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Re: The number of rooms at Hotel G is 10 less than twice the number of roo [#permalink]
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Bunuel wrote:
The Official Guide For GMAT® Quantitative Review, 2ND Edition

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

Problem Solving
Question: 13
Category: Algebra Simultaneous equations
Page: 63
Difficulty: 600


GMAT Club is introducing a new project: The Official Guide For GMAT® Quantitative Review, 2ND Edition - Quantitative Questions Project

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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
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Re: The number of rooms at Hotel G is 10 less than twice the number of roo [#permalink]
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CrackVerbalGMAT wrote:
Bunuel wrote:
The Official Guide For GMAT® Quantitative Review, 2ND Edition

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

Problem Solving
Question: 13
Category: Algebra Simultaneous equations
Page: 63
Difficulty: 600


GMAT Club is introducing a new project: The Official Guide For GMAT® Quantitative Review, 2ND Edition - Quantitative Questions Project

Each week we'll be posting several questions from The Official Guide For GMAT® Quantitative Review, 2ND Edition and then after couple of days we'll provide Official Answer (OA) to them along with a slution.

We'll be glad if you participate in development of this project:
1. Please provide your solutions to the questions;
2. Please vote for the best solutions by pressing Kudos button;
3. Please vote for the questions themselves by pressing Kudos button;
4. Please share your views on difficulty level of the questions, so that we have most precise evaluation.

Thank you!



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


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 \(2/3(425)\)
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Re: The number of rooms at Hotel G is 10 less than twice the number of roo [#permalink]
arunspanda wrote:
CrackVerbalGMAT wrote:
Bunuel wrote:
The Official Guide For GMAT® Quantitative Review, 2ND Edition

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

Problem Solving
Question: 13
Category: Algebra Simultaneous equations
Page: 63
Difficulty: 600


GMAT Club is introducing a new project: The Official Guide For GMAT® Quantitative Review, 2ND Edition - Quantitative Questions Project

Each week we'll be posting several questions from The Official Guide For GMAT® Quantitative Review, 2ND Edition and then after couple of days we'll provide Official Answer (OA) to them along with a slution.

We'll be glad if you participate in development of this project:
1. Please provide your solutions to the questions;
2. Please vote for the best solutions by pressing Kudos button;
3. Please vote for the questions themselves by pressing Kudos button;
4. Please share your views on difficulty level of the questions, so that we have most precise evaluation.

Thank you!



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


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 \(2/3(425)\)


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.
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Re: The number of rooms at Hotel G is 10 less than twice the number of roo [#permalink]
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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
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Re: The number of rooms at Hotel G is 10 less than twice the number of roo [#permalink]
Expert Reply
Bunuel wrote:
The Official Guide For GMAT® Quantitative Review, 2ND Edition

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


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
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Re: The number of rooms at Hotel G is 10 less than twice the number of roo [#permalink]
Expert Reply
Top Contributor
Bunuel wrote:
The Official Guide For GMAT® Quantitative Review, 2ND Edition

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


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
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Re: The number of rooms at Hotel G is 10 less than twice the number of roo [#permalink]
Bunuel wrote:
The Official Guide For GMAT® Quantitative Review, 2ND Edition

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

Problem Solving
Question: 13
Category: Algebra Simultaneous equations
Page: 63
Difficulty: 600


GMAT Club is introducing a new project: The Official Guide For GMAT® Quantitative Review, 2ND Edition - Quantitative Questions Project

Each week we'll be posting several questions from The Official Guide For GMAT® Quantitative Review, 2ND Edition and then after couple of days we'll provide Official Answer (OA) to them along with a slution.

We'll be glad if you participate in development of this project:
1. Please provide your solutions to the questions;
2. Please vote for the best solutions by pressing Kudos button;
3. Please vote for the questions themselves by pressing Kudos button;
4. Please share your views on difficulty level of the questions, so that we have most precise evaluation.

Thank you!


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
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