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Bunuel wrote:

Is \(x^2y^3w^4z^1 < 0\) ?

(1) yz < 0
(2) z < 0

Hi,
there are two sets ofanswer-
1) A as the answer --- Not speaking about any of the variables being 0..
2) E as the answer--- Correctly taking 0 as an option for variables ..

lets see the equation first and what is required..

\(x^2y^3w^4z^1 < 0\)
1) when all are non-zero integers..\(x^2w^4\) will be > 0, we have to check if y and z are of opposite sign..

2) if any of the integer is 0.. if any integer is zero, entire equation will be 0
...

X is negative only when the power is odd.
Hence (d)

When positive integer y is divided by 51, the remainder is x. What is the remainder when y is divided by 17?

(1) When y is divided by 34 the remainder is zero.
(2) x = 17

Given - y is divided by 51, the remainder is x.

y = 51Q+x (Q is an integer) or y = 17 (3Q) + X. ; have to find out the remainder when y is divided by 17.

Statement 1:

y is a multiple of 34. Values that suit this are: 0, 34, 102 etc. All of these are divisible by 17 (as 34 = 17 x 2).

Hence sufficient as remainder for
...

Given: B gives an hour lead to A.
A finishes in 4 hours
Distance = 60 miles

St1: B crosses A in 1 hour --> When B crosses A, time taken by A = 2hrs; time taken by B = 1hr
Hence, Speed of B is double the speed of A
If A takes 4 hours, B takes 2 hours to complete.
Sufficient

St2: Time taken by A = 4
B leaves 1 hour after A and completes 1 hour before A --> Time taken by B = 2 hours.
Sufficient

Answer: D

(1)
For t from 1 to 10:
S=t^2 = {1, 2, 9, 16, 25, 36, 49, 64, 81, 100}
Not sufficient > Possible Answer: BCE

(2)
For r from 4 to 5:
S=r^3={16, 64, 125}
Not sufficient > Possible Answer CE

(1)+(2)
Common term is 64. Hence S=64. Answer is C

for

Classic C trap question.
Requires two values for both variables, but when we look closer we see that option B has 6!, which has 2 and 5 as factors. These values always have 0 as digits number. And we don't even need to know value of y.

Hence B is the answer.

Three points T, U and V on the number line have coordinates t, u, and v respectively. Is T between points U and V?

(1)\(t^2<4<u^2<v^2\) . Since all parts of the inequality are non-negative, we can safely take the square root from it:\(|t| < 2 < |u| < |v|\) . It's possible that T is between U and V, for example, if t=0, u=-3 and v=4, as well as it's possible that it's not, for example, t=0, u=3 and v=4. Not sufficient.

(2) u<0<v. Clearly insufficient.

(1) Since from (2) u<0<v,
...

nevedove wrote:

If x-y=8, which of the following must be true?

I. Both x and y are positive
II. If x is positive, y must be positive
III. If x is negative, y must be negative

A) I only
B) II only
C) III only
D) I and II
E) II and III

Given that:\(x=y+8\) .

I. Both x and y are positive. Not necessarily true. Consider x=7 and y=-1.

II. If x is positive, y must be positive. Not necessarily true. Consider the same numbers.

III. If x is negative, y must be negative. If x is negative, then we have that\( x=negative=y+8\)
...

Baten80 wrote:

If x and y are nonzero integers, is x^y<y^x?

(1) x = y^2
(2) y>2

If x and y are nonzero integers, is x^y < y^x ?

(1) x = y^2 --> if\(x=y=1\) , then\(x^y=1=y^x\) , so the answer would be NOBUT if\(y=3\) and\(x=9\) , then\(x^y=9^3<y^x=3^9\) , so the answer would be YES. Not sufficient.

(2) y > 2. No info about\(x\) , not sufficient.

(1)+(2) From (1)\(x = y^2\) , thus the question becomes: is\((y^2)^y<y^{(y^2)}\) ? --> is\(y^{2y}<y^{(y^2)}\) ? Now, since from (2)\( y=integer>2\)
...

Only digit numbers are involve hence A is sufficient.

stonecold wrote:

I am a bit confused here..
What does EVENLY DIVIDE MEAN ..
I solved it correctly but still feel i dont understand this term

It means divide without a remainder.

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mimisoko9 wrote:

I get that statement A is sufficient alone and that, therefore, gives us an answer to the problem. We don't need to solve it. However,
Can it be written as: n + (n+1) + (n+2) + (n+3) + ....?
...Gives you 5n + 10 = 875

Yes, you can write this way too.

amritar wrote:

I dont understand why after both statements, Its Data sufficient.
The first statement gives us there are all negative elements in the set and second statement combined gives us that 5 of them are negative.
So the S={-1,-2,-3,-4,-5,-x,-y,... } How does this make the both statements sufficient together?

Apologise but then i feel they are not sufficient together.

When combined we have that there are 5 negative integers in the set. Therefore their product is negative. Please read the solutions provided
...

If x is the number of positive integers that will leave no remainder when divided into 1,880, what is the value of x?

A. 4
B. 6
C. 8
D. 12
E. 16

How many positive integers will divide evenly into 520?

A. 8
B. 12
C. 16
D. 18
E. 20

If n and q are positive integers, what is the units digit of q?

(1) q = (n)(n + 1)(n + 2)(n + 3)(n + 4)(n + 5)
(2) (n + 1) + n = 9

When n is divided by 21, the remainder is 4. What is the remainder when n + 16 is divided by 7?

A. 2
B. 3
C. 4
D. 5
E. 6

What number is the units digit of 357^110?

A. 1
B. 3
C. 5
D. 7
E. 9

If x, y, and z are positive integers, what is the value of x?

(1) (2^x)(3^y)(5^z)=300n
(2) n is a multiple of 5.

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