if b < 1 and 2x - b = 0 - The Beat The GMAT Forum - Expert GMAT Help & MBA Admissions Advice

if b < 1 and 2x - b = 0

Expert replies

Previous Topic Next Topic

redng: Junior | Next Rank: 30 Posts; Posts: 10; Joined: Mon Mar 12, 2012 7:08 pmFollowed by: 1 member

by redng » Wed May 02, 2012 3:20 pm

If b<1 and 2x-b=0, which of the following must be true?

A. x > -1
B. x < -2
C. x = 2
D. x < 3
E. x > 3

OA: D

source: Kaplan GMAT Diagnostic Quiz

I though it was B, can someone explain? thanks

Like this post

Source: Beat The GMAT — Problem Solving | Wed May 02, 2012 3:20 pm

karthikchandru: Junior | Next Rank: 30 Posts; Posts: 17; Joined: Wed Feb 22, 2012 6:31 pm; Thanked: 3 times

by karthikchandru » Wed May 02, 2012 7:25 pm

It pretty much boils down to x<1/2 because b<1 and b=2x.
Now, answer choice B says that x<-2. However, x can be -1 in which case this statement doesn't hold true. But, with answer choice D: x<3, if x=-1 it would still hold true. Moreover, x cannot be, say, 1 because it is given that x<1/2.
Hope this helps.

Like this post

Stuart@KaplanGMAT: GMAT Instructor; Posts: 3225; Joined: Tue Jan 08, 2008 2:40 pmFollowed by: 614 members; Location: Toronto; Thanked: 1710 times; GMAT Score:800

by Stuart@KaplanGMAT » Wed May 02, 2012 11:31 pm

redng wrote:If b<1 and 2x-b=0, which of the following must be true?
A. x > -1
B. x < -2
C. x = 2
D. x < 3
E. x > 3
OA: D

source: Kaplan GMAT Diagnostic Quiz

I though it was B, can someone explain? thanks

Hi! Like many GMAT questions, we should start by simplifying the question itself.

We know that b < 1 and that 2x-b=0. We can rewrite the equation as:

2x = b

Putting the two statements together:

2x = b < 1
2x < 1
x < 1/2

Now we need to find the answer that MUST be true, given that x < 1/2.

A) x > -1. Nope! If x = -100, then x < 1/2 and (A) is false.
B) x < -2. Nope! If x = 0 then x < 1/2 and (B) is false.
C) x = 2. Nope, if x < 1/2 it can't be equal to 2.
D) x < 3. YES! If x is less than a number smaller than 3, it's always going to be less than 3 as well. Choose (D)!

Stuart Kovinsky | Kaplan GMAT Faculty | Toronto

Kaplan Exclusive: The Official Test Day Experience | Ready to Take a Free Practice Test? | Kaplan/Beat the GMAT Member Discount
BTG100 for $100 off a full course

Like this post

aneesh.kg: Master | Next Rank: 500 Posts; Posts: 385; Joined: Mon Apr 16, 2012 8:40 amFollowed by: 29 members; Location: Pune, India; Thanked: 186 times

by aneesh.kg » Wed May 02, 2012 11:47 pm

Let's solve it using Co-ordinate Geometry.
We'll draw b and x axes.

Figure below shows the b < 1 region.

Drawing the line b = 2x.

Mark the point of intersection as shown below.

In the figure shown: if x < 0.5, x will surely be smaller than 3 in our favourable part of the line (shown in purple). None of the other options are a certainty.

Option [spoiler](D) [/spoiler]is true.

See another problem solved easily with the help of Co-ordinate Geometry:
https://www.beatthegmat.com/if-y-0-is-y- ... tml#469314

Aneesh Bangia
GMAT Math Coach
[email protected]

GMATPad:
Facebook Page: https://www.facebook.com/GMATPad

Like this post

Jeff@TargetTestPrep: GMAT Instructor; Posts: 1462; Joined: Thu Apr 09, 2015 9:34 amFollowed by: 22 members; Location: New York, NY; Thanked: 39 times

hi

by Jeff@TargetTestPrep » Mon Feb 26, 2018 10:26 am

redng wrote:If b<1 and 2x-b=0, which of the following must be true?
A. x > -1
B. x < -2
C. x = 2
D. x < 3
E. x > 3

Manipulating the equation we have 2x = b, thus:

2x < 1

x < 1/2

Thus, x must be less than 3.

Note that the correct answer x < 3 may be confusing. Here's the logic: we determined algebraically that x must be less than 1/2. Thus, some possible values for x are 1/4 , 0, -2/3, -5, and so on. Note that each of these values is, indeed, less than 3 (which is answer choice D). In fact, any value of x that satisfies x < 1/2 will ALSO satisfy x < 3. Hence, answer choice D is correct.

Answer: D

Jeffrey Miller
Head of GMAT Instruction
[email protected]

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

Like this post

deloitte247: Legendary Member; Posts: 2214; Joined: Fri Mar 02, 2018 2:22 pmFollowed by: 5 members

TTT

by deloitte247 » Sat Mar 03, 2018 1:26 pm

If 2x-b=0
b=2x
Also , b<1
or 2x<1
Divide through by 2
we obtain x< 1/2...
The answer is x< 1/2...
Based on my understanding, i am convince that none of these options given are right<i class="em em-scream"></i><i class="em em-confused"></i>

Like this post

GMAT/MBA Expert

[email protected]: Elite Legendary Member; Posts: 10392; Joined: Sun Jun 23, 2013 6:38 pmFollowed by: 511 members; Location: Palo Alto, CA; Thanked: 2867 times; GMAT Score:800

by [email protected] » Sun Mar 04, 2018 4:16 pm

Hi redng,

We're told that B < 1 and 2(X) - B = 0. We're asked which of the following MUST be true (which really means "which of the following is ALWAYS true no matter how many different examples we come up with)." We can answer this question by TESTing VALUES.

Since B < 1, let's start with B = 0....
IF... B=0, then 2X - 0 = 0 means that X = 0
Eliminate Answers B, C and E.

Next, let's look for something NEGATIVE....
IF... B = -2, then 2X - (-2) = 0 means that 2X + 2 = 0 and X = -1
Eliminate Answers A

Final Answer: D

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

Like this post

Post new topic Post Reply

• Page 1 of 1

GMAT Course Reviews

559 reviews

1168 reviews

431 reviews

359 reviews

147 reviews

5/5

5 Star (560 Reviews)

"Target Test Prep is the closest to the official version of the GMAT exam, about 99% accuracy in terms of the quality and quantity of information. The course has excellently created singular sets of focused lessons and tests for every possible topic that one could come across in the official GMAT exam."

"The TTP course maximizes the efficiency of the time you spend studying. It will take time and effort but I could almost guarantee that if you complete the course exactly as it is laid out you will get an amazing score. They also have a very responsive team willing to help with any questions you might have."

"TTP has two things that I think no other test prep company offers: A teaching approach that reinforces understanding and an attitude that will give you the mental preparedness needed to succeed on the test. TTP gives you a deep understanding of the concept you need to know while teaching you how to think."

Write a Review