If a is a positive integer less than 3 and b is a positive integer les

Question

If a is a positive integer less than 3 and b is a positive integer less than 11, what is the value of the decimal expression of a/b when rounded to the nearest tenths?

(1) When the decimal expression of a/b is rounded to the nearest hundredths the value of the hundredths digit is 1.

(2) When the decimal expression of a/b is rounded to the nearest ten-thousandths the value of the ten-thousandths digit is 9.

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chetan2u · Answer

0<a<3, so a can be 1 or 2.
0<b<11, so b can be anything from 1 to 10.

(1) When the decimal expression of a/b is rounded to the nearest hundredths the value of the hundredths digit is 1.
So  0.x05\leq{\frac{a}{b}}<{0.x15} 
The answer has more to do with b than a, as a has only 2 values.
Now, when b=1, 2, 5 or 10, we will have no hundredths digit..Example  \frac{1}{10}=0.2 \ \ and \ \ \frac{1}{2}=0.5 
when b=4,  \frac{a}{4}=\frac{1}{4}=0.25 \ \ or \ \ \frac{2}{4}=0.5 .. b
eq{4} 
when b=3,  \frac{a}{3}=\frac{1}{3}=0.333 \ \ or \ \ \frac{2}{3}=0.6666 ... b
eq{3} 
when b=6,  \frac{a}{6}=\frac{1}{6}=0.166667 \ \ or \ \ \frac{2}{6}=0.3333 ... b
eq{6} 
when b=7,  \frac{a}{7}=\frac{1}{7}=0.14285 \ \ or \ \ \frac{2}{7}=0.284 ... b
eq{7} 
when b=8,  \frac{a}{8}=\frac{1}{8}=0.125 \ \ or \ \ \frac{2}{8}=0.25 ... b
eq{8} 
when b=9,  \frac{a}{9}=\frac{1}{9}=0.111 \ \ or \ \ \frac{2}{9}=0.2222 ... b={9} \ \ a=1 
 \frac{a}{b}=\frac{1}{9}=0.1111 
answer = 0.1
sufficient

(2) When the decimal expression of a/b is rounded to the nearest ten-thousandths the value of the ten-thousandths digit is 9.
So  0.xyz85\leq{\frac{a}{b}}<{0.xyz95} 
We have already done the calculations above, and only value that fits in is a=1 and b=7 =>  \frac{a}{7}=\frac{1}{7}=0.14285 .
 \frac{a}{b}=\frac{1}{7}=0.14287 
answer = 0.1
Sufficient

D

It would be better if the statement II is 'the value of the ten-thousandths digit is 1', so that value of b is 9 in each case.

LipiSinha · Answer

Memorizing the decimal values of a few basic fractions goes a long way in this question.
As per the question stem, a = {1, 2} and b = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

Here, we can easily discard fractions that have 2, 4, 5, 8, and 10 as denominators as these will yield terminating decimals with no value in the hundredths place (only 1/8 gives us 0.125).

We know that 1/3 gives us a recurring decimal of 0.333 , 1/6 = 0.167 and 2/3 = 0.667.

Therefore, we only need to convert the following fractions:
1/7 = 0.14285
1/9 = 0.1111
2/7 = 0.28571
2/9 - 0.2222

Statement 1: When the decimal expression of a/b is rounded to the nearest hundredths the value of the hundredths digit is 1.
The only fraction that fits here is 1/9, and it gives us a value of a/b as 0.1 when rounded to the nearest tens.

Hence, Sufficient

Statement 2: When the decimal expression of a/b is rounded to the nearest ten-thousandths the value of the ten-thousandths digit is 9.
The only fraction that fits here is 1/7. This too gives a value of 0.1 when rounded to the nearest tens.

Hence, Sufficient.

The answer will be D.

carouselambra · Answer

Hi, just had a small question - I was able to prove that (A) is sufficient.
But got confused for (B)

In DS, do we know have consistent answers across the answer choices?
For example, if (A) says that a/b=1/9, the (B) will also say that a/b=1/9.

We do not have discrepancy, do we?

LipiSinha · Answer

I too had the same question in my mind. But, I think, in this question since the value of a/b in both the statements remain the same (0.1), the consistency holds.

Posted from my mobile device

chetan2u · Answer

Yeah the statements should give same value even for variables a and b, but the answer would be D as you are to read each statement separately. 
But you will not have this situation in actuals

TarunKumar1234 · Answer

If a is a positive integer less than 3 and b is a positive integer less than 11, what is the value of the decimal expression of a/b when rounded to the nearest tenths?

a= 1 or 2, b= 1,2..10, and a/b=?

Stat1: When the decimal expression of a/b is rounded to the nearest hundredths the value of the hundredths digit is 1.
To reach hundredths value, we need denominator, b= 3 or 5 or 6 or 7 or 9,
to get hundredths as 1, only, 1/9 is possible. Sufficient.

Stat2: When the decimal expression of a/b is rounded to the nearest ten-thousandths the value of the ten-thousandths digit is 9.
To reach ten-hundredths value, we need denominator, b= 3 or 6 or 7 or 9,
to get ten-hundredths as 1, only, 1/7 is possible. Sufficient.

So, I think D.

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If a is a positive integer less than 3 and b is a positive integer les

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GMAT Data Sufficiency (DS) Questions

If a is a positive integer less than 3 and b is a positive integer les

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