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. | What is the value of |x|? | |||

Stmt.(1) | x = -|x| . | |||

Stmt.(2) | x^{2} = 4. |
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(a) A | (b) B | (c) C | (d) D | |

Expl. of Statement (1) |
The absolute value of x, |x|, is always positive or 0, so this only determines that x is negative or 0; NOT SUFFICIENT. | |||

Expl. of Statement (2) |
Exactly two values of x (x= ±2) are possible, each of which gives the value 2 for |x| SUFFICIENT. | |||

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

2. | If x is negative, is x < – 3 ? | |||

Stmt. (1) | x^{2} > 9. |
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Stmt. (2) | x^{3 }< -9. |
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(a) A | (b) B | (c) C | (d) D | |

Expl. of Statement (1) |
Given that x^{2}> 9, it follows that x < -3 or x > 3, a result that can be obtained in a variety of ways. For example, consider the equivalent equation (|x|) >9 that reduces to |x| >3,or consider when the two factors of x^{2} —9 are both positive and when the two factors of x^{2} —9 are both negative, or consider where the graph of the parabola y = x^{2} – 9 is above the x-axis, etc. Since it is also given that x is negative, it follows thatx< -3; SUFFICIENT. |
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Expl. of Statement (2) |
Given that x^{3 }< -9, if x = -4, then x^{3 } = -64, and so x^{3 }<-9 and it is true that x < -3. However, if x = —3, then x = —27, and so x^{3 } < —9, but it is not true that x < —3; NOT SUFFICIENT. |
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Answer | (A) [Each statement alone is not sufficient.] |

3. | If x and y are integers, is xy even? | |||

Stmt. (1) | x = y + l | |||

Stmt. (2) | x/y is an even integer.. | |||

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

Expl. of Statement (1) |
Determine if xy is even; Since x and y are consecutive integers, one of these two numbers is even, and hence their product is even. For example, if x is even, then x = 2m for some integer m, and thus xy =(2m)y =(my)(2), which is an integer multiple of 2, so xy is even; SUFFICIENT. | |||

Expl. of Statement (2) |
If x /y is even, then x/y= 2n for some integer n, and thus x = 2ny. From this it follows that xy =(2ny)(y) =(ny^{2})(2), which is an integer multiple of 2, so xy is even; SUFFICIENT. |
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Answer | (B) [Each statement alone is sufficient.] |

4. | Paula and Sandy were among those people who sold raffle tickets to raise money for Club X. If Paula and Sandy sold a total of 100 of the tickets, how many of the tickets did Paula sell? | |||

Stmt. (1) | Sandy sold 2/3 as many of the raffle tickets as Paula did.. | |||

Stmt. (2) | Sandy sold 8 percent of all the raffle tickets sold for Club X.. | |||

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

Expl. of Statement (1) |
If Paula sold p tickets and Sandy sold s tickets, then p + s = 100. Since Sandy sold 2/3 as many tickets as Paula, s= (2/3)p. The value of p can be determined by solving the two equations simultaneously; SUFFICIENT. | |||

Expl. of Statement (2) |
Since the total number of the raffle tickets sold is unknown, the number of tickets that Sandy or Paula sold cannot be determined NOT SUFFICIENT. | |||

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

5. | What is the number of cans that can be packed in a certain carton?? | |||

Stmt. (1) | The interior volume of this carton is 2,304 cubic inches.. | |||

Stmt. (2) | The exterior of each can is 6 inches high and has a diameter of 4 inches.. | |||

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

Expl. of Statement (1) |
No information about the size of the cans is given; NOT SUFFICIENT. | |||

Expl. of Statement (2) |
No information about the size of the carton is given; NOT SUFFICIENT. | |||

Taking (1) + (2) Together |
Taking (1) and (2) together, there is still not enough information to answer the question. If the carton is a rectangular solid that is 1 inch by 1 inch by 2,304 inches and the cans are cylindrical with the given dimensions, then 0 cans can be packed into the carton. However, if the carton is a rectangular solid that is 16 inches by 12 inches by 12 inches and the cans are cylindrical with the given dimensions, then 1 or more cans can be packed into the carton. | |||

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

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In qns 4 for stmt 2 it is given not sufficient, but the total number of tickets sold is given as 100. So it should be sufficient i suppose, am i right?

Paula and Sandy** were among those people who sold raffle tickets** to raise money for Club X.wmb nue th

we know the number of tickets sold by paula and sandy only..i.e 100.but we dnt knw the total number of raffle tickets sold..

No, here 100 is total number of tkt sell by those two only not for the entire GRP

best ever article i have ever come through….

In quest 1, the value of x is considered only ‘2’, but if we consider other values of x then then stmt is not true.

someone plz correct me if i am wrong?

Hello Sumedh,

You cannot take value of x other than 2, -2. In Stmt (2) it it given that, x

^{2 }= 4. So, only x = +2 , -2 will satisfy this condition. For example let’s take x= 3, -3 then value of x^{2}will be 9 .Please let us know if more information is required.

But value of x can also be sqrt(4) or – sqrt(4). Isn’t it?

x square = 4

so X=+- 2

there… no need to consider the any value

Its very useful to prepare for elitmus…..you give the detail information about the topic…

CAN YOU SHARE MORE OF THE DATA SUFFICIENCY PROBLEMS REGARDING THE ELITMUS, THE PROBLEMS ARE VERY ACCURATE THAT COMES IN ELITMUS BUT CAN WE HAVE SOME MORE PROBLEMS THIS WILL HELP US PRACTICE MORE.

in the question number 3 stmnt 1: X=Y+1 so X-Y=1 means difference between the two number will be 1 like 3,2 or 70, 69 satisfying but see stmnt 2 its not satisfying. here you have mentioned both the statements are sufficient ? how maybe answer will be A .

i have a doubt in question no.5……. since the volume of rectangular box is given and the volume of cylindrical can can be determined ……we can calculate no. of cans inside that box….. i.e 30……so why option D….can anybody help

if the breadth of the box is 1 inch how can u fit a can of diameter 4 inch in it

In 2nd question as you explain that if we take x=-3 then i wont satisfy the statement…what if i take x=-3 for 1st statment as well??..It too dont satisfy coz -3 square will never greater than 9….(-3)^2>9??..plss explain

i need more examples on these.please send me on my mail.