Last visit was: 15 Aug 2024, 14:38 It is currently 15 Aug 2024, 14:38
Toolkit
GMAT 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

every week, we’ll send you an estimated GMAT 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.

# If a and b are different values and a b = a - b, then in terms of

SORT BY:
Tags:
Show Tags
Hide Tags
Math Expert
Joined: 02 Sep 2009
Posts: 94970
Own Kudos [?]: 649871 [44]
Given Kudos: 86948
SVP
Joined: 27 Dec 2012
Status:The Best Or Nothing
Posts: 1558
Own Kudos [?]: 7327 [19]
Given Kudos: 193
Location: India
Concentration: General Management, Technology
WE:Information Technology (Computer Software)
Tutor
Joined: 16 Oct 2010
Posts: 15220
Own Kudos [?]: 67357 [8]
Given Kudos: 437
Location: Pune, India
General Discussion
Manager
Joined: 05 Jun 2014
Posts: 57
Own Kudos [?]: 82 [5]
Given Kudos: 51
GMAT 1: 630 Q42 V35
Re: If a and b are different values and a b = a - b, then in terms of [#permalink]
3
Kudos
2
Bookmarks
(√a)^2 - (√b)^2 = √a - √b -----> ( √a + √b) ( √a - √b) = √a - √b -------> √a + √b = 1, so

√a = 1 - √b, square both sides and solve. Answer is C.
Intern
Joined: 06 May 2014
Posts: 4
Own Kudos [?]: 8 [3]
Given Kudos: 3
Re: If a and b are different values and a b = a - b, then in terms of [#permalink]
1
Kudos
2
Bookmarks
(√a)^2 - (√b)^2 = √a - √b -----> ( √a + √b) ( √a - √b) = √a - √b -------> √a + √b = 1, so

√a = 1 - √b, square both sides and solve. Answer is C.

Solution-
a-b=√a - √b
=> (√a + √b)(√a- √b)= √a- √b
so, either √a=√b
=> a=b

or, √a+√b=1
=> a=1+b-2√b

In my opinion, As b is not equal to a therefore, C should be answer
Intern
Joined: 03 Dec 2015
Posts: 1
Own Kudos [?]: [0]
Given Kudos: 7
Re: If a and b are different values and a b = a - b, then in terms of [#permalink]
I'm having trouble understanding how the left side of the equation, when squared, isn't (a-b)(a-b)?

Why are we able to rewrite the left side as difference of squares, and how did we get radicals on the left side?
Intern
Joined: 11 Oct 2012
Posts: 29
Own Kudos [?]: 25 [0]
Given Kudos: 74
GMAT 1: 610 Q42 V32
Re: If a and b are different values and a b = a - b, then in terms of [#permalink]
frankkn wrote:
I'm having trouble understanding how the left side of the equation, when squared, isn't (a-b)(a-b)?

Why are we able to rewrite the left side as difference of squares, and how did we get radicals on the left side?

Frankkn,
The left side uses the formula (a+b)(a-b)=a^2-b^2;
so , a - b has been rewritten as (√a+√b)(√a-√b).

Hope that helps !
Board of Directors
Joined: 17 Jul 2014
Posts: 2144
Own Kudos [?]: 1192 [0]
Given Kudos: 236
Location: United States (IL)
Concentration: Finance, Economics
GMAT 1: 650 Q49 V30
GPA: 3.92
WE:General Management (Transportation)
Re: If a and b are different values and a b = a - b, then in terms of [#permalink]
Bunuel wrote:

Tough and Tricky questions: Algebra.

If a and b are different values and a – b = √a - √b, then in terms of b, a equals:

A. √b
B. b
C. b - 2√b + 1
D. b + 2√b + 1
E. b^2 – 2b√b + b

Kudos for a correct solution.

Bunuel - I don't think the question is worded correctly..should the a and b be INTEGERS, then the answer is C, but if not, then C is definitely not the answer.
if a and b are integers, then the difference between their roots is as well an integer.
we then have the first part the difference of 2 squares:
[sqrt(a) - sqrt(b)]*[sqrt(a)+sqrt(b) = sqrt(a) - sqrt(b)
we can conclude that sqrt(a)+sqrt(b) = 1
sqrt(a) = 1 - sqrt(b) - square both sides:
a = 1+b-2*sqrt(b)
or b - 2*sqrt(b) +1

C.

but I see that this works only if both a and b are integers and perfect squares...
anyone to explain why the "integer" part is not that important?
Tutor
Joined: 16 Oct 2010
Posts: 15220
Own Kudos [?]: 67357 [0]
Given Kudos: 437
Location: Pune, India
Re: If a and b are different values and a b = a - b, then in terms of [#permalink]
frankkn wrote:
I'm having trouble understanding how the left side of the equation, when squared, isn't (a-b)(a-b)?

Why are we able to rewrite the left side as difference of squares, and how did we get radicals on the left side?

What is: $$(\sqrt{a} + \sqrt{b}) * (\sqrt{a} - \sqrt{b})$$?

