Each question is followed by two statements. You have to decide whether the information provided in the statements is sufficient for answering the question. |

Mark A |
If the question can be answered by using one of the statements alone, but cannot be answered by using the other statements alone. |

Mark B |
If the question can be answered by using either statement alone. |

Mark C |
If the question can be answered by using both statements together, but cannot be answered by using the either statement alone. |

Mark D |
If the question cannot be answered even by using both the statements together. |

1. | If n is an integer, is n even ? | |||

Stmt.(1) | n^{2} -1 is an odd integer. |
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Stmt.(2) | 3n + 4 is an even integer. | |||

(a) A | (b) B | (c) C | (d) D | |

Expl. of Statement (1) |
Since n^{2} —1 is odd, n^{2} is even and so n is even; SUFFICIENT. |
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Expl. of Statement (2) |
Since 3n+ 4 is even, 3n is even and so n is even; SUFFICIENT. | |||

Answer | (B) [Each statement alone is sufficient.] |

2. | If n is an integer, is n+ 1 odd ? | |||

Stmt. (1) | n+ 2 is an even integer. | |||

Stmt. (2) | n-1 is an odd integer. | |||

(a) A | (b) B | (c) C | (d) D | |

Expl. of Statement (1) |
Since n+ 2 is even, n is an even integer, and therefore n+1 would be an odd integer; SUFFICIENT. | |||

Expl. of Statement (2) |
Since n-1 is an odd integer, n is an even integer. Therefore n+ 1 would be an odd integer; SUFFICIENT. | |||

Answer | (B) [Each statement alone is sufficient.] |

3. | Is x a negative number ? | |||

Stmt. (1) | 9x > 10x. | |||

Stmt. (2) | x + 3 is positive. | |||

(a) A | (b) B | (c) C | (d) D | |

Expl. of Statement (1) |
Subtracting 9x from both sides of 9x > lOx gives 0 > x, which expresses the condition that x is negative; SUFFICIENT. | |||

Expl. of Statement (2) |
Subtracting 3 from both sides of x+ 3 > 0 gives x > -3, and x > -3 is true for some negative numbers (such as -2 and -1) and for some numbers that aren’t negative (such as 0 and 1); NOT SUFFICIENT. | |||

Answer | (A) [Each statement alone is not sufficient.] |

4. | What is the tens digit of positive integer x ? | |||

Stmt. (1) | x divided by 100 has a remainder of 30. | |||

Stmt. (2) | x divided by 110 has a remainder of 30. | |||

(a) A | (b) B | (c) C | (d) D | |

Expl. of Statement (1) |
Having a remainder of 30 when x is divided by 100 can only happen if x has a tens digit of 3 and a ones digit of 0, as in 130, 230, 630, and so forth; SUFFICIENT. | |||

Expl. of Statement (2) |
When 140 is divided by 110, the quotient is 1 R 30. However, 250 divided by 110 yields a quotient of 2 R 30, and 360 divided by 110 gives a quotient of 3 R 30. Since there is no consistency in the tens digit, more information is needed; NOT SUFFICIENT. | |||

Answer | (A) [Each statement alone is not sufficient.] |

5. | If k is an integer such that 56 < k < 66, what is the value of k ? | |||

Stmt. (1) | If k were divided by 2, the remainder would be 1. | |||

Stmt. (2) | If k + 1 were divided by 3, the remainder would be O. | |||

(a) A | (b) B | (c) C | (d) D | |

Expl. of Statement (1) |
Determine the value of the integer k, where 56<k< 66 It is given that the remainder is 1 when k is divided by 2, which implies that k is odd Therefore, the value of k can be 57, 59, 61,63, or 65; NOT SUFFICIENT. | |||

Expl. of Statement (2) |
It is given that the remainder is 0 when k + 1 is divided by 3, which implies that k + 1 is divisible by 3. Since 56 <k <66 (equivalently, 57 <k+1 <67), the value of k + 1 can be 60, 63, or 66 so the value of k can be 59, 62 or 65; NOT SUFFICIENT. | |||

Taking (1) + (2) Together |
Taking (1) and (2) together, 59 and 65 appear in both lists of possible values for k; NOT sufficient.. | |||

Answer | (D) [Each statement alone and together is not sufficient.] |

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I have doubt on Data Sufficiency Solved Problems 01 question 5. In question 5 ,the value of k can be determined by using both statement together. ans is 59 and 65

Detail solution is not given here?

But bro you should aware of the point that in data sufficient questions should have unique value not multiple value .

So option is D

Because we have not a unique value yet have multiple value.

5th question right ans is option c .

sol. k possible values – 57,58,…….65.

a) if we divided it by 2 so possible values are – 58,60,62,64.

if we take k=62

b) if we divided it by 3 so possible values are -k+1=62+1=63. and it divided by 3 .

so ans is 63.

k cannot be 62 because k is odd as it leaves remainder 1 according to first statement.

so u r wrong , solution is fine

if we divided it by 2 and remainder is 1, so possible values are – 59,61,63,65.

in first question…. if we take n=3, then n^2-1 is even . so how can u say that the statement 1 sufficient .?

n^2-1 could be both even or odd .

if u take n=3,then value comes in even,but in statement value should be odd thats y u r wrong..

Krishna broah you can not be more wrong than this

As you said ans is 63 but acc. to statement 2nd k+1 when divided by 3 leaves 0 as remainder

But if we divide 64 i.e (k+1=63+1=64) it leaves a remainder of 1 so wrong

Nitish brew if we divide it by 2 and remainder is 1 then 57 is also to be considered

Broda abmishra yes n^2-1 could be even or odd but as given in statement 1 n^2-1 is odd is the thing which helps us know that n is even

n^2-1 being odd or even is a general case where as n^2-1 being odd is a more specific case

what is the answer for 5th question.??..acc to statment 1 possible values are 57, 59, 61, 63 and 65…if we ignore the information from 1st stmt then possible values are 60 63 and 66 and among these nly 62 satisfying the information given the 2nd stmt….63(k+1) divided by 3 gives 0 rem so answer shuld be 62 ri8?.. plss explain me