BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

Inequalities

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Moderator
Posts: 772
Joined: Wed Aug 30, 2017 6:29 pm
Followed by:6 members

Inequalities

by BTGmoderatorRO » Sat Oct 28, 2017 2:45 am
If a is less than b, which of the following numbers is greater than a and less than b ?

(A) (a + b)/2
(B) ab/2
(C) b^2 - a^2
(D) ab
(E) b - a

which of the above options is the correct answer based on your calculation?
i don't seem to get any right :oops:
Top
Source: — Problem Solving |
User avatar
GMAT Instructor
Posts: 15539
Joined: Tue May 25, 2010 12:04 pm
Location: New York, NY
Thanked: 13060 times
Followed by:1906 members
GMAT Score:790

by GMATGuruNY » Sat Oct 28, 2017 3:18 am
The question stem should read as follows:
If a is less than b, which of the following expressions MUST BE greater than a but less than b?

(A) (a + b)/2
(B) ab/2
(C) b^2 - a^2
(D) ab
(E) b - a
Test a=0 and b=1 in the answer choices:

(A) (a + b)/2 --> (0+1)/2 = 1/2.
(B) ab/2 --> (0*1)/2 = 0.
(C) b² - a² --> 1² - 0² = 1.
(D) ab --> 0*1 = 0.
(E) b - a --> 1-0 = 1.

Eliminate B, C, D and E, which do not yield values between a=0 and b=1,

The correct answer is A.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Top
User avatar
GMAT Instructor
Posts: 555
Joined: Wed Oct 04, 2017 4:18 pm
Thanked: 180 times
Followed by:12 members

by EconomistGMATTutor » Sat Oct 28, 2017 3:24 am
Hello Roland. I hope you're well.

You can pick two numbers and try option by option. Let's take a=1 and b=2. Now,

$$Option\ E:\ b-a=2-1=1,$$ this is not greater than a. INCORRECT.

$$Option\ D:\ ab=1\cdot2=2,$$ this is not less than b. INCORRECT.

$$Option\ C:\ b^2-a^2=2^2-1^2=4-1=3,$$ this is not less than b. INCORRECT.

$$Option\ B:\ ab/2=1\cdot2/2=1,$$ this is not greater than a. INCORRECT.

$$Option\ A:\ (a+b)/2=(1+2)/2=3/2=1,5,$$ this is greater than a and less than b. CORRECT.

So, the correct option is A.

I hope this can help you.

I'm available if you'd like any follow up.

Regards.
GMAT Prep From The Economist
We offer 70+ point score improvement money back guarantee.
Our average student improves 98 points.

Image
Top

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 8086
Joined: Sat Apr 25, 2015 10:56 am
Location: Los Angeles, CA
Thanked: 43 times
Followed by:29 members

by Scott@TargetTestPrep » Tue Nov 12, 2019 7:19 pm
BTGmoderatorRO wrote:If a is less than b, which of the following numbers is greater than a and less than b ?

(A) (a + b)/2
(B) ab/2
(C) b^2 - a^2
(D) ab
(E) b - a

which of the above options is the correct answer based on your calculation?
i don't seem to get any right :oops:
Let's let a = 3 and b = 4 and test each answer choice:

A) (a + b)/2 = (3 + 4)/2 = 3.5

We see that (a + b)/2 is greater than a and less than b.

We could stop here, but let's double-check the remaining answer choices.

B) ab/2 = 3(4)/2 = 6

We see that ab/2 is greater than b.

C) b^2 - a^2 = 16 - 9 = 7

We see that b^2 - a^2 is greater than b.

D) ab = 3(4) = 12

We see that ab is greater than b.

E) b - a = 4 - 3 = 1

We see that b - a is less than a.

The only answer choice that produced a value between a and b is A.

Alternate solution:

We are looking for a number that is between the two numbers a and b. We see that (a + b)/2 is the average of the two numbers and the average of any two numbers is always between the two numbers.

Answer: A

Scott Woodbury-Stewart
Founder and CEO
[email protected]

Image

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

ImageImage
Top

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 16207
Joined: Mon Dec 08, 2008 6:26 pm
Location: Vancouver, BC
Thanked: 5254 times
Followed by:1268 members
GMAT Score:770

by Brent@GMATPrepNow » Wed Nov 13, 2019 7:01 am
BTGmoderatorRO wrote:If a is less than b, which of the following numbers is greater than a and less than b ?

(A) (a + b)/2
(B) ab/2
(C) b^2 - a^2
(D) ab
(E) b - a
If a and b are DIFFERENT numbers, then the average of a and b will always be BETWEEN a and b
Since we're told a < b, we know a and b are DIFFERENT.
So, their average, (a +b)/2 must be BETWEEN a and b

Answer: A

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
Image
Top
Post new topic Post Reply
• Page 1 of 1