# Aptitude - Problems on Numbers - Discussion

Discussion Forum : Problems on Numbers - Data Sufficiency 2 (Q.No. 1)

*Directions to Solve*

Each of the questions given below consists of a question followed by three statements. You have to study the question and the statements and decide which of the statement(s) is/are necessary to answer the question.

1.

What is the two-digit number? | |

I. | The difference between the two-digit number and the number formed by interchanging the digits is 27. |

II. | The difference between the two digits is 3. |

III. | The digit at unit's place is less than that at ten's place by 3. |

Answer: Option

Explanation:

Let the tens and units digit be *x* and *y* respectively.

I. (10*x* + *y*) - (10*y* + *x*) *x* - *y* = 3.

II. *x* - *y* = 3.

III. *x* - *y* = 3.

Thus, even all the given three statements together do not give the answer.

Correct answer is (E).

Discussion:

15 comments Page 1 of 2.
Nagendra singh said:
5 years ago

The correct answer is 2 option. 1 and 3 can give the answer of the question.

From statement 1

( 10x + y) - ( 10y + x ) = 27,

9( x-y) = 27,

x-y = 3.

From the 1st statement, we get the second statement so no need of a 2nd statement

3 statement:-

The unit place is less than 3 by tens place.

So we have the condition to check;

1, 4

2, 5

3, 6

4, 7

5, 8

6, 9

By checking all condition we found a number 52.

52 - 25 = 27.

The difference of digit is also 3.

Difference of unit's place and ten's is also 3

From statement 1

( 10x + y) - ( 10y + x ) = 27,

9( x-y) = 27,

x-y = 3.

From the 1st statement, we get the second statement so no need of a 2nd statement

3 statement:-

The unit place is less than 3 by tens place.

So we have the condition to check;

1, 4

2, 5

3, 6

4, 7

5, 8

6, 9

By checking all condition we found a number 52.

52 - 25 = 27.

The difference of digit is also 3.

Difference of unit's place and ten's is also 3

(1)

Kylin said:
6 years ago

@Afreen

Consider xy as number,

then according to 3 number it will be like

1) xy - yx=27

2) x - y=3

3) x>y

There are 10 digits 0-9.

So according to 2 second and third statement (x - y=3 and x>y).

x y xy-yx.

9 6 96-69 = 27

8 5 85-58=27

7 4 74-47=27

6 3 63-36=27

5 2 52-25=27

4 1 41-14=27.

Consider xy as number,

then according to 3 number it will be like

1) xy - yx=27

2) x - y=3

3) x>y

There are 10 digits 0-9.

So according to 2 second and third statement (x - y=3 and x>y).

x y xy-yx.

9 6 96-69 = 27

8 5 85-58=27

7 4 74-47=27

6 3 63-36=27

5 2 52-25=27

4 1 41-14=27.

Afreen said:
9 years ago

What is the use of 3rd statement? Can anyone explain about it?

Mridhula Joju said:
9 years ago

Even with the first statement we can get both the statements 2 & 3. And from the first statement itself we can get different numbers as the answer.

Shweta said:
10 years ago

The explanation is not sufficient for me as I know there is no connection between any of the statement. Anyone can clarify it please.

Suresh maidaragi said:
10 years ago

I hope everyone can solve this, here 1st and 2nd or 1 and 3 statements are more than enough to find the two digit number.

Solution: Consider two digit number as xy lets take 1st and 2nd statements xy-yx=27 by trial and error we can take 9 as first digit and 6 as second digit now the number become 96 right so.

From statement 1 96-67=27 from statement 2 9-6=3 or we can assume 1st and 3rd statement from 3rd we assure that 96 follows. Therefore option D is correct.

Solution: Consider two digit number as xy lets take 1st and 2nd statements xy-yx=27 by trial and error we can take 9 as first digit and 6 as second digit now the number become 96 right so.

From statement 1 96-67=27 from statement 2 9-6=3 or we can assume 1st and 3rd statement from 3rd we assure that 96 follows. Therefore option D is correct.

Divya said:
1 decade ago

@Vineet.

Just look at the first statement. It is the diff of the 2 digits and interchange of the digits is given as 27, not the given number and interchange is 27.

Just look at the first statement. It is the diff of the 2 digits and interchange of the digits is given as 27, not the given number and interchange is 27.

Pavithra said:
1 decade ago

Hi.

In the first step why have they considered 10 in the equation (10x+y) - (10y-x) please share the information?

In the first step why have they considered 10 in the equation (10x+y) - (10y-x) please share the information?

Riya said:
1 decade ago

But actually they are right because 2 of the data give similar information. So we cannot get the answer. Yes of course we can assume by hit and trial but cannot get the answer from given data.

Vineet Verma said:
1 decade ago

You dont need to be genius to solve this,

41-14=27 and 4-1=3

52-25=27 and 5-2=3

63-36=27 and 6-3=3

74-47=27 and 7-4=3

85-58=27 and 8-5=3

96-69=27 and 9-6=3

41-14=27 and 4-1=3

52-25=27 and 5-2=3

63-36=27 and 6-3=3

74-47=27 and 7-4=3

85-58=27 and 8-5=3

96-69=27 and 9-6=3

(3)

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