a. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. b. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient. c. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. d. EACH statement ALONE is sufficient. e. statemet (1) and (2) TOGETHER are NOT sufficient.
a. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. b. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient. c. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. d. EACH statement ALONE is sufficient. e. statemet (1) and (2) TOGETHER are NOT sufficient.
1) x > 0
(x-1)^2 > 4
absolute(x-1) > 2
x-1 > 2 or -(x-1) > 2 x > 3 or x-1 0 so x > 3----hence sufficient
2) x > 0 (x-2)^2 > 9 absolute(x-2) > 3
x-2 > 3 or -(x-2)>3 x>5 or x-2 x > 5 or x 0 so x > 5 i.e. x > 3......hence sufficient
For all non-zero integers n, n* = (n+2)/n. What is the value of x? (1) x* = x (2) x* = -2-x
The answer to this ques is stated as (C). I have a conflict with the solution provided in the book (Kaplan 800): Statement (2) implies, (x+2)/x = -(x+2). Cancelling (x+2) both sides, we have x = -1. So the answer must be (B). Can someone clarify why we need to deliberately make it a quadratic equation (instead of cancelling (x+2) both sides) and end up with answer (C).
Once u cancel out (x+2) from both sides, ur actually ruling out the possibility of x=-2 which can be one of the valid solutions
HTH...
For all non-zero integers n, n* = (n+2)/n. What is the value of x? (1) x* = x (2) x* = -2-x
The answer to this ques is stated as (C). I have a conflict with the solution provided in the book (Kaplan 800): Statement (2) implies, (x+2)/x = -(x+2). Cancelling (x+2) both sides, we have x = -1. So the answer must be (B). Can someone clarify why we need to deliberately make it a quadratic equation (instead of cancelling (x+2) both sides) and end up with answer (C).
For all non-zero integers n, n* = (n+2)/n. What is the value of x? (1) x* = x (2) x* = -2-x
The answer to this ques is stated as (C). I have a conflict with the solution provided in the book (Kaplan 800): Statement (2) implies, (x+2)/x = -(x+2). Cancelling (x+2) both sides, we have x = -1. So the answer must be (B). Can someone clarify why we need to deliberately make it a quadratic equation (instead of cancelling (x+2) both sides) and end up with answer (C).
Statement 1:
x = (x+2)/x
x^2 = x + 2
x(x-1) = 2
Put x = 2, or x = -1, so two values of x produce result - insufficient
Statement 2:
-2-x = (x+2)/x -(x+2) = (x+2)/x .....(You cant cancel x+2, you don't know for sure x+2 is not 0, canceling in reality is dividing both sides by x+2 and division by 0 is undefined) x^2 + 2x = -x -2 x^2+3x+2 =0 (x+2)(x+1)=0 x=-2 and x=-1.....Insufficient
Combining both 1 and 2, gives you x=-1 hence sufficient
Came across dis DS question on tcyonline....plz can u help me getting dis one. d ans ws tricky to me. Will post it wen we get some replies.
Senorita and Rozy play a game and the loser pays the winner half of what the loser has. Who emerges richer at the end of 4 games? (Both of them start with the same amount).
For this one, I thought the ans should be C.. unfortunately its E.
Can someone please explain.
Identical cylindrical objects are placed to snugly fit in a rectangular box. The length of each cylinder is equal to the length of the rectangular box. What percentage of volume in the box is not occupied?
(1) The cylindrical objects are placed in two identical layers.
(2) The radius of each cylinder is 1 cm. and the dimensions of the rectangular box are 12 cm 8 cm 4 cm.
Came across dis DS question on tcyonline....plz can u help me getting dis one. d ans ws tricky to me. Will post it wen we get some replies.
Senorita and Rozy play a game and the loser pays the winner half of what the loser has. Who emerges richer at the end of 4 games? (Both of them start with the same amount).
(1) Senorita loses three games.
(2) Rozy loses one game.
Hi i am not sure how the answer is D but i think it should be E.
The number of winning vs losing is not important. Who wins the last wins the game, so who lost the game last is the real question?
Just think a person who wins first three but loses last one has to give half share of what he has, and other person already has some amount so the other guy will be richer.
Take value of 72 for example (as its divisible by 8 or to be on safe side take value of 144. And try for case 1)
(1) Sequence for Senorita can be LLLW, LLWL, LWLL, or WLLL. In first case she wins, in rest she loses. so not sufficient (2) Sequence for Rozy can be WWWL, WWLW, WLWW, LWWW, In last case she wins, in rest she loses so not sufficient
Combining two doesn't help as they same the same thing. in fact C cant be answer because both 1 and 2 are saying the same thing and giving no additional information when put in juxtaposition
For this one, I thought the ans should be C.. unfortunately its E.
Can someone please explain.
Identical cylindrical objects are placed to snugly fit in a rectangular box. The length of each cylinder is equal to the length of the rectangular box. What percentage of volume in the box is not occupied?
