difficult DS. please help!

[ss1]

If 4x = 5y = 10z, what is the value of x + y + z ?
(1) x – y = 6
(2) y + z = 36

If Sara's age is exactly twice Bill's age, what is Sara's age?
(1) Four years ago, Sara's age was exactly 3 times Bill's age.
(2) Eight years from now, Sara's age will be exactly 1.5 times Bill's age.
I can never understand how to make an equation: for statement (1), is the equation S-4 = 3{(2B)-4} (incorporating the present ages, and converting them into past ages), or is it simply S-4= 3(B-4)?

if xy > 0, does (x - 1)(y - 1) = 1 ?
(1) x + y = xy
(2) x = y

My answer: D OA: A. why? If you put : (x-1)(x-1), you get x^2 –x-x+1, and then x^2-2x=1-1 - x(x-2)=0, so x=0 or x=2. Now x cannot be 0, since xy>0, then x must be 2, and we can find y



Is 5^k less than 1,000 ?
(1) 5^(k-1)<3000
(2) 5^(k-1)= [5^k] - 500


If p1 and p2 are the populations and r1 and r2 are the numbers of representatives of District 1 and District 2, respectively, the ratio of the population to the number of representatives is greater for which of the two districts ?
(1) p1 > p2
(2) r2 > r1

C
dep from S: 7:08 EST (eastern standard time), arrival at T: 08:10
The table above shows the morning schedule for train X. If Juan took train X on Monday morning, did he arrive at station T on schedule?
(1) Juan arrived at station T on Monday morning 1 hour and 2 minutes after he left station S.
(2) Juan arrived at his office at 8:30 (EST) on Monday morning, which was 20 minutes after he arrived at station T.

B
If where p and q are nonzero integers, is n an integer ?
(1) is an integer.
(2) is an integer.
D

Is [(x-3)^2]^0.5=3-x ?
(1) x ≠ 3
(2) – x | x | > 0
B

What was Jean's insurance premium in 1995?
(1) The ratio of Jean's insurance premium in 1995 to her insurance premium in 1994 was .
(2) Jean's insurance premium in 1995 was 20 percent more than her insurance premium in 1994.
E

[clock60]

the Q1 answer is D
4x=5y=10z
(1) x-y=6
4x=10z, x=(5/2)z
5y=10z, y=2z
(5/2)z-2z=6, so z=12, y=2*12=24, x=(5/2)*12=30
x+y+z=12+24+30=66 sufficient
(2)y+z=36
4x=5y,y=(4/5)x,
4x=10z, z=(2/5)x
(4/5)*x+(2/5)*x=36, x=30, y=(4/5)*30=24. z=(2/5)*30=12
x+y+z=30+24+12=66 sufficient
so D

[clock60]

Q2 the answer is D
present Sare age-S
present Bill age-B
Sare is is exactly twice Bill's age,it means that S=2B find S-??
(1) (S-4)=3(B-4)
S-4=3B-12.
3B-S=8 and in the prob we are given that S=2B
3B-2B=8, B=2. S=2*8=16 sufficient
(2) S+8=1,5(B+8)
2S-3B=8, and S=2B
2*2B-3B=8, B=8, S=2*8=16 sufficient

[clock60]

if xy > 0, does (x - 1)(y - 1) = 1 ?
(1) x + y = xy
(2) x = y
my answer A
let us simplify given coondition
does (x-1)(y-1)=1. xy-x-y+1=1 does xy=x+y???
(1)the 1 st directly says xy=x+y sufficient
(2) x=y, if x=y=2 then 2*2=2+2
but if x=y=3 then 3+3=6, 3*3=9 as we have yes and no answers so insufficient
A

[clock60]

Is 5^k less than 1,000 ?
(1) 5^(k-1)<3000
(2) 5^(k-1)= [5^k] - 500
my answer is B
(1) 5^k<5*3000 not sufficient
(2) 5^k-(5^k)/5=500
5^k(5-1)=5*500
5^k=625
5^k=5^4
k=4 and 5^4<1000 so B

[clock60]

If p1 and p2 are the populations and r1 and r2 are the numbers of representatives of District 1 and District 2, respectively, the ratio of the population to the number of representatives is greater for which of the two districts ?
(1) p1 > p2
(2) r2 > r1
my pick for E
i guest we need to compare
r1/p1 and r2/p2
(1) insufficient
(2) insufficient
together insufficient
p1=10.p2=20 (p1>p2)
r2=2.r1=1 (r2>r1)
and 1/10=2/20 (equal)
p1=10, p2=15
r2=2,r1=1
and 1/10<2/15
so E

[clock60]

Is [(x-3)^2]^0.5=3-x ?
(1) x ≠ 3
(2) – x | x | > 0
the question asks is|x-3|=3-x
|x-3|=3-x if x<3 so the final question is x<3
(1) insufficient
(2) -x|x|>0
|x|>0 it means that -x must be>0 or -x>0, x<0
if x<0 it is less than 3 so B

[3Gs]

Hi ss1,

if xy > 0, does (x - 1)(y - 1) = 1 ?
(1) x + y = xy
(2) x = y

equation x=y holds true only for x = y = 2 e.g. not if x=y=3,4 etc so answer is A

[ss1]

thank you guys, they seem so simple now. can anyone answer this one:
dep from S: 7:08 EST (eastern standard time), arrival at T: 08:10
The table above shows the morning schedule for train X. If Juan took train X on Monday morning, did he arrive at station T on schedule?
(1) Juan arrived at station T on Monday morning 1 hour and 2 minutes after he left station S.
(2) Juan arrived at his office at 8:30 (EST) on Monday morning, which was 20 minutes after he arrived at station T.


and also the answer for this is C, and I get E as well.
If p1 and p2 are the populations and r1 and r2 are the numbers of representatives of District 1 and District 2, respectively, the ratio of the population to the number of representatives is greater for which of the two districts ?
(1) p1 > p2
(2) r2 > r1

[aarok]

Originally Posted by ss1

thank you guys, they seem so simple now. can anyone answer this one:
dep from S: 7:08 EST (eastern standard time), arrival at T: 08:10
The table above shows the morning schedule for train X. If Juan took train X on Monday morning, did he arrive at station T on schedule?
(1) Juan arrived at station T on Monday morning 1 hour and 2 minutes after he left station S.
(2) Juan arrived at his office at 8:30 (EST) on Monday morning, which was 20 minutes after he arrived at station T.


and also the answer for this is C, and I get E as well.
If p1 and p2 are the populations and r1 and r2 are the numbers of representatives of District 1 and District 2, respectively, the ratio of the population to the number of representatives is greater for which of the two districts ?
(1) p1 > p2
(2) r2 > r1

Well, you have a fraction p1/r1=p2/r2. if p1>p2 and r2>r1 we can conclude that p1/r1>p2/r2