need help on these questions

[queborg]

1

In the xy-plane, line n passes through the origin and has slope 4. If points (1, c) and (d, 2) are on line n, what is the value of c/d ?

A.0.25

B.0.5

C.2

D.4

E.8


2
The charge for a single room at Hotel P is 25 percent less than the charge for a single room at Hotel R and 10 percent less than the charge for a single room at Hotel G. The charge for a single room at Hotel R is what percent greater than the charge for a single room at Hotel G ?

A. 15%
B. 20%
C. 40%
D. 50%
E.150%

3
If d = 1 / 2^3 * 5^7 is expressed as a terminating decimal, how many nonzero digits will d have?

A.One
B.Two
C.Three
D.Seven
E.Ten

4 If M is the least common multiple of 90, 196, and 300, which of the following is NOT a factor of M ?

A. 600
B. 700
C. 900
D.2,100
E.4,900
thanks a ton

[onthego]

1)
y = mx + s (where m is the slope and s is constant)


y = 4x + s

0 = 4(0) + s (since this passes through origin)
=> s=0
y=4x is the equation

substituting values of 2 coordinates in this eq.
c=4(1) ----eq1
2=4(d)
=> d = 1/2 ----eq2

dividing eq1 and eq2
c/d=8


2)

Let rate in R = x
=> rate in P = .75x ----1

Let rate in G = y
=> rate in P = .9y ------2

equating 1 n 2
.75x=.9y
or x = 1.2 y
so rate in Hotel R is 20% more than G

[onthego]

3)

I am not sure if this d = 1 / 2^3 * 5^7 means d = 1 /( 2^3 * 5^7) or this means d = 5^7/ 2^3?

If its the first one.

1/(2^3 * 5^3 * 5^4)

1/(10^3*5^4)

multiplying num and den by 10^4
10^4/(10^7*5^4)

(10/5)^4/(10^7)

or 2^4/10^7
so it has 7 decimal digits


4) Finding LCM of 90, 196 and 300

=> 9 * 25 * 49 * 4
=> 9 * 49 * 100

so 600 is not a factor

[gmatcraze]

Originally Posted by onthego

3)

I am not sure if this d = 1 / 2^3 * 5^7 means d = 1 /( 2^3 * 5^7) or this means d = 5^7/ 2^3?

If its the first one.

1/(2^3 * 5^3 * 5^4)

1/(10^3*5^4)

multiplying num and den by 10^4
10^4/(10^7*5^4)

(10/5)^4/(10^7)

or 2^4/10^7
so it has 7 decimal digits

The question asks for non-zero digits, so how can we conclude that there are 7 decimal digits since these 7 digits are inclusive of zero? Isn't the answer 1?? What is the OA?

[shahdevine]

2.


Given:
P=.75R
P=.9G

Step 1: Set equations equal and find ratio of R to G

.75R=.9G
90/75=R/G
R/G=1.2/1

.2 equals excess that R is greater than G --> 20%

B

[chimerical]

Originally Posted by gmatcraze

The question asks for non-zero digits, so how can we conclude that there are 7 decimal digits since these 7 digits are inclusive of zero? Isn't the answer 1?? What is the OA?

It simplifies to 16/(10^7) so there should be two non-zero digits.

[gmatcraze]

Originally Posted by chimerical

It simplifies to 16/(10^7) so there should be two non-zero digits.

I agree, there should be two non-zero digits .... can somebody else also help to confirm on this solution. Thanks.

[winna.7]

agree with chimerical.. Solving , we get 16*10power-7 . so the answer should be 2..

[gmatcraze]

Originally Posted by onthego

3)


4) Finding LCM of 90, 196 and 300

=> 9 * 25 * 49 * 4
=> 9 * 49 * 100

so 600 is not a factor

How did you determine that 600 is not a factor ?

[gmataug08]

Originally Posted by gmatcraze

How did you determine that 600 is not a factor ?

LCM : 9 x 100 x 49

can be rephrased as 9 x 100 x 7 x 7 -> 700 is a valid factor

can be rephrased as 9 x 100 x 49 -> 900 is a valid factor

can be rephrased as 3 x 3 x 100 x 7 x 7 -> 2100 is a valid factor

can be rephrased as 9 x 100 x 49 -> 4900 is a valid factor

can't be rephrased similarly for 600 , hence 600 is the answer