(1) The cylindrical objects are placed in two identical layers.
(2) The radius of each cylinder is 1 cm. and the dimensions of the rectangular box are 12 cm 8 cm 4 cm.
Hi plz dont mention answer plz before others attempting.
Rephrased the question as how many cylinders are there in rectangular box?
1. not sufficient - doesn't tell anything about dimensions of box and cylinder 2. gives dimension of box, gives radius of cylinder - great but what about length? It can be either 12, 8 or 4 so depending on its length numbers would change.
- cylinder radius is 1, so diameter is 2. In nutshell how many rectangular boxes can be cut with squares as their bases with length of 2 from a given box of 12 x 8 x 4?
If length of cylinder is 12, there are (8x4)/4 or 8 cylinders (12 x 8 x 4 - 8 x pi x 12 ) If length of cylinder is 8, there are (12x4)/4 or 12 cylinders (12 x 8 x 4 - 12 x pi x 8 ) If length of cylinder is 4, there are (8x12)/4 or 24 cylinders (12 x 8 x 4 - 24 x pi x 4 )
Once u cancel out (x+2) from both sides, ur actually ruling out the possibility of x=-2 which can be one of the valid solutions
HTH...
Statement 1:
x = (x+2)/x
x^2 = x + 2
x(x-1) = 2
Put x = 2, or x = -1, so two values of x produce result - insufficient
Statement 2:
-2-x = (x+2)/x -(x+2) = (x+2)/x .....(You cant cancel x+2, you don't know for sure x+2 is not 0, canceling in reality is dividing both sides by x+2 and division by 0 is undefined) x^2 + 2x = -x -2 x^2+3x+2 =0 (x+2)(x+1)=0 x=-2 and x=-1.....Insufficient
Combining both 1 and 2, gives you x=-1 hence sufficient
Thanks! Agreed with the explanation. But how about this equation: 2xy = 4x? While solving, we cancel x on both sides. By the same hypothesis, here too we don't know for sure if x is not 0. Pls explain!
Twelve jurors must be picked from a pool of n potential jurors. If m of the potential jurors are rejected by the defense counsel and the prosecuting attorney, how many different possible juries could be picked from the remaining potential jurors?
(1) If one less potential juror had been rejected, it would be possible to create 13 different juries. (2) n = m + 12
Pls explain why Statement (1) is Sufficient/Insufficient.
Thanks! Agreed with the explanation. But how about this equation: 2xy = 4x? While solving, we cancel x on both sides. By the same hypothesis, here too we don't know for sure if x is not 0. Pls explain!
You can cancel if you know that x is non-zero for example if problem says "x and y are positive integers" but you can't cancel if it says "x and y are non-negative integers" While former excludes 0, later includes it.
For stmnt 1, xC12 = 13 : where x is the no. of jurors available for selection (n-m+1) (x!)(x-12)!/12! = 13 This would be satisfied for x=13; a unique value
@ps25...pls confirm....
Twelve jurors must be picked from a pool of n potential jurors. If m of the potential jurors are rejected by the defense counsel and the prosecuting attorney, how many different possible juries could be picked from the remaining potential jurors?
(1) If one less potential juror had been rejected, it would be possible to create 13 different juries. (2) n = m + 12
Pls explain why Statement (1) is Sufficient/Insufficient.
ps25 Says
You can cancel if you know that x is non-zero for example if problem says "x and y are positive integers" but you can't cancel if it says "x and y are non-negative integers" While former excludes 0, later includes it.
For stmnt 1, xC12 = 13 : where x is the no. of jurors available for selection (n-m+1) (x!)(x-12)!/12! = 13 This would be satisfied for x=13; a unique value
@ps25...pls confirm....
Yes the statement 1 is sufficient
Given in the problem -
Selecting 12 from group of n : n! / (12! x (n-12)!)
m are rejected then n-m remain
Selecting 12 from group of n - m : (n-m)! / (12! x (n-m-12)!)
Statement 1 :
(n-m+1)!/ (12! x (n -m +1 -12) ! ) = 13
This means that n - m + 1 = 13.
n - m = 12
Answer is 1
Statement 2 :
Answer is 1 (you have only 12 people left, and you must chose all of them to form a jury of 12)
In a certain store, the price of five pens is equal to the price of a notebook. What is the cost of a ruler in this store?
1. The cost of four pens and two notebooks is 10 dollars more than the cost of six rulers.
2. The cost of seven notebooks is 25 dollars more than the cost of 15 rulers.
As MBAQuest said it is E
n=5p 1) 4p+2n = 10+6r 4p+10p=14p=10+6r 7p=3r+5
2) 7n = 15r+25 35p=15r+25 7p=3r+5
Same equation on both sides. Not known where p and r integers (positive) or can they be even fractions. But cant be zero or negative. They cant be proper fractions ( considering they are only integers -
n=10,p=2,r=3 or n=25,p=5,r=10 satisfy the equation.
