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

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If 50,000 < x < 60,000 and x is an integer, what is x?  [#permalink]

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New post 28 Jan 2015, 07:01
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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.

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Re: If 50,000 < x < 60,000 and x is an integer, what is x?  [#permalink]

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New post 28 Jan 2015, 07:49
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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
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Re: If 50,000 < x < 60,000 and x is an integer, what is x?  [#permalink]

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New post 28 Jan 2015, 18:03
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Bunuel wrote:
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.



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
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Re: If 50,000 < x < 60,000 and x is an integer, what is x?  [#permalink]

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New post 28 Jan 2015, 18:23
2
Bunuel wrote:
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.


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
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Re: If 50,000 < x < 60,000 and x is an integer, what is x?  [#permalink]

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New post 28 Jan 2015, 21:17
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Bunuel wrote:
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.


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.
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Re: If 50,000 < x < 60,000 and x is an integer, what is x?  [#permalink]

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New post 28 Jan 2015, 21:36
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Note: 58,888 is not divisible by 3 or 6

Posted from my mobile device
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Re: If 50,000 < x < 60,000 and x is an integer, what is x?  [#permalink]

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New post 28 Jan 2015, 21:57
peachfuzz wrote:
Note: 58,888 is not divisible by 3 or 6

Posted from my mobile device


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

Either way answer is still C. Thanks.
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Re: If 50,000 < x < 60,000 and x is an integer, what is x?  [#permalink]

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New post 02 Feb 2015, 02:37
Bunuel wrote:
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.


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.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
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Re: If 50,000 < x < 60,000 and x is an integer, what is x?  [#permalink]

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