If 50,000

Question

If 50,000 < x < 60,000 and x is an integer, what is x?

(1) Every digit of x except its leading digit is the same.

(2) x is divisible by 6.

Kudos for a correct  solution .

DesiGmat · Answer

Here we go----

50,000 < x < 60,000 and x is an integer

St1: Every digit of x except its leading digit is the same.

x could be 51,111; 52,222; 53,333 and so on

Clearly not sufficient

St2: x is divisible by 6.

This can also give multiple values.
So not sufficient.

Combining...

Every digit of x except its leading digit is the same, and x is divisible by 6.
Simple words -> X has to be multiple of 2 and 3

Possible values left

52,222
54,444
56,666
58,888

Only 54,444 is divisible by 6

Option C is correct

peachfuzz · Answer

Statement 1: 
x can equal:
51,111
52,222
53,333
54,444
56,666
57,777
58,888
59,999
insufficient.

Statement 2:
x is divisible by 6. we already know there are multiple solutions. For example, x could be 54,444 or 54,450 as they are both divisible by 6.
insufficient.

Combined, we know that x=54,444.
Answer: C

alonsorondon · Answer

Statement 1:

It could be any option from 5nnnn , 1 <= n <= 9. (51111,52222,53333,..,5nnnn). Multiple answers.  Insufficent.

Statement 2:

Any number in that range divisible by 2 and 3. For example, 51,102 (Last digit pair, and sum of digits = multiple of 3), or 51,105 (Same reasoning). Multiple answers.  Insufficient .

Statement 1 and 2 :

From Stmt 2 we know that it needs to be divisible by 2 and 3. From Stmt 1 we know that all the units after the first one repeat, so the only available option that fits is  54,444.  (Last digit pair, and the sum of its units is 21, which is a multiple of 3)

Answer choice: C

82vkgmat · Answer

Answer = C.
1) Clearly not sufficient. 51111, 52222.... many solutions
2) Also not sufficient... several number divisible by 6.

Combining the two, we can have only 4 possibilities
52222
54444
56666
58888
To be divisible by 6, number should be even and divisible by 3 - which only 58888 is in the above list. 
So answer = C.

peachfuzz · Answer

Note: 58,888 is not divisible by 3 or 6

Posted from my mobile device

82vkgmat · Answer

Aaah I feel stupid. It is 54444 - total = 21 so divisible by 3 and is also even.

Either way answer is still C. Thanks.

Bunuel · Answer

VERITAS PREP OFFICIAL SOLUTION:

From S1, we could have 51,111 or 52,222 or 53,333, etc. INSUFFICIENT

From S2, we could have 50,004 or 50,010, etc. INSUFFICIENT

Combining the statements however, we must have a number that is EVEN and whose digits sum to a multiple of 3. Of the four potential even numbers (52,222, 54,444, 56,666, and 58,888), the only number that divides by 3 is 54,444. Hence the two statements together are SUFFICIENT.

vidyasagar151 · Answer

(1) and (2) alone are insufficient. Now consider both together

From (1), possible values
51,111
52,222
53,333
54,444
56,666
57,777
58,888
59,999

From (2) , we need to consider only even values, as they are divisible by 6.
52,222
54,444
56,666
58,888

6 = 2*3. As we already have values divisible by 2, 
now we need to check from above which values are divisible by 3.
If get only one value which is divisible by 3, then 'C' is the answer.

A value is divisible by 3 only if sum of its digit is divisible by 3.

So 4x+5 should be divisible by 3. (x={2,4,6,8}).
For x=4 it is divisible by 3, and for any other value of x it is not divisible by 3.

So Answer is C

If 50,000 < x < 60,000 and x is an integer, what is x?

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