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

 It is currently 20 Nov 2019, 15:34 ### 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 > b and c < d , which of the following MUST be true?

Author Message
TAGS:

### Hide Tags

Math Expert V
Joined: 02 Sep 2009
Posts: 59182
If a > b and c < d , which of the following MUST be true?  [#permalink]

### Show Tags

1
3 00:00

Difficulty:   55% (hard)

Question Stats: 55% (01:35) correct 45% (01:30) wrong based on 75 sessions

### HideShow timer Statistics

Competition Mode Question

If $$a>b$$ and $$c<d$$, which of the following MUST be true?

A. $$a−d>c−b$$
B. $$a+d>b$$
C. $$b+c>a−d$$
D. $$b−d<a−c$$
E. $$a^2+d^2>b^2+c^2$$

_________________
Senior Manager  P
Joined: 31 May 2018
Posts: 451
Location: United States
Concentration: Finance, Marketing
Re: If a > b and c < d , which of the following MUST be true?  [#permalink]

### Show Tags

1
given a > b and c < d

a-b > 0 and c-d < 0
from here we know that
a-b > c-d

a-c > b-d

b-d < a-c

Manager  S
Joined: 14 May 2018
Posts: 96
Re: If a > b and c < d , which of the following MUST be true?  [#permalink]

### Show Tags

1
Ans: D
Because, a>b , c<d. In inequalities, opposite signs can be subtracted. Or, c<d --> -c>-d . On adding a>b
+ (-c>-d)
= a-c>b-d
only d gives this answer choice
Senior Manager  P
Joined: 18 May 2019
Posts: 463
Re: If a > b and c < d , which of the following MUST be true?  [#permalink]

### Show Tags

We are given a>b and c<d, we are to determine which of the answer choices must be true.
D is the answer. This is because a>b and c<d, hence b-d will always be less than a-c. We are subtracting a smaller number, c, from a, where a>b and subtracting a bigger number, d, where d>c from b. Definitely, a-c will always be greater than b-d.

In A, a-d>c-b, is not always true. when a=5, b=4, c=1, d=7, a-d(-2)>c-b(-3)
however if a=5, b=4, c=6, and d=7; a-d(-2)<c-b(3).

Similarly, in B, a+d>b is not always true. This is because, we don't know whether a,b, and d are greater than zero or otherwise. when a,b, and d are all greater than 0, then a+d>b. However, if a and b are positive and d is negative, it is possible than a+d<b. Hence B is not always true.

C b+c>a-d. This is also not always true. Depending on the magnitudes of a,b,c, and d, b+c>a-d. in other instances, b+c<a-d. To illustrate, let a=5, b=4, c=6 and d=7 then b+c(10)>a-d(-2). However, if a=5, b=4, c=-6 and d=-1, then b+c(-2)<a-d(6)

E a^2 + d^2 > b^2 + c^2. This is not always true. It is true for a,b,c, and d greater than zero. However, if a,b,c, and d are all negative, then it is not true.
SVP  P
Joined: 03 Jun 2019
Posts: 1853
Location: India
Re: If a > b and c < d , which of the following MUST be true?  [#permalink]

### Show Tags

1
If a>b and c<d, which of the following MUST be true?

A. a−d>c−b
B. a+d>b
C. b+c>a−d
D. b−d<a−c
E. $$a^2+d^2>b^2+c^2$$

a>b
d>c
a+d>b+c
b-d<a-c

IMO D
_________________
"Success is not final; failure is not fatal: It is the courage to continue that counts."

Please provide kudos if you like my post. Kudos encourage active discussions.

My GMAT Resources: -

Efficient Learning
All you need to know about GMAT quant

Tele: +91-11-40396815
Mobile : +91-9910661622
E-mail : kinshook.chaturvedi@gmail.com
Senior Manager  P
Joined: 07 Mar 2019
Posts: 386
Location: India
GMAT 1: 580 Q43 V27 WE: Sales (Energy and Utilities)
Re: If a > b and c < d , which of the following MUST be true?  [#permalink]

### Show Tags

If a > b and c < d, which of the following MUST be true?

A. a−d > c−b
B. a+d > b
C. b+c > a−d
D. b−d < a−c
E. $$a^2 + d^2 > b^2 + c^2$$

Following cases are possible:

1. b < a < c < d
2. c < d < b < a
3. b < a = c < d
4. c < d = b < a
5. b < c < a = d
6. c < b < a = d
7. b = c < a < d
8. b = c < d < a

Attachment:
File comment: abcd abcd.JPG [ 30.76 KiB | Viewed 820 times ]

Only case 1 and 2 are sufficient.

_________________
Ephemeral Epiphany..!

GMATPREP1 590(Q48,V23) March 6, 2019
GMATPREP2 610(Q44,V29) June 10, 2019
GMATPREPSoft1 680(Q48,V35) June 26, 2019
Director  P
Joined: 24 Nov 2016
Posts: 809
Location: United States
Re: If a > b and c < d , which of the following MUST be true?  [#permalink]

### Show Tags

Quote:
If a>b and c<d, which of the following MUST be true?

A. a−d>c−b
B. a+d>b
C. b+c>a−d
D. b−d<a−c
E. $$a^2+d^2>b^2+c^2$$

given: a>b and c<d have different signs, we can subtract them, maintaining the former sign.
a>b-(c<d)=a-c>b-d…b-d<a-c

Manager  S
Joined: 24 Sep 2014
Posts: 51
Concentration: General Management, Technology
Re: If a > b and c < d , which of the following MUST be true?  [#permalink]

### Show Tags

If a>b and c<d, which of the following MUST be true?
a>b --> a-b>0 -- (1)
c<d --> d>c --> d-c>0 --(2)
add (1) + (2) (now, we can add because both (1) & (2) have > 0 on rhs)
(a-b)+(d-c)>0
(a+d)-(b+c)>0
(a+d)>(b+c) --(3)

A. a−d>c−b
Incorrect, after rearranging, we can't get (3)
B. a+d>b
Incorrect, we can't get (3)
C. b+c>a−d
Incorrect, we can't get (3) after rearranging
D. b−d<a−c
Correct, after rearranging, (b+c)<(a+d) --> (a+d)>(b+c) which is (3)
E. (a^2 +d^2) >(b^2 +c^2)
Incorrect, we can't get (3) after rearranging
Manager  G
Joined: 17 Jul 2014
Posts: 173
Re: If a > b and c < d , which of the following MUST be true?  [#permalink]

### Show Tags

If a>b and c<d , which of the following MUST be true?

A. a−d>c−b
B. a+d>b
C. b+c>a−d
D. b−d<a−c
E. $$a^2$$+$$d^2$$>$$b^2$$+$$c^2$$

Eq1 : a > b
Eq2 : c<d ...Multiply both sides by -1, -c > -d
Add 1 & 2 - a-c > b-d

Scan the answer choices that match above expression

D it is.
SC Moderator P
Status: GMAT - Pulling Quant and Verbal together
Joined: 04 Sep 2017
Posts: 240
Location: United States (OH)
GPA: 3.6
WE: Sales (Computer Software)
If a > b and c < d , which of the following MUST be true?  [#permalink]

### Show Tags

Bunuel wrote:

Competition Mode Question

If $$a>b$$ and $$c<d$$, which of the following MUST be true?

A. $$a−d>c−b$$
B. $$a+d>b$$
C. $$b+c>a−d$$
D. $$b−d<a−c$$
E. $$a^2+d^2>b^2+c^2$$

Nice question. Manipulate the answer choices to just be addition on both sides.

A) $$a−d>c−b$$ -------> a+b>c+d Clearly not necessarily true.

B) $$a+d>b$$ What if d is a high magnitude negative number?
Example:
a=1
b=0
d=-100
c=-101

1-100>0.... Not true

C) $$b+c>a−d$$ --------> b+c+d>a Clearly not necessarily true. Make a = a huge number

D) $$b−d<a−c$$ --------> b+c<a+d True. Both sides are pure addition and the larger numbers are on the same side.

E) $$a^2+d^2>b^2+c^2$$ Trap Answer. What if our small numbers are high magnitude negative numbers?
Example:
a=0
b=-10
d=0
c=-10

0+0>100+100

_________________
Would I rather be feared or loved? Easy. Both. I want people to be afraid of how much they love me.

How to sort questions by Topic, Difficulty, and Source:
https://gmatclub.com/forum/search.php?view=search_tags If a > b and c < d , which of the following MUST be true?   [#permalink] 02 Nov 2019, 14:17
Display posts from previous: Sort by

# If a > b and c < d , which of the following MUST be true?  