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10√10 = a√b Which of the following could be a + b ?
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03 Oct 2020, 12:57

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Question Stats:

\(10\sqrt{10}\)\( = a\sqrt{b}\) Which of the following could be \(a + b\)?

Indicate all the possible values?

A. 45

B. 252

C. 1000

Kuddos to right answers !!

Indicate all the possible values?

A. 45

B. 252

C. 1000

Kuddos to right answers !!

Show: ::

A and B

Retired Moderator

Joined: **10 Apr 2015 **

Posts: **6218**

Given Kudos: **136 **

Re: 10√10 = a√b Which of the following could be a + b ?
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04 Oct 2020, 06:09

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Sunsha wrote:

\(10\sqrt{10}\)\( = a\sqrt{b}\) Which of the following could be \(a + b\)?

Indicate all the possible values?

A. 45

B. 252

C. 1000

Kuddos to right answers !!

Indicate all the possible values?

A. 45

B. 252

C. 1000

Kuddos to right answers !!

Show: ::

A and B

\(10\sqrt{10}=(\sqrt{100})(\sqrt{10})=\sqrt{1000}\)

1000 = (2)(2)(2)(5)(5)(5)

Let's use the above prime factorization to see see how many different perfect squares we can factor out 1000.

For example, 1000 = 4 x 250 (where 4 is a perfect square)

So, \(\sqrt{1000} = \sqrt{4} \times \sqrt{250} = 2\sqrt{250}\)

In this case, \(a = 2\) and \(b = 250\), which means \(a + b = 2 + 250 = 252\)

So, answer choice B works.

Also, 1000 = 25 x 40 (where 25 is a perfect square)

So, \(\sqrt{1000} = \sqrt{25} \times \sqrt{40} = 5\sqrt{40}\)

In this case, \(a = 5\) and \(b = 40\), which means \(a + b = 5 + 40 = 45\)

So, answer choice A works.

What about answer choice C?

The only way to get CLOSE to a sum of 1000, is to factor out a 1 from 1000

In other words, let's examine 1000 = 1 x 1000 (where 1 is a perfect square)

Here, \(\sqrt{1000} = \sqrt{1} \times \sqrt{1000} = 1\sqrt{1000}\)

In this case, \(a = 1\) and \(b = 1000\), which means \(a + b = 1 + 1000 = 1001\)

Close, but no good.

Answer: A, B

Cheers,

Brent

Re: 10√10 = a√b Which of the following could be a + b ?
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04 Oct 2020, 06:30

Thank you Brent ! You have explained it in a very simple way !!

Thanks,

Sunitee

Thanks,

Sunitee

Re: 1010 = ab Which of the following could be a + b ?
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13 Jan 2024, 07:36

Hello from the GRE Prep Club BumpBot!

Thanks to another GRE Prep 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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Thanks to another GRE Prep 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).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.

gmatclubot

Re: 1010 = ab Which of the following could be a + b ? [#permalink]

13 Jan 2024, 07:36
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