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Prop Of Numbers

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Prop Of Numbers

by heshamelaziry » Thu Nov 05, 2009 9:54 am

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If * represents a digit in the 7-digit number 3, 62*, 215, what is the value of *?

(1) The sum of the 7 digits is equal to 4 times an integer.
(2) The missing digit is different from any of the other digits in the number

OA C
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by NikolayZ » Thu Nov 05, 2009 10:01 am

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Hey again mate.

We have 362X215
1)3+6+2+X+2+1+5=4y insufficient, as x can be anything, so y can be anything.
2)if x differs from any of digits then it may be - 4,7,8,9, insufficient.

1+2)
19+x=4y,
plug in all 4 numbers from the stmt 2. The right X is X, when added to 19, will be divisible by 4.
Try to solve it, *=9.
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by chipbmk » Thu Nov 05, 2009 10:49 am

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NikolayZ wrote:Hey again mate.

We have 362X215
1)3+6+2+X+2+1+5=4y insufficient, as x can be anything, so y can be anything.
2)if x differs from any of digits then it may be - 4,7,8,9, insufficient.

1+2)
19+x=4y,
plug in all 4 numbers from the stmt 2. The right X is X, when added to 19, will be divisible by 4.
Try to solve it, *=9.
I agree with everything Nikolay said, the only thing I would add to make it slightly more clear is this.

When looking at statement 1 consider all of the possibilities 1-9, you will find that 19+x=4(y) can only work with the numbers 1,5,9.

So when combining statements 1&2, you know the answer needs to be found in both statements. 9 is the only number that works for both statements. (1,5,9 and 4,7,8,9)
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by Stuart@KaplanGMAT » Thu Nov 05, 2009 10:52 am

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NikolayZ wrote:Hey again mate.

We have 362X215
1)3+6+2+X+2+1+5=4y insufficient, as x can be anything, so y can be anything.
2)if x differs from any of digits then it may be - 4,7,8,9, insufficient.

1+2)
19+x=4y,
plug in all 4 numbers from the stmt 2. The right X is X, when added to 19, will be divisible by 4.
Try to solve it, *=9.
Just a point on statement (1) - x can't be anything, we can actually narrow it down to 3 possibilities.

19 + x must be a multiple of 4 and x is a digit from 0 to 9. So, 19 + x could be 20, 24 or 28, giving us possible x values of 1, 5 and 9.

Now, we didn't actually need to calculate that if we understood that since x varies between 0 and 9, there will be at least two values within that range that give us a multiple of 4 (if you have 4 consecutive integers, you have 1 multiple of 4; 8 consecutive integers guarantees 2 multiples of 4; we have 10 consecutive integers, so there will be either 2 or 3 multiples of 4 in the set).
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Re: Prop Of Numbers

by Brent@GMATPrepNow » Tue Mar 22, 2022 9:03 am

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heshamelaziry wrote: ↑
Thu Nov 05, 2009 9:54 am
 If * represents a digit in the 7-digit number 3, 62*, 215, what is the value of *?

(1) The sum of the 7 digits is equal to 4 times an integer.
(2) The missing digit is different from any of the other digits in the number

OA C
Given: * represents a digit in the 7-digit number 3,62$,215

Target question: What is the value of *?

Statement 1: The sum of the 7 digits is equal to 4 times an integer.
In other words, the sum is a multiple of 4.
We have: 3 + 6 + 2 + * + 2 + 1 + 5 = 19 + *
19 + * will be a multiple of 4 when * = 1, 5 or 9
Since we can’t answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: The missing digit is different from any of the other digits in the number
In other words, * cannot equal 3, 6, 2, 1 or 5, which means * COULD equal 0, 4, 7, 8, or 9
Since we can’t answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 tells us that * could equal 1, 5 or 9
Statement 2 tells us that * could equal 0, 4, 7, 8, or 9
The only value that satisfies both statements is * = 9
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer: C

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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