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

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Manager
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If a is a positive integer less than 3 and b is a positive integer les  [#permalink]

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23 Sep 2016, 05:19
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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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If a is a positive integer less than 3 and b is a positive integer les  [#permalink]

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23 Sep 2016, 05:55
duahsolo wrote:
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.

We are given a = 1 or 2

b could be 1,2,3,.. 10

Now, Statement 1 : Only fraction that could give the value of hundredths digit 1 is 1/9. So, Sufficient.

Statement 2 : Only fraction that could give the value of ten-thousandths digit 9 is 1/7. So, Sufficient.
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Re: If a is a positive integer less than 3 and b is a positive integer les  [#permalink]

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23 Sep 2016, 05:59
1
a < 3; b < 11; a/b rounded to nearest tenths = ?

St1: Rounding to nearest hundredth, a/b = 0._1
Put a = 2 and plug values of b from 3 to 10 --> Rounding to the hundredths digit does not result in 1.
a = 1; b = 10 --> a/b = 0.1 --> Not possible
a = 1; b = 9 --> a/b = 0.11 --> Possible
a = 1; b = 8 --> a/b = 0.13 --> Not possible
As b decreases value of a/b increases and hundredths digit does not equal to 1 --> Only possible value of a/b = 0.11
Value of a/b rounded to nearest tenth = 0.1
Sufficient

St2: Rounding to nearest ten thousandth, a/b = 0._ _ _ 9
We need a recurring values to find this
Possible values = 2/3 = 1/6 = 0.6667 --> Not possible
2/6 = 1/3 = 0.3333 --> Not possible
2/7 = 0.28571 = 0.2857 --> Not possible
2/9 = 0.2222; 1/9 = 0.1111 --> Not possible
1/7 = 0.14285 = 0.1429 --> Possible
a/b rounded to the nearest tenth = 0.1
Sufficient

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Re: If a is a positive integer less than 3 and b is a positive integer les  [#permalink]

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23 Sep 2016, 06:01
abhimahna wrote:
duahsolo wrote:
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.

We are given a = 1 or 2

b could be 1,2,3,.. 10

Now, Statement 1 : Only fraction that could give the value of hundredths digit 1 is 1/9. So, Sufficient.

Statement 2 : Only fraction that could give the value of ten-thousandths digit 9 is 1/9. So, Sufficient.

Small correction. The above highlighted part must be 1/7.
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Re: If a is a positive integer less than 3 and b is a positive integer les  [#permalink]

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23 Sep 2016, 06:15
Vyshak wrote:
abhimahna wrote:
duahsolo wrote:
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.

We are given a = 1 or 2

b could be 1,2,3,.. 10

Now, Statement 1 : Only fraction that could give the value of hundredths digit 1 is 1/9. So, Sufficient.

Statement 2 : Only fraction that could give the value of ten-thousandths digit 9 is 1/9. So, Sufficient.

Small correction. The above highlighted part must be 1/7.

Yeah, it was a typo. Its 1/7 .

Edited the original solution. Thanks
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Re: If a is a positive integer less than 3 and b is a positive integer les  [#permalink]

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23 Feb 2017, 06:04
Prompt analysis
a<3 and b<11

Superset
The answer will be a positive single digit.

Translation

In order to find the digit, we need:
1# exact value of a and b.
2# the properties of a/b.
3# two equation to find a and b.

Statement Analysis
St1: Rounding to nearest hundredth, a/b = 0._1
Put a = 2 and plug values of b from 3 to 10 --> Rounding to the hundredths digit does not result in 1.
a = 1; b = 10 --> a/b = 0.1 --> Not possible
a = 1; b = 9 --> a/b = 0.11 --> Possible
a = 1; b = 8 --> a/b = 0.13 --> Not possible
As b decreases value of a/b increases and hundredths digit does not equal to 1 --> Only possible value of a/b = 0.11
Value of a/b rounded to nearest tenth = 0.1
Sufficient

St2: Rounding to nearest ten thousandth, a/b = 0._ _ _ 9
We need a recurring values to find this
Possible values = 2/3 = 1/6 = 0.6667 --> Not possible
2/6 = 1/3 = 0.3333 --> Not possible
2/7 = 0.28571 = 0.2857 --> Not possible
2/9 = 0.2222; 1/9 = 0.1111 --> Not possible
1/7 = 0.14285 = 0.1429 --> Possible
a/b rounded to the nearest tenth = 0.1
Sufficient
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Re: If a is a positive integer less than 3 and b is a positive integer les  [#permalink]

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09 Mar 2017, 06:15
These type question generally take too much time to solve.
Is there a way to solve such questions within 2 minutes?
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Re: If a is a positive integer less than 3 and b is a positive integer les  [#permalink]

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09 Mar 2017, 06:29
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harsh901105 wrote:
These type question generally take too much time to solve.
Is there a way to solve such questions within 2 minutes?

The quickest way to solve such questions is to learn fractions from 1/2 to 1/25. This will help you get the results in few seconds.
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Re: If a is a positive integer less than 3 and b is a positive integer les  [#permalink]

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24 May 2017, 02:19
harsh901105 wrote:
These type question generally take too much time to solve.
Is there a way to solve such questions within 2 minutes?

The only way to solve this problem faster than others is to know the value of fractions upto 1/20 & do calculation AFAP..

Even though you will take around 1.5 to 2 minutes with full concentration.. if you get stuck somewhere it will take more time..
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Re: If a is a positive integer less than 3 and b is a positive integer les  [#permalink]

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24 May 2017, 10:26
Quick question: I've read somewhere that statements 1 and 2, while they must be analysed separate from each other, they do need to be consistent, meaning that if answer is D-EACH, then the solution found must be the same.

Is this not true? Cause this problem goes against that...

Thanks!
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If a is a positive integer less than 3 and b is a positive integer les  [#permalink]

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02 Nov 2017, 21:39
Statement 1 and Statement 2 are contradicting each other.

Statement 1 : a = 1, b = 9
Statement 2 : a = 1, b = 7

Both the statements yield diff (a/b) ratios
If a is a positive integer less than 3 and b is a positive integer les &nbs [#permalink] 02 Nov 2017, 21:39
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