The number of rooms at Hotel G is 10 less than twice the number of roo

Question

The number of rooms at Hotel G is 10 less than twice the number of rooms at Hotel H. If the total number of rooms at Hotel G and Hotel H is 425, what is the number of rooms at Hotel G?

(A) 140
(B) 180
(C) 200
(D) 240
(E) 280

Bunuel · Answer

SOLUTION

The number of rooms at Hotel G is 10 less than twice the number of rooms at Hotel H. If the total number of rooms at Hotel G and Hotel H is 425, what is the number of rooms at Hotel G?

(A) 140
(B) 180
(C) 200
(D) 240
(E) 280

The number of rooms at Hotel G is 10 less than twice the number of rooms at Hotel H --> G = 2H - 10;
The total number of rooms at Hotel G and Hotel His 425 --> G + H = 425.

Solving gives G = 280.

Answer: E.

nutshell · Answer

Let G be the no. of rooms at hotel G and H be the no. of rooms at hotel H.

G = 2H - 10;
G + H = 425; H = 425 - G;

Since we have to find G,
G = 2H - 10 = 2(425 - G) - 10 
G = 850 - 2G - 10;
3G = 840;
G = 840/3
G = 280;

Ans is (E).

CrackverbalGMAT · Answer

A very good contender for back solving. Let us start with option C.

Hotel G Hotel H Total
(A) 140
(B) 180
(C) 200 210/2 = 105 200 + 105 = 305
(D) 240
(E) 280

We were supposed to get 425 however we got 305 hence we should move down

Hotel G Hotel H Total
(A) 140
(B) 180
(C) 200 210/2 = 105 200 + 105 = 305
(D) 240
(E) 280 290/2 = 145 280 + 145 = 425 (BINGO!)

Pushpinder Gill

arunspanda · Answer

The solution looks very elegant.

Do you advise to start back solving from Option (E), since G/(G+H) is close to 2/3 or, the solution is approximately close to  2/3(425)

CrackverbalGMAT · Answer

I would advise you to start with option C and then move up or down according to the condition as the answer options are always in ascending or descending order.

WoundedTiger · Answer

The number of rooms at Hotel G is 10 less than twice the number of rooms at Hotel H. If the total number of rooms at Hotel G and Hotel His 425, what is the number of rooms at Hotel G?

(A) 140
(B) 180
(C) 200
(D) 240
(E) 280

Sol: Let no. of room in Hotel H be X. Then No. of rooms in Hotel G is 10 less than twice the no. of rooms at Hotel H i.e No. of rooms =2X-10
Given 
X+2X-10=425 or 3x=435 X=145---->No. of rooms in Hotel H
Hotel G = 2*145-10= 280 
Ans E

ScottTargetTestPrep · Answer

We can let the number of rooms in hotel G = g and the number of rooms in hotel H = h and create the two equations:

g = 2h - 10

and

g + h = 425

Substituting the first equation for g in the second equation, we have:

2h - 10 + h = 425

3h = 435

h = 145

So g = 2(145) - 10 = 280.

Answer: E

BrentGMATPrepNow · Answer

We can also solve the question using 1 variable

Let  x  = number of rooms at Hotel H

The number of rooms at Hotel G is 10 less than twice the number of rooms at Hotel H  
So,  2x - 10  = number of rooms at Hotel G

The total number of rooms at Hotel G and Hotel H is 425  
We can write:  x  + ( 2x - 10 ) = 425
Simplify: 3x - 10 = 425
Solve: x =  145

2x - 10  = number of rooms at Hotel G
So, the number of rooms at Hotel G = 2( 145 ) - 10
= 280

Answer: E

Cheers,
Brent

Kinshook · Answer

Given: 
1. The number of rooms at Hotel G is 10 less than twice the number of rooms at Hotel H.
2. The total number of rooms at Hotel G and Hotel H is 425

Asked: What is the number of rooms at Hotel G?

Let the number of rooms at hotel G be g and at hotel H be h.
g = 2h -10 ;  h = \frac{g+10}{2} . (1)
g + h = 425 (2)
 g + \frac{g + 10}{2} = 425 
3g + 10 = 850
g = 840/3 = 280

IMO E

totaltestprepNick · Answer

E https://www.youtube.com/watch?v=CJzOXSs2RTA Nick Slavkovich, GMAT/GRE tutor with 20+ years of experience tutoring@totaltestprep.net

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