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

 It is currently 13 Oct 2019, 20:43

### 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

# M22-10

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 58335

### Show Tags

16 Sep 2014, 01:16
00:00

Difficulty:

15% (low)

Question Stats:

76% (01:19) correct 24% (01:39) wrong based on 108 sessions

### HideShow timer Statistics

$$@$$ represents the tens digit in integer $$A = 1543@2$$. What is the value of $$@$$ ?

(1) $$A$$ is divisible by 9

(2) $$A$$ is divisible by 4

_________________
Math Expert
Joined: 02 Sep 2009
Posts: 58335

### Show Tags

16 Sep 2014, 01:16
Official Solution:

(1) $$A$$ is divisible by 9. In order an integer to be divisible by 9, the sum of its digit must be divisible by 9. Hence $$1+5+4+3+@+2=15+@$$ must be divisible by 9, and since $$@$$ is a digit then it can only equal to 3. Sufficient.

(2) $$A$$ is divisible by 4. In order an integer to be divisible by 4, its last two digits must be divisible by 4. Hence $$@2$$ must be divisible by 4, which is possible if $$@=1$$, $$@=3$$, $$@=5$$, $$@=7$$, or $$@=9$$. Not sufficient.

_________________
Senior Manager
Joined: 08 Jun 2015
Posts: 420
Location: India
GMAT 1: 640 Q48 V29
GMAT 2: 700 Q48 V38
GPA: 3.33

### Show Tags

05 Jan 2018, 07:18
+1 for A. A number is divisible by 9 if sum of individual digits is divisible by 9. The sum of digits in this case is 15+@.

Statement 1 : The max sum possible is 24. From 15 to 25, only 18 is divisible by 9. Hence we get a unique value for @.
Statement 2 : The number is divisible by 4 if @2 is divisible by 4. @ could be 1,3, or 5. Ie no unique value !!!

Hence the answer is option A.
_________________
" The few , the fearless "
Intern
Joined: 27 Apr 2016
Posts: 18

### Show Tags

10 Jul 2019, 09:03
Bunuel wrote:
Official Solution:

(1) $$A$$ is divisible by 9. In order an integer to be divisible by 9, the sum of its digit must be divisible by 9. Hence $$1+5+4+3+@+2=15+@$$ must be divisible by 9, and since $$@$$ is a digit then it can only equal to 3. Sufficient.

(2) $$A$$ is divisible by 4. In order an integer to be divisible by 4, its last two digits must be divisible by 4. Hence $$@2$$ must be divisible by 4, which is possible if $$@=1$$, $$@=3$$, $$@=5$$, $$@=7$$, or $$@=9$$. Not sufficient.

I really didn't get this. So if A = 1543@2 and the sum of the digit is 15, then can be 0, or 3 (adding to 18), or 6 (adding to 21) or 9 (adding to 24). All these numbers make it divisible by 3 and hence insufficient.
As for statement 2, again the last 2 digits can be either 3 or 9 as 32 and 92 are divisible by 4. Again insufficient.
So shouldn't the answer be E?
Please explain where am I going wrong?
Math Expert
Joined: 02 Sep 2009
Posts: 58335

### Show Tags

10 Jul 2019, 09:16
archimaitreya25 wrote:
Bunuel wrote:
Official Solution:

(1) $$A$$ is divisible by 9. In order an integer to be divisible by 9, the sum of its digit must be divisible by 9. Hence $$1+5+4+3+@+2=15+@$$ must be divisible by 9, and since $$@$$ is a digit then it can only equal to 3. Sufficient.

(2) $$A$$ is divisible by 4. In order an integer to be divisible by 4, its last two digits must be divisible by 4. Hence $$@2$$ must be divisible by 4, which is possible if $$@=1$$, $$@=3$$, $$@=5$$, $$@=7$$, or $$@=9$$. Not sufficient.

I really didn't get this. So if A = 1543@2 and the sum of the digit is 15, then can be 0, or 3 (adding to 18), or 6 (adding to 21) or 9 (adding to 24). All these numbers make it divisible by 3 and hence insufficient.
As for statement 2, again the last 2 digits can be either 3 or 9 as 32 and 92 are divisible by 4. Again insufficient.
So shouldn't the answer be E?
Please explain where am I going wrong?

(1) says that A is divisible by 9, not by 3.
_________________
GMAT Club Legend
Joined: 18 Aug 2017
Posts: 4976
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)

### Show Tags

11 Jul 2019, 10:20
Bunuel wrote:
$$@$$ represents the tens digit in integer $$A = 1543@2$$. What is the value of $$@$$ ?

(1) $$A$$ is divisible by 9

(2) $$A$$ is divisible by 4

#1
Has to be 3 sufficient
#2
can be 1,3, 4, so on insufficient
IMOA
_________________
If you liked my solution then please give Kudos. Kudos encourage active discussions.
Re: M22-10   [#permalink] 11 Jul 2019, 10:20
Display posts from previous: Sort by

# M22-10

Moderators: chetan2u, Bunuel