Is 9,5a8 divisible by 6, where a is some number from the set {0, 1, 2,

Question

Is 9,5a8 divisible by 6, where a is some number from the set {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}?

(1) a is even
(2) a is prime

JerryAtDreamScore · Answer

Breaking Down the Info:

We currently have the sum of digits of 9 + 5 + 8 = 22. Then we need a = {2, 5, 8} for the number to be divisible by 3 and thus 6. Any number outside of this set would make the number not divisible by 6.

Statement 1 Alone:

We may choose a = {0, 2, 4, 6, 8}, which somewhat overlaps the set above, so insufficient.

Statement 2 Alone:

a = {2, 3, 5, 7}, which somewhat overlaps the set above, so insufficient.

Both Statements Combined:

Combining the sets in both statements gives us a = 2. Sufficeint.

Answer: C

AritraKundu · Answer

The number is 95a8
Concept 1: Any number is divisible by 6 if it is divisible by both 2 and 3
Concept 2: Any number with even units digit is divisible by 2
Concept 3: Summation of all digits of the number should be divisible by 3 to make the number divisible by 3

Our number has 8 in units digit which makes the number divisible by 2
Now checking for 3
9+5+a+8=22+a

22+0=22
22+1=23
22+2=24 (divisible by 3)
22+3=25
22+4=26
22+5=27 (divisible by 3)
22+6=28
22+7=29
22+8=30 (divisible by 3)
22+9=31

So, a can be 2, 5, 8

Statement 1: a is even = a can be 0 (then number is not divisible by 3), a can be 2 (the number is divisible by 3), You may test for more but simply its insufficient as we are getting mutiple options

Statement 2: a is prime = a can be 2 (then the number is divisible by 3), a can be 3 (then the number is not divisible by 3) so clearly not sufficient

Both together a is even and prime which makes it 2 an evident answer

Answer C

GMATWhizTeam · Answer

Step 1: Analyse Question Stem

The digit ‘a’ could take any value from the set {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}
We have to find out if the number 95a8 is divisible by 6.

A number is divisible by 6 if it is divisible by both 2 and 3. 
For a number to be divisible by 2, the units digit of the number should be even; for a number to be divisible by 3, the sum of its digits should be divisible by 3.

The units digit of the given number is 8, therefore, it is definitely divisible by 2; therefore, if we have to find if the number is divisible by 6, we have to check if the sum of the digits is divisible by 3.

The sum of the digits of the given number = 9 + 5 + 8 + a = 22 + a. For this to be divisible by 3, a should be 2 or 5 or 8.

Step 2: Analyse Statements Independently (And eliminate options) – AD / BCE

Statement 1:  a is even

If a = 2, then the number is divisible by 3 and hence by 6.
If a = 4, the number is not divisible by 3 and hence not divisible by 6.

The data in statement 1 is insufficient to find out if the number is divisible by 6.
Statement 1 alone is insufficient. Answer options A and D can be eliminated.

Statement 2:  a is prime

If a = 2, then the number is divisible by 3 and hence by 6.
If a = 3, the number is not divisible by 3 and hence not divisible by 6.

The data in statement 2 is insufficient to find out if the number is divisible by 6.
Statement 2 alone is insufficient. Answer option B can be eliminated.

Step 3: Analyse Statements by combining

From statement 1:  a is even 
 From statement 2:  a is prime

Combining both, we can say that a is an even prime i.e. a = 2.

When a = 2, the number is divisible by 3 and hence by 6.

The combination of statements is sufficient to say that the number 95a8 is divisible by 6.
Statements 1 and 2 together are sufficient. Answer option E can be eliminated.

The correct answer option is C.

Is 9,5a8 divisible by 6, where a is some number from the set {0, 1, 2,

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Is 9,5a8 divisible by 6, where a is some number from the set {0, 1, 2,

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