Last visit was: 19 May 2024, 03:44 It is currently 19 May 2024, 03:44
Decision Tracker
My Rewards
Unanswered
Active Topics
New posts
New comers' posts
Close
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
Your Progress

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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

If i and d are integers, what is the value of i? (1) The remainder wh

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 93338
Own Kudos [?]: 624922 [0]
Given Kudos: 81901
Send PM
CAT Tests Forum Quiz Mode
If i and d are integers, what is the value of i? (1) The remainder wh [#permalink] If i and d are integers, what is the value of i? (1) The remainder wh   12 May 2021, 05:30
Expert Reply
00:00
A
B
C
D
E

Difficulty:

65% (hard)

Question Stats:

56% (02:13) correct 44% (02:08) wrong based on 82 sessions
Hide Show timer Statistics
If i and d are integers, what is the value of i?

(1) The remainder when i is divided by (d+2) is the same as when i is divided by d
(2) The quotient when i is divided by (d+2) is d
ShowHide Answer
Official Answer
E
Most Helpful Reply
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 93338
Own Kudos [?]: 624922 [0]
Given Kudos: 81901
Send PM
CAT Tests Forum Quiz Mode
Re: If i and d are integers, what is the value of i? (1) The remainder wh [#permalink] If i and d are integers, what is the value of i? (1) The remainder wh   15 May 2021, 02:45
Expert Reply
Bunuel wrote:
If i and d are integers, what is the value of i?

(1) The remainder when i is divided by (d+2) is the same as when i is divided by d
(2) The quotient when i is divided by (d+2) is d


It can be done algebraically but picking numbers would probably be faster/easier.

If i and d are integers, what is the value of i?

(1) The remainder when i is divided by (d+2) is the same as when i is divided by d --> let the remainder be 0 to simplify the case. So, we have that i is divisible by both d and d+2 --> if d=1 then d+2=3 and i can be ANY multiple of 3. Not sufficient.

(2) The quotient when i is divided by (d+2) is d --> let the remainder be 0 to simplify the case. Now, if d=2 then d+2=4, so i=8 (8/4=2: i=8 divided by d+2=4 yields the quotient of d=2) but if d=3 then d+2=5 and i=15 (15/5=3). Not sufficient.

(1)+(2) Notice that two values of i from (2) works for (1) as well: 8 is divisible d=2 and d+2=4 and 15 is divisible by d=3 and d+2=5.

Answer: E.

Hope it's clear.
General Discussion
User avatar
D
Nidzo
Director
Director
Joined: 26 Nov 2019
Posts: 840
Own Kudos [?]: 846 [0]
Given Kudos: 59
Location: South Africa
Send PM
GMAT ToolKit User
Re: If i and d are integers, what is the value of i? (1) The remainder wh [#permalink] If i and d are integers, what is the value of i? (1) The remainder wh   12 May 2021, 07:02
No values given, so answer will very likely be E.

1.) let d = 2 and i = 5
i/(d+2): 5/4 has a remainder of 1.
i/(d): 5/2 has a remainder of 1.

However, let d = 5 and i = 2
i/(d+2): 2/7 has a remainder of 2
i/(d): 2/5 has a remainder of 2

As we are asked for a specific value INSUFFICIENT

2.) let d = 2 and i = 10
i/(d+2): 10/4 quotient is 2 (d)

let d = 1 and i = 4
i/(d+2): 4/3 quotient is 1 (d)

Multiple possibilities work INSUFFICIENT

Together: Still cannot arrive to a single value for i

ANSWER E
User avatar
L
Kinshook
GMAT Club Legend
GMAT Club Legend
Joined: 03 Jun 2019
Posts: 5350
Own Kudos [?]: 4010 [0]
Given Kudos: 160
Location: India
Schools: HBS '22 CBS '22 Wharton '22
GMAT 1: 690 Q50 V34
WE:Engineering (Transportation)
Send PM
Reviews Badge Forum Quiz Mode
Re: If i and d are integers, what is the value of i? (1) The remainder wh [#permalink] If i and d are integers, what is the value of i? (1) The remainder wh   15 May 2021, 04:16
Asked: If i and d are integers, what is the value of i?

(1) The remainder when i is divided by (d+2) is the same as when i is divided by d
(d+2) m + r = d * n + r = i where m & n are integers
(d+2)m = dn
There are too many unknowns to determine value of i.
NOT SUFFICIENT

(2) The quotient when i is divided by (d+2) is d
d ( d+2) + r = i
where r < d
The equation does not give enough information to find out value of i uniquely
Let us take d = 2; d ( d+2) = 6 = i-r ;
r = {0,1}
Therefore i={5,6}
But if we take d = 3; d(d+2) = 12 = i-r
r = {0,1,2}
I= {12.11.10}
NOT SUFFICIENT

(1) + (2)
(1) The remainder when i is divided by (d+2) is the same as when i is divided by d
(d+2) m + r = d * n + r = i where m & n are integers
(d+2)m = dn
(2) The quotient when i is divided by (d+2) is d
d ( d+2) + r = i
d(d+2) = (d+2)m = dn = i - r
m = d
n = d+2
The equations combined do not give enough information to find out value of i uniquely
Let us take d = 2; d ( d+2) = 6 = i-r ;
r = {0,1}
Therefore i={5,6}
But if we take d = 3; d(d+2) = 12 = i-r
r = {0,1,2}
I= {12.11.10}
NOT SUFFICIENT

IMO E
avatar
B
Thekingmaker
Manager
Manager
Joined: 28 Nov 2020
Posts: 118
Own Kudos [?]: 25 [0]
Given Kudos: 96
Send PM
Re: If i and d are integers, what is the value of i? (1) The remainder wh [#permalink] If i and d are integers, what is the value of i? (1) The remainder wh   31 May 2021, 22:30
all the statements individually would provide 1, 3 and 2,4 as possiblities (maybe even an infinite number of other possiblities too ) even they are combined these possiblities aren't eliminated hence the answer IMO E
GMAT Club Bot
gmatclubot
Re: If i and d are integers, what is the value of i? (1) The remainder wh [#permalink]
31 May 2021, 22:30
Moderator:
Bunuel
Math Expert
93338 posts