Last visit was: 06 Oct 2024, 05:12 It is currently 06 Oct 2024, 05:12

Close

GRE Prep Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GRE score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel
avatar
Intern
Intern
Joined: 19 Aug 2017
Posts: 2
Own Kudos [?]: 2 [2]
Given Kudos: 0
Send PM
Verbal Expert
Joined: 18 Apr 2015
Posts: 29634
Own Kudos [?]: 35532 [0]
Given Kudos: 25775
Send PM
avatar
Intern
Intern
Joined: 11 Aug 2017
Posts: 4
Own Kudos [?]: 2 [0]
Given Kudos: 0
Send PM
avatar
Intern
Intern
Joined: 19 Aug 2017
Posts: 2
Own Kudos [?]: 2 [0]
Given Kudos: 0
Send PM
Re: If a - b = 16 [#permalink]
avdesh0490 wrote:
but for substitution method it should be mentioned that a and b are integers:

Keeping this in mind write all the numbers which sums equal to 8 i.e 1+7,2+6,3+5,4+4
Now look for the difference of squares which is equal to 16 , 25-9 = 16.
Numbers are 25,9 so the ans is 15



I didn't notice this. Can you write down your explanation thoroughly?
avatar
Intern
Intern
Joined: 12 Nov 2018
Posts: 25
Own Kudos [?]: 15 [0]
Given Kudos: 0
Send PM
Re: If a - b = 16 [#permalink]
1
a and b are perfect squares as the addition of their square roots equal to an integer (8). In this case, only a=25 and b=9 match the conditions. So, answer is 15 ( after some calculation, right ?
Verbal Expert
Joined: 18 Apr 2015
Posts: 29634
Own Kudos [?]: 35532 [0]
Given Kudos: 25775
Send PM
Re: If a - b = 16 [#permalink]
Expert Reply
\(\sqrt{a} + \sqrt{b} =8\)

For a under square root and b as well to give 8 a and b must be perfect squares such as \(\sqrt{16} + \sqrt{16} = 4+4=8\)

However, a-b=16 which seems to contradict the statement of before.

BUT this gives us a clue: a and b must be a perfect square. As such, for a-b =16 follow that a must be 25 and b must be 9, which are perfect squares.

\(25 \times 9= 225\) which is a perfect square and is equal to 15

E is the answer
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Own Kudos [?]: 12109 [2]
Given Kudos: 136
Send PM
Re: If a - b = 16 [#permalink]
2
msdjaw wrote:
If \(a - b = 16\) and \(\sqrt{a} + \sqrt{b} = 8\), what is the value of \(\sqrt{ab}\) ?

A. 2

B. 4

C. 8

D. 12

E. 15



GIVEN: √a + √b = 8


GIVEN: a - b = 16
We can think of a - b as a difference of squares, since (√a)² = a, and (√b)² = b

So, take a - b = 16
Rewrite as: (√a + √b)(√a - √b) = 16
Substitute to get: (8)(√a - √b) = 16
Divide both sides by 8 to get: √a - √b = 2

We now have:
√a + √b = 8
√a - √b = 2
ADD the equations to get: 2√a = 10, which means √a = 5

Take:
√a + √b = 8
√a - √b = 2
SUBTRACT the bottom equation from the top equation to get: 2√b = 6, which means √b = 3

So, √(ab) = (√a)(√b) = (5)(3) = 15

Answer: E

Cheers,
Brent
avatar
Intern
Intern
Joined: 30 Oct 2019
Posts: 29
Own Kudos [?]: 31 [0]
Given Kudos: 0
Send PM
Re: If a - b = 16 [#permalink]
1
msdjaw wrote:
If \(a - b = 16\) and \(\sqrt{a} + \sqrt{b} = 8\), what is the value of \(\sqrt{ab}\) ?

A. 2

B. 4

C. 8

D. 12

E. 15

Hello!

I have the answer to this question in my book using other methods. However, whenever I try to solve this question using the substitution method, my solution is not the same as what my book says. Would you please be kind enough to solve this question for me using the SUBSTITUTION method?

I know there are easier methods as well but I need to know what mistake I am making by using the substitution method.





Here is an algebraic solution to the problem.
First of all, we need to simplify the question.
Let's say: The sum of two numbers/integers is equal to 8 and the difference between the square of the two numbers/integers is equal to 16. Find the two numbers/integers and calculate the value of the square root of the product of the two numbers/integers.

Let's \(\sqrt{a}\) be the first number/integer and \(\sqrt{b}\) the second number/integer

\(\sqrt{a}+\sqrt{b}=8\)
\(\sqrt{a}^2-\sqrt{b}^2=16\)
\((\sqrt{a}+\sqrt{b})(\sqrt{a}-\sqrt{b}) =16\)
\(8(\sqrt{a}-\sqrt{b})=16\)
\(\sqrt{a}-\sqrt{b}=2\)

Then solve the two equations
\(\sqrt{a}+\sqrt{b}=8\)
\(\sqrt{a}-\sqrt{b}=2\)
\(2\sqrt{a}=10\)
\(\sqrt{a}=5\)
\(\sqrt{b}=3\)

Thus, \(a=25\)
and \(b=9\)
\(\sqrt{ab}=\sqrt{25*9}\)

The answer is 15.
I hope that the formula will work
User avatar
GRE Prep Club Legend
GRE Prep Club Legend
Joined: 07 Jan 2021
Posts: 4938
Own Kudos [?]: 72 [0]
Given Kudos: 0
Send PM
Re: If a - b = 16 [#permalink]
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).

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.
Prep Club for GRE Bot
Re: If a - b = 16 [#permalink]
Moderators:
GRE Instructor
76 posts
GRE Forum Moderator
37 posts
Moderator
1108 posts
GRE Instructor
222 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne