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

 It is currently 19 Jun 2018, 12:57

### 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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# If for integers a, b, c, and d, a + b + c + d = 4, does d = 1?

Author Message
TAGS:

### Hide Tags

Intern
Joined: 24 Feb 2016
Posts: 27
Location: India
Schools: LBS (A)
GMAT 1: 650 Q45 V34
GPA: 4
If for integers a, b, c, and d, a + b + c + d = 4, does d = 1? [#permalink]

### Show Tags

Updated on: 21 Oct 2017, 01:02
00:00

Difficulty:

85% (hard)

Question Stats:

35% (00:40) correct 65% (01:06) wrong based on 37 sessions

### HideShow timer Statistics

If for integers a, b, c, and d, a + b + c + d = 4, does d = 1?

(1) abc = 1

Originally posted by arabella on 21 Oct 2017, 00:53.
Last edited by Bunuel on 21 Oct 2017, 01:02, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
PS Forum Moderator
Joined: 25 Feb 2013
Posts: 1142
Location: India
GPA: 3.82
If for integers a, b, c, and d, a + b + c + d = 4, does d = 1? [#permalink]

### Show Tags

Updated on: 21 Oct 2017, 01:26
1
arabella wrote:
If for integers a, b, c, and d, a + b + c + d = 4, does d = 1?

(1) abc = 1

$$d= 4-(a+b+c)$$

Statement 1: as all are integers so this implies that $$|a|=|b|=|c|=1$$

now if all are positive then $$d=4-(1+1+1)=1$$

but if any two are negative and the 3rd is positive then $$d=4-(1-1-1)=5$$. Hence insufficient

Statement 2: this implies that $$|a|=|d|=1$$. but $$d$$ can be positive or negative. hence no unique value. Insufficient

Combining 1 & 2, if $$a=1$$, then $$d=1$$

but if $$a=-1$$, then either $$b$$ or $$c$$ is $$-1$$ and the remaining is $$1$$ for Statement 1 to hold true

so $$d=4-(-1-1+1)=5$$

but from statement 2, if $$a=-1$$ then $$d=-1$$. so this implies that $$a$$ is not equal to $$-1$$. Hence $$a=d=1$$ Sufficient

Option C

Originally posted by niks18 on 21 Oct 2017, 01:08.
Last edited by niks18 on 21 Oct 2017, 01:26, edited 3 times in total.
Intern
Joined: 20 Aug 2016
Posts: 23
GMAT 1: 570 Q46 V23
WE: Information Technology (Other)
Re: If for integers a, b, c, and d, a + b + c + d = 4, does d = 1? [#permalink]

### Show Tags

21 Oct 2017, 01:12
1
statement 1

abc =1
=>either of 2 variables are negative and = -1,

Then for a+b+c+d = 4

-2+1+d = 4
=> d = 5

or all of them are 1 (As they can't be fractions -> mentioned Integers)
=> 3+d= 4
=>d = 1

We have 2 sol. d can be 1 or 5
_____________________________________________________

statement 2

=> a, d = 1 or a, d = -1

We have 2 sol, d can be 1 or -1
_________________________________

Combining both eq.
we have d =1

Answer is C: Both statement sufficient.
Re: If for integers a, b, c, and d, a + b + c + d = 4, does d = 1?   [#permalink] 21 Oct 2017, 01:12
Display posts from previous: Sort by

# If for integers a, b, c, and d, a + b + c + d = 4, does d = 1?

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.