Data Sufficiency

In the decimal representation of x, where 0< x< 1, is the tenths digit of x nonzero?
1) 16x is an integer
2) 8x is an integer

The right answer is B

Can anybody help solve this? What is 10ths digit in decimal representation?

e.g. in 0.502, 0 is in tenth's digit place?

There is a difference between tenth and tens digit.

71.234

tenth digit = 2
units digit = 1
tens digit = 7

Hope this helps

kulksnikhil wrote:In the decimal representation of x, where 0< x< 1, is the tenths digit of x nonzero?
1) 16x is an integer
2) 8x is an integer

The right answer is B

Can anybody help solve this? What is 10ths digit in decimal representation?

e.g. in 0.502, 0 is in tenth's digit place?

0<x<1
1. 16x is an integer => x could 1/16, 2/16 ...... 15/16. For some of them tenths digit is 0 for others its non-zero.
2] 8x is an integer => x could be 1/8, 2/8 .... 7/8. For all of these tenths digit is never 0. "NO" to question. So sifficient

gmat_enthus wrote:

kulksnikhil wrote:In the decimal representation of x, where 0< x< 1, is the tenths digit of x nonzero?
1) 16x is an integer
2) 8x is an integer

The right answer is B

Can anybody help solve this? What is 10ths digit in decimal representation?

e.g. in 0.502, 0 is in tenth's digit place?

0<x<1
1. 16x is an integer => x could 1/16, 2/16 ...... 15/16. For some of them tenths digit is 0 for others its non-zero.
2] 8x is an integer => x could be 1/8, 2/8 .... 7/8. For all of these tenths digit is never 0. "NO" to question. So sifficient

that's a sound reasoning...thanks.

the final remainder (which leads to the tenths decimal value) when divided by 8 will always have a quotient >= 1 (since 8 < 10). On the other hand for 16 it could be >= 0 (since 16 > 10).

So B is sufficient.

The answer should be E.

Statement 1: Let x=0.25, 16x=4 (16x is integer and the tenths digit of x is non-zero)
Let x=0.5, 16x=8 (16x is integer and the tenths digit of x is zero)
Thus, Statement 1 is insufficient

Statement 2: Let x=0.25, 8x=2 (8x is integer and the tenths digit of x is non-zero)
Let x=0.5, 8x=4 (8x is integer and the tenths digit of x is zero)
Thus, statement 2 is also insufficient

Hi pankajks2010,

I could be wrong but I thought the tenth digit was the number which comes right after the decimal?
For example, 0.52 -> 5 is the tenth digit? Wouldn't this make B sufficient?

Please share your thoughts. Thanks!

Hi pankajks2010,

I could be wrong but I thought the tenth digit was the number which comes right after the decimal?
For example, 0.52 -> 5 is the tenth digit? Wouldn't this make B sufficient?

Please share your thoughts. Thanks!

jerseyny wrote:Hi pankajks2010,

I could be wrong but I thought the tenth digit was the number which comes right after the decimal?
For example, 0.52 -> 5 is the tenth digit? Wouldn't this make B sufficient?

Please share your thoughts. Thanks!

Thanks mate for pointing this out..Yes, I am wrong here..

gmat_enthus wrote:

kulksnikhil wrote:In the decimal representation of x, where 0< x< 1, is the tenths digit of x nonzero?
1) 16x is an integer
2) 8x is an integer

The right answer is B

Can anybody help solve this? What is 10ths digit in decimal representation?

e.g. in 0.502, 0 is in tenth's digit place?

0<x<1
1. 16x is an integer => x could 1/16, 2/16 ...... 15/16. For some of them tenths digit is 0 for others its non-zero.
2] 8x is an integer => x could be 1/8, 2/8 .... 7/8. For all of these tenths digit is never 0. "NO" to question. So sifficient

But 4/8=1/2=0.5 .Apparently,its tenth digit is 0

gmat_enthus wrote:

kulksnikhil wrote:In the decimal representation of x, where 0< x< 1, is the tenths digit of x nonzero?
1) 16x is an integer
2) 8x is an integer

The right answer is B

Can anybody help solve this? What is 10ths digit in decimal representation?

e.g. in 0.502, 0 is in tenth's digit place?

0<x<1
1. 16x is an integer => x could 1/16, 2/16 ...... 15/16. For some of them tenths digit is 0 for others its non-zero.
2] 8x is an integer => x could be 1/8, 2/8 .... 7/8. For all of these tenths digit is never 0. "NO" to question. So sifficient

But 4/8=1/2=0.5 .Apparently,its tenth digit is 0

Sxiyuan wrote:But 4/8=1/2=0.5 .Apparently,its tenth digit is 0

Hi! I'm assuming that this last part in quotes is your actually comment/question.

It's important to know the place names for the various digits in a numbers, so let's do a quick review, using the example of:

12345.6789

We start numbering to the left and the right of the decimal place. Let's start on the left!

5 = ones or units digit
4 = tens digit
3 = hundreds digit
2 = thousands digit
1 = ten thousands digit

and to the right:

6 = tenths digit
7 = hundredths digit
8 = thousandths digit
9 = ten thousandths digit

Here's another way to think about the digits:

the numbers to the left of the decimal get MULTIPLIED by their digit name; and
the numbers to the right of the decimal get DIVIDED by their digit name.

So, going back to our example of 12345.6789, we could express that number as:

1*10000 + 2*1000 + 3*100 + 4*10 + 5*1
+
6/10 + 7/100 + 8/1000 + 9/10000

Hence the names for the digits!

As an aside, you'll notice that there's no "oneths" or "unitths" digit - that's because there's no number to the right of the decimal that you divide by 1 to get it's value. They're also silly-sounding words!

I hope that clears things up,

Stuart