 11:56
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25% (medium)

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82% (00:43) correct 18% (00:50) wrong based on 31 sessions

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Is the product of two numbers greater than 100?

(1) The sum of the two numbers is greater than 50.
(2) Each of the numbers is greater than 10.

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Re: Is the product of two numbers greater than 100?  [#permalink]

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26 Aug 2017, 12:05
1- Not sufficient. First example-49+2=51, 49*2=98 so prpdict is not greater than 100. Now another example- 48+3=51 but 48*3=154. Hence not sufficient

2-sufficient. Lowest pair of numbers greater than 10 would be 11*11=121, which is greater than 100.

Hence, B - only statement 2 is sufficient

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Is the product of two numbers greater than 100?  [#permalink]

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Updated on: 26 Aug 2017, 12:18
Is the product of two numbers greater than 100?

(1) The sum of the two numbers is greater than 50.
(2) Each of the numbers is greater than 10.

Statement 1: two number can be 50 & 1. the sum is 51 but the product is 50. similarly the two number can be 20 & 40. the sum is 60 and the product is 800. So we get a Yes & No. Hence insufficient

Statement 2: Logically if the two numbers are greater than 10 then their products will be greater than 10. Hence Sufficient

Mathematically, let the numbers be $$a$$ & $$b$$
given that $$a>10$$----(1) &
$$b>10$$------(2)
as both $$a$$ & $$b$$ are positive, we can multiply the inequality without changing the sign. hence multiplying inequality 1 & 2 will give us

$$a*b>10*10$$ or $$ab>100$$ . Hence sufficient.

Option B

Originally posted by niks18 on 26 Aug 2017, 12:07.
Last edited by niks18 on 26 Aug 2017, 12:18, edited 3 times in total.
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Re: Is the product of two numbers greater than 100?  [#permalink]

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26 Aug 2017, 12:13
Anamil wrote:
1- Not sufficient. First example-49+2=51, 49*2=98 so prpdict is not greater than 100. Now another example- 48+3=51 but 48*3=154. Hence not sufficient

2-sufficient. Lowest pair of numbers greater than 10 would be 11*11=121, which is greater than 100.

Hence, B - only statement 2 is sufficient

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Hi Anamil

the highlighted portion is technically not correct. as we are given two numbers are greater than 10 and NOT INTEGERS,
so the two numbers could be 10.0000001 or 10.00000000001
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Re: Is the product of two numbers greater than 100?  [#permalink]

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26 Aug 2017, 12:18
niks18 wrote:
Anamil wrote:
1- Not sufficient. First example-49+2=51, 49*2=98 so prpdict is not greater than 100. Now another example- 48+3=51 but 48*3=154. Hence not sufficient

2-sufficient. Lowest pair of numbers greater than 10 would be 11*11=121, which is greater than 100.

Hence, B - only statement 2 is sufficient

Sent from my ONEPLUS A5000 using GMAT Club Forum mobile app

Hi Anamil

the highlighted portion is technically not correct. as we are given two numbers are greater than 10 and NOT INTEGERS,
so the two numbers could be 10.0000001 or 10.00000000001

Thanks for pointing that out

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Re: Is the product of two numbers greater than 100?   [#permalink] 26 Aug 2017, 12:18
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