GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 21 Oct 2019, 18:38 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 > 12 and b < 7, which of the following must be true?

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

Hide Tags

Math Expert V
Joined: 02 Sep 2009
Posts: 58396
If a > 12 and b < 7, which of the following must be true?  [#permalink]

Show Tags 00:00

Difficulty:   25% (medium)

Question Stats: 72% (01:12) correct 28% (01:36) wrong based on 78 sessions

HideShow timer Statistics

If a > 12 and b < 7, which of the following must be true?

I. a + b > 12
II. a – b > 5
III. a + b < 19

A. I only
B. II only
C. III only
D. I and II only
E. I and III only

_________________
Director  V
Joined: 06 Jan 2015
Posts: 689
Location: India
Concentration: Operations, Finance
GPA: 3.35
WE: Information Technology (Computer Software)
Re: If a > 12 and b < 7, which of the following must be true?  [#permalink]

Show Tags

Bunuel wrote:
If a > 12 and b < 7, which of the following must be true?

I. a + b > 12
II. a – b > 5
III. a + b < 19

A. I only
B. II only
C. III only
D. I and II only
E. I and III only

If a > 12 and b < 7

Consider a=13 & b=-13

Hence a + b > 12 not true

Consider a=20 & b= 6 --> a + b < 19 Not true

Consider a least value be 13 & for b be 6

a – b > 5 True

Hence B
_________________
आत्मनॊ मोक्षार्थम् जगद्धिताय च

Resource: GMATPrep RCs With Solution
Intern  B
Joined: 27 Jan 2019
Posts: 4
GPA: 3.04
Re: If a > 12 and b < 7, which of the following must be true?  [#permalink]

Show Tags

A) If b is negative then a+b is not always greater than 12.
C) If a is big number then a+b is not always less than 19.
B) As a> 12 & b <7 so minimum difference will be 5 even if b is negative, difference wont be below 5.

So, Answer should be B ONLY.
GMAT Club Legend  D
Joined: 18 Aug 2017
Posts: 5027
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
Re: If a > 12 and b < 7, which of the following must be true?  [#permalink]

Show Tags

Bunuel wrote:
If a > 12 and b < 7, which of the following must be true?

I. a + b > 12
II. a – b > 5
III. a + b < 19

A. I only
B. II only
C. III only
D. I and II only
E. I and III only

consider a = 13 and b =6 and -ve values
we can test the cases and find that only a-b>5 is possible
IMO B
Intern  Joined: 07 Feb 2019
Posts: 14
Re: If a > 12 and b < 7, which of the following must be true?  [#permalink]

Show Tags

Here,in the question, answer is must be..but answer B is not must be.B can be answer not must be that wanted in the question .

Posted from my mobile device
Math Expert V
Joined: 02 Sep 2009
Posts: 58396
Re: If a > 12 and b < 7, which of the following must be true?  [#permalink]

Show Tags

Talha95 wrote:
If a > 12 and b < 7, which of the following must be true?

I. a + b > 12
II. a – b > 5
III. a + b < 19

A. I only
B. II only
C. III only
D. I and II only
E. I and III only

Here,in the question, answer is must be..but answer B is not must be.B can be answer not must be that wanted in the question .

Posted from my mobile device

The second option is always true, so it must be true.

Recall that we can subtract inequalities when their signs are in the opposite directions:

If $$a>b$$ and $$c<d$$ (signs in opposite direction: $$>$$ and $$<$$) --> $$a-c>b-d$$ (take the sign of the inequality you subtract from).
Example: $$3<4$$ and $$5>1$$ --> $$3-5<4-1$$.

So, if we subtract b < 7 from a > 12, we get a - b > 5, which is the second

Hope it's clear.

For more check Manipulating Inequalities.
_________________
GMAT Tutor G
Joined: 24 Jun 2008
Posts: 1802
Re: If a > 12 and b < 7, which of the following must be true?  [#permalink]

Show Tags

A different (and equivalent) way to look at the algebra here, if you don't know rules about subtracting inequalities: you can add two inequalities that face in the same direction. So if you just rewrite the second inequality so it is a "greater than", we have:

a > 12
7 > b

and we can now add these:

a + 7 > b + 12
a - b > 5

So II must be true.
_________________
GMAT Tutor in Toronto

If you are looking for online GMAT math tutoring, or if you are interested in buying my advanced Quant books and problem sets, please contact me at ianstewartgmat at gmail.com
VP  V
Joined: 23 Feb 2015
Posts: 1263
If a > 12 and b < 7, which of the following must be true?  [#permalink]

Show Tags

Talha95 wrote:
Here,in the question, answer is must be..but answer B is not must be.B can be answer not must be that wanted in the question .

Posted from my mobile device

b<7
Multiply by( -1 )
-b>-7
Now add this with first one.
a>12
-b>-7
So, a-b>5
So the correct answer must be B.
_________________
“The heights by great men reached and kept were not attained in sudden flight but, they while their companions slept, they were toiling upwards in the night.”

Do you need official questions for Quant?
3700 Unique Official GMAT Quant Questions
------
SEARCH FOR ALL TAGS
GMAT Club Tests If a > 12 and b < 7, which of the following must be true?   [#permalink] 22 Feb 2019, 18:32
Display posts from previous: Sort by

If a > 12 and b < 7, which of the following must be true?

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

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