[gradpostgrad23]

Originally Posted by deepakraam

Solve this

If k is a positive constant and y = |x - k| - |x + k|, what is the maximum value of y?

(1) x < 0

(2) k = 3

My take:

the maximum value of y will occur when the negative part equates to zero. thus |x + k| = 0 => x = -k

thus y = |-2k|

thus maximum value of y depends on only 2k. therefore B.

[gradpostgrad23]

Originally Posted by friend9921

Another two,

Is X greater than Y?
1. 6X=5Y
2. X^2<Y^2

My take:

Stament 1 says 6x=5y. so x/y = 5/6. that's cool we can get it by having both x and y as positive or both negative. So can't tell anything. So Insuff.

St 2 says x2<y2. Like above, take two values EACH for x and y, say x=5,-5 and y=6,-6. Here too, nothing can be said. SO st2 insuff.

Take them together. Use the above four values. Don't rack your brains(like I did) with any more values. You realize answer is E. Khoda Pahad nikla chuhe ka baby. Hope it helps.

[gradpostgrad23]

Originally Posted by friend9921

Another two,


Is X greater than Y?
1. X - Y > |X| - |Y|
2. |X|>X AND |Y|=Y

My take:

I apply a strategy of looking at St.2 generally. That way, I avoid taking the two stmts together at the start.

We can infer from st.2 that X is NEGATIVE and Y is either ZERO or Positive.
So X is always < Y

St. 1 says X - Y > |X| - |Y| If this is the case, Y has to be necessarily negative. If we try taking X also Negative, then the condition fails. Thus, only Y is negative. X can be zero or any positive number for the situation to hold true. Thus X > Y, a concrete answer. Therfore, st1. suff.


Therefore, D.

Please correct me if I am going wrong somewhere.

[gradpostgrad23]

If, on a coordinate plane, point A has the coordinates (-3,4), how far is point A from point E?

1) Point E is on the Y axis four units from the origin.
2) If point A were twice as far from point E, it would be the distance from point E as point C is at coordinates (0,-2)



Help needed with this question. It had come on my Kap GMAT. I marked E. OA is C. Please Explain.

[xyz3000]

If, on a coordinate plane, point A has the coordinates (-3,4), how far is point A from point E?

1) Point E is on the Y axis four units from the origin.
2) If point A were twice as far from point E, it would be the distance from point E as point C is at coordinates (0,-2)


1. E is (0, 4) or (0, -4) . Insuff on its own
2. 2AE = CE, where C(0,-2) (this gives an equation of a circle) Insuff on its own.

Combined together, sufficient

[xyz3000]

Is X greater than Y?
1. X - Y > |X| - |Y|
2. |X|>X AND |Y|=Y

2. |x| > x only when x is -ve; |y| = y when y is non-negative. Therefore y > x, sufficient.

1. |y| - y > |x | - x

Consider 4 possible cases.
(+ve, +ve) Invalid
(-ve, -ve) y < x < 0
(-ve, +ve) 0 > -2x or x is +ve, Invalid
(+ve, -ve) -2y > 0 or y < 0

In other words, the above inequality holds true when y < x < 0

Sufficient on its own.

D

[xyz3000]

If k is a positive constant and y = |x - k| - |x + k|, what is the maximum value of y?

(1) x < 0

(2) k = 3


==-k=====0=====k==

y is max, when it is +ve; in which case, |x-k| > | x+k|. iow, the point x should be on the negative side. Then, y becomes the distance between -k and k, which is 2k.

---x===-k===0===k---

(1) is not required; and useless as well.
(2) k = 3; sufficient on its own.

B is the answer

[xyz3000]

x is an integer and x raised to any odd integer is greater than zero; is w - z greater than 5 times the quantity 7^x-1 - 5^x?

1. z < 25 and w = 7^x
2. x = 4

Let A = 5* 7^(x-1) - 5*5^x + z - w, fine whether A > 0 or 0 or < 0

1. A = 7^(x-1) - 5^x - 7^x - (25 - epsilon)
A = -2.7^(x-1) - 25.5^(x-1) - (25-epsilon)

When x >=1, A < 0.
Since x^odd > 0, it means x is a positive integer.

Sufficient on its own.

A is the answer.

[xyz3000]

What is the remainder of a positive integer N when it is divided by 2?

1. N contains odd numbers as factors
2. N is a multiple of 15

N contains odd numbers as factors. In which case, N is odd. Sufficient.

A is the answer.


Or if (1) is restated as N contains odd number of factors. In which case, N is a perfect square. Insufficient. In this case, E is the answer.

[xyz3000]

Q2: On the number line shown, is 0 halfway between r and s ?
1) s is to the right of 0.
2) The distance between t and r is the same as the distance between t and -s.

<------r----------s---t------> (This is a number line with r, s and t placed on it)


2. |t-r| = |t+s|, find whether r+s = 0

square it, t^2 + r^2 - 2rt = t^2 + s^2 + 2ts
(r+s)(r-s-2t) = 0
either r+s = 0 or r - s = 2t

r-s = 2t --> r-t = t -s. In other words, t gotta be in between r and s.
The diagram shows that t is not in between and r and s.

Therefore r - s <> 2t. therefore, r +s = 0. Sufficient.


Answer is B