GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 13 Oct 2019, 20:25

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Adriana´s room contains N identical light bulbs with independent switc

Author Message
TAGS:

### Hide Tags

GMATH Teacher
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 935

### Show Tags

07 Feb 2019, 10:37
00:00

Difficulty:

55% (hard)

Question Stats:

52% (02:02) correct 48% (02:39) wrong based on 46 sessions

### HideShow timer Statistics

GMATH practice exercise (Quant Class 18)

Adriana´s room contains N identical light bulbs with independent switches, and this room is considered well lighted only if at least two of the light bulbs are switched on. If there are exactly 26 different ways to make Adriana´s room well lighted, what is the value of N?

(A) 4
(B) 5
(C) 6
(D) 7
(E) 8

_________________
Fabio Skilnik :: GMATH method creator (Math for the GMAT)
Our high-level "quant" preparation starts here: https://gmath.net
Manager
Joined: 05 Feb 2016
Posts: 168
Location: India
Concentration: General Management, Marketing
WE: Information Technology (Computer Software)

### Show Tags

07 Feb 2019, 11:42
fskilnik wrote:
GMATH practice exercise (Quant Class 18)

Adriana´s room contains N identical light bulbs with independent switches, and this room is considered well lighted only if at least two of the light bulbs are switched on. If there are exactly 26 different ways to make Adriana´s room well lighted, what is the value of N?

(A) 4
(B) 5
(C) 6
(D) 7
(E) 8

$$xC2+xC3+..+xCx=26$$
putting value 5
$$5C2+5C3+5C4+5C5=26$$
B
Director
Joined: 09 Mar 2018
Posts: 997
Location: India
Re: Adriana´s room contains N identical light bulbs with independent switc  [#permalink]

### Show Tags

07 Feb 2019, 11:58
fskilnik wrote:
GMATH practice exercise (Quant Class 18)

Adriana´s room contains N identical light bulbs with independent switches, and this room is considered well lighted only if at least two of the light bulbs are switched on. If there are exactly 26 different ways to make Adriana´s room well lighted, what is the value of N?

(A) 4
(B) 5
(C) 6
(D) 7
(E) 8

keyword: at least two of the light bulbs are switched on

We are given the total ways, we need to find the n => $$nC_x$$ = 26

$$xC_2 + xC_3 + xC_4$$ = 26

We can try back solving here, Only 5 works perfectly.

$$5C_2$$ +$$5C_3$$ + $$5C_4$$ + $$5C_5$$ = 26

B
_________________
If you notice any discrepancy in my reasoning, please let me know. Lets improve together.

Quote which i can relate to.
Many of life's failures happen with people who do not realize how close they were to success when they gave up.
GMATH Teacher
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 935
Re: Adriana´s room contains N identical light bulbs with independent switc  [#permalink]

### Show Tags

08 Feb 2019, 06:37
fskilnik wrote:
GMATH practice exercise (Quant Class 18)

Adriana´s room contains N identical light bulbs with independent switches, and this room is considered well lighted only if at least two of the light bulbs are switched on. If there are exactly 26 different ways to make Adriana´s room well lighted, what is the value of N?

(A) 4
(B) 5
(C) 6
(D) 7
(E) 8

Our "official solution" (similar to the previous contributions) is the following:

$$?\,\,\,:\,\,\,N \ge 4\,\,{\mathop{\rm int}} \,\,{\rm{such}}\,\,{\rm{that}}\,\,\,B\left( N \right) = 26\,,\,\,\,{\rm{where}}\,\,\,B\left( N \right) = C\left( {N,2} \right) + C\left( {N,3} \right) + \ldots + C\left( {N,N} \right)\,\,\,\,\,\,\,\left( * \right)$$

$$\left( {\rm{A}} \right)\,\,\,N = 4\,\,\,\,\, \Rightarrow \,\,\,\,B\left( 4 \right)\,\, = \,\,C\left( {4,2} \right) + C\left( {4,3} \right) + C\left( {4,4} \right)\,\, = \,\,{{4 \cdot 3} \over 2} + 4 + 1\,\, = \,\,11\,\,\,\,\,\,\,\left\langle {{\rm{NO}}} \right\rangle$$

$$\left( {\rm{B}} \right)\,\,\,N = 5\,\,\,\,\, \Rightarrow \,\,\,\,B\left( 5 \right)\,\, = \,\,C\left( {5,2} \right) + C\left( {5,3} \right) + C\left( {5,4} \right) + C\left( {5,5} \right)\,\, = \,\,2 \cdot \left( {{{5 \cdot 4 \cdot 3} \over {3 \cdot 2}}} \right) + 5 + 1\,\, = \,\,20 + 5 + 1\,\,\,\,\,\,\,\left\langle {{\rm{YES}}\,{\rm{!}}} \right\rangle$$

The correct answer is therefore (B).

We follow the notations and rationale taught in the GMATH method.

Regards,
Fabio.
_________________
Fabio Skilnik :: GMATH method creator (Math for the GMAT)
Our high-level "quant" preparation starts here: https://gmath.net
Intern
Joined: 24 Dec 2018
Posts: 34
Re: Adriana´s room contains N identical light bulbs with independent switc  [#permalink]

### Show Tags

05 May 2019, 11:32
Bunuel
Is there any conventional approach to this question (without plugging in)?
_________________
+1 Kudos if you like the Question
Re: Adriana´s room contains N identical light bulbs with independent switc   [#permalink] 05 May 2019, 11:32
Display posts from previous: Sort by