Using the algebraic identity: $$(x + y)*(x - y) = x^2 - y^2$$, we get

$$(\sqrt{a} + \sqrt{b}) * (\sqrt{a} - \sqrt{b}) = (\sqrt{a})^2 - (\sqrt{b})^2$$

$$= a - b$$
Director
Joined: 20 Dec 2015
Status:Learning
Posts: 864
Own Kudos [?]: 573 [1]
Given Kudos: 755
Location: India
Concentration: Operations, Marketing
GMAT 1: 670 Q48 V36
GRE 1: Q157 V157
GPA: 3.4
WE:Engineering (Manufacturing)
Re: If a and b are different values and a b = a - b, then in terms of [#permalink]
IMO C
Indeed it is a simple yet tricky question.
(√a+√b)(√a-√b)=a^2-b^2
(√a+√b)=1
√a=1-√b........(1)
Squaring 1
We have b - 2√b + 1
GMAT Club Legend
Joined: 12 Sep 2015
Posts: 6804
Own Kudos [?]: 31016 [2]
Given Kudos: 799
Re: If a and b are different values and a b = a - b, then in terms of [#permalink]
2
Kudos
Top Contributor
Bunuel wrote:

Tough and Tricky questions: Algebra.

If a and b are different values and a – b = √a - √b, then in terms of b, a equals:

A. √b
B. b
C. b - 2√b + 1
D. b + 2√b + 1
E. b^2 – 2b√b + b

Kudos for a correct solution.

Key concept: $$(x^2 - y^2) = (x + y)(x - y)$$ AKA, factoring a difference of squares

Now all we need to do is recognize that a = (√a)² and b = (√b)²

So, we can now take: a – b = √a - √b
Rewrite the left side as follows: (√a)² – (√b)² = √a - √b
Factor the left side: (√a + √b)(√a - √b) = √a - √b
Divide both sides by (√a - √b) to get: (√a + √b) = 1
Subtract √b from both sides to get: √a = 1 - √b
Square both sides to get: (√a)² = (1 - √b)²
In other words: (√a)² = (1 - √b)(1 - √b)
Expand and simplify both sides: a = 1 - 2√b + b

Intern
Joined: 02 Dec 2019
Posts: 3
Own Kudos [?]: 0 [0]
Given Kudos: 2
Re: If a and b are different values and a b = a - b, then in terms of [#permalink]
How can you divide by (Square root A - Square root B) to get 1 on the right hand side of the equation? I thought that when you divide you always need to know whether its a positive or negative term. We would have no way of knowing whether that term is positive, thus equaling positive 1 on the right hand side of the equation or whether the term is negative, thus equaling negative 1 on the right hand side of the equation???
Intern
Joined: 26 Oct 2018
Posts: 49
Own Kudos [?]: 14 [0]
Given Kudos: 470
GMAT 1: 640 Q40 V37
Re: If a and b are different values and a b = a - b, then in terms of [#permalink]
Bunuel wrote:

Tough and Tricky questions: Algebra.

If a and b are different values and a – b = √a - √b, then in terms of b, a equals:

A. √b
B. b
C. b - 2√b + 1
D. b + 2√b + 1
E. b^2 – 2b√b + b

Kudos for a correct solution.

Here is another method:

We need a in terms of b. The options are in variable b. So what I instinctively want to do is plug in some values to get the answer.
a and b should be distinct.
$$a - b = \sqrt{a} - \sqrt{b}$$

So obviously, 1 comes to mind since $$1 = \sqrt{1}$$. But both a and b cannot be 1 since they must be distinct so I think of another value for which $$a = \sqrt{a}$$ and sure enough, it is 0.

If a = 0 and b = 1, then a – b = √a - √b (condition satisfied)
Put b = 1 in the options. Only options (C) and (E) give 0.

If a = 1 and b = 0, then again a – b = √a - √b (condition satisfied)
Put b = 0 in options (C) and (E); only option (C) gives 1.

—-
I used this method by picking a = 1 and b=0 and got down to two options C and D - but didn’t know how to eliminate further. So I just guessed C but per your method, we should verify the value of not just a (whether that’s equal to 1) but also whether the value of b is 1 when when a=0 right?

Posted from my mobile device
Intern
Joined: 11 Apr 2020
Posts: 13
Own Kudos [?]: 1 [0]
Given Kudos: 59
Schools: HEC MiM "23
Re: If a and b are different values and a b = a - b, then in terms of [#permalink]
Why is B wrong.
When we substitute a=b then we get LHS = RHS
Then why is it still wrong?

Posted from my mobile device
Math Expert
Joined: 02 Sep 2009
Posts: 94970
Own Kudos [?]: 649871 [1]
Given Kudos: 86948
Re: If a and b are different values and a b = a - b, then in terms of [#permalink]
1
Kudos
Vinayak1996 wrote:
Why is B wrong.
When we substitute a=b then we get LHS = RHS
Then why is it still wrong?

Posted from my mobile device

Check the highlighted part in the question stem:
If a and b are different values...
Non-Human User
Joined: 09 Sep 2013
Posts: 34442
Own Kudos [?]: 865 [0]
Given Kudos: 0
Re: If a and b are different values and a b = a - b, then in terms of [#permalink]
Hello from the GMAT Club BumpBot!

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).

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.
Re: If a and b are different values and a b = a - b, then in terms of [#permalink]
Moderator:
Math Expert
94970 posts