GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 29 Feb 2020, 02:52

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

D and F represent two distinct digits. If the number 457D89F is divisi

Author Message
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 61537
D and F represent two distinct digits. If the number 457D89F is divisi  [#permalink]

Show Tags

01 Nov 2019, 03:49
1
12
00:00

Difficulty:

75% (hard)

Question Stats:

55% (02:10) correct 45% (02:29) wrong based on 219 sessions

HideShow timer Statistics

D and F represent two distinct digits. If the number 457D89F is divisible by 36, what is the value of (D+F)?

A. 3
B. 6
C. 9
D. 10
E. 12

Are You Up For the Challenge: 700 Level Questions

_________________
Math Expert
Joined: 02 Aug 2009
Posts: 8254
Re: D and F represent two distinct digits. If the number 457D89F is divisi  [#permalink]

Show Tags

01 Nov 2019, 07:37
4
1
Bunuel wrote:
D and F represent two distinct digits. If the number 457D89F is divisible by 36, what is the value of (D+F)?

A. 3
B. 6
C. 9
D. 10
E. 12

Are You Up For the Challenge: 700 Level Questions

$$36=4*9$$

Divisibility rule of 9
The digits add up to a multiple of 9..
So, 4+5+7+D+8+9+F=33+D+F
The immediate multiple above 33 is 36, so D+F=3, or D+F=3+9=12

To check between the two check for --
Divisibility rule of 4
The last two digits should be divisible by 4, so 9F should be divisible by 4...
F can be 2 or 6 as 92 and 96 are divisible by 4

Now D+F=3...F can be 2, so D=1...Possible
D+F=12...F can be 6, so D is 6, but D and F are DISTINCT...NOT Possible

A
_________________
General Discussion
Senior Manager
Joined: 23 Nov 2018
Posts: 253
GMAT 1: 650 Q49 V28
GPA: 4
Re: D and F represent two distinct digits. If the number 457D89F is divisi  [#permalink]

Show Tags

01 Nov 2019, 04:18
3
D and F represent two distinct digits. If the number 457D89F is divisible by 36, what is the value of (D+F)?

36= 9*4 therefore when we add up the digits the number should be divisible by 9

A. 3----33+3=36
B. 6---- 33+6=39
C. 9---33+9=42
D. 10---33+10=43
E. 12---33+12=45

therefore options A and E are divisible by 9

between options A and E 457D89F---must also be divisible by 4

F can take the values- 2, 6

3= 1+2, 3+0--- therefore D=1 and F=2
12= 9+3, 8+4,7+5------ none of these sums contain 2 or 6

option A is the correct option!!
_________________
GMAT Club Legend
Joined: 18 Aug 2017
Posts: 5926
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
Re: D and F represent two distinct digits. If the number 457D89F is divisi  [#permalink]

Show Tags

Updated on: 02 Nov 2019, 01:28
Bunuel wrote:
D and F represent two distinct digits. If the number 457D89F is divisible by 36, what is the value of (D+F)?

A. 3
B. 6
C. 9
D. 10
E. 12

factor of 36 ; 2^2*3^2
so the no has to be even and divisible by 9
457D89F
we can hae 4571892 ; D+F ; 1+2 ; 3
IMO A

Originally posted by Archit3110 on 01 Nov 2019, 03:56.
Last edited by Archit3110 on 02 Nov 2019, 01:28, edited 1 time in total.
Senior Manager
Joined: 21 Jun 2017
Posts: 412
Location: India
Concentration: Finance, Economics
Schools: IIM
GMAT 1: 620 Q47 V30
GPA: 3
WE: Corporate Finance (Commercial Banking)
Re: D and F represent two distinct digits. If the number 457D89F is divisi  [#permalink]

Show Tags

01 Nov 2019, 04:25
Between A and E....since the number has to be divisible by 9 also. E is a contender . Hoewever, per the restrictions of question and considering the fact that last two digits have to be divisible by 4 as well, possible combinations are

90 that means F is 0 and D is 12 but D shd be single digit. Discard
92 Discard, same reasoning as above
96 . Discard as this makes D=F=6

Posted from my mobile device
Manager
Joined: 27 Mar 2016
Posts: 114
GMAT 1: 590 Q44 V22
Re: D and F represent two distinct digits. If the number 457D89F is divisi  [#permalink]

Show Tags

03 Nov 2019, 08:36
To be divisible by 36, it has to be divisible by 9 &4
to be divisible 4, last 2 digits should be divisible 4 which means it can be either 92 or 96. Hence F could be 2 or 6
to be divisible by 9, sum should be divisible 9 i.e 33+D+F should be divisible by 9
if F =2 D=1 F+D =3
if F=6 D=7 F+D =13 (Not an option )
SVP
Joined: 03 Jun 2019
Posts: 2025
Location: India
GMAT 1: 690 Q50 V34
WE: Engineering (Transportation)
Re: D and F represent two distinct digits. If the number 457D89F is divisi  [#permalink]

Show Tags

16 Nov 2019, 06:53
Bunuel wrote:
D and F represent two distinct digits. If the number 457D89F is divisible by 36, what is the value of (D+F)?

A. 3
B. 6
C. 9
D. 10
E. 12

Are You Up For the Challenge: 700 Level Questions

Since 457D89F is divisible by 9
(4+5+7+D+8+9+F) is divisible by 9
D + F + 6 is divisible by 9.
Only A 3 & E 12 satisfy the condition

Since 457D89F is divisible by 4
9F is divisible by 4
F is 2 or 6
If F = 2; D = 1; D+F=3 since D=10 is not possible
If F = 6; D = 6; Not possible since D & F are different digits.

D + F + 3

IMO A
Re: D and F represent two distinct digits. If the number 457D89F is divisi   [#permalink] 16 Nov 2019, 06:53
Display posts from previous: Sort by