Expand Messages
• A room has 50 lockers all closed. There are 50 people waiting outside the room.The first person goes in and opens all lockers,the second person goes in and
Message 1 of 4 , May 28, 2004
A room has 50 lockers all closed. There are 50 people waiting outside
the room.The first person goes in and opens all lockers,the second
person goes in and closes lockers which are multiple of 2,the third
person change the state of all the lockers which are multiple of 3,
till 50.How many lockers are closed ?

(a)32 (b) 25 (c) 43 (d) None of these.

• Suprovo, First of all the second person closes all the doors with even numbers on them ie (25 , Starting 2 and ending 50) State after 1st person comes out: 25
Message 2 of 4 , Jun 3, 2004
Suprovo,
First of all the second person closes all the doors with even numbers on them ie (25 , Starting 2 and ending 50)
State after 1st person comes out: 25 closed and 25 open

Next the third person changes the state of all with multiple of 3

Total number of doors divisible by 3 is 16 but this includes the ones divisible by 2 also... So got to check for the number of doors divisible by 6 (lcm of 2 and 3)
Number of doors divisible by 6 is 8
That leaves us with 8 doors that are only divisible by 3 and 8 that are also divisible by 2........

So 8 doors will be closed which are divisible by 3 and 8 doors will be again opened which were closed by the second person......(so 17 will remain closed).

Answer: 8+ 17 = 25 doors closed

Regards
Sabyasachi Sen
National Grid Transco Plc.
Tel: +91-40-55386000 Extn - 6312
Dial Comm: 7122204
Mobile: +91-40-32440560
-----Original Message-----
From: Suprovo Das [mailto:suprovo_2200@...]
Sent: Saturday, May 29, 2004 12:23 AM
To: ascent4cat@yahoogroups.com

A room has 50 lockers all closed. There are 50 people waiting outside
the room.The first person goes in and opens all lockers,the second
person goes in and closes lockers which are multiple of 2,the third
person change the state of all the lockers which are multiple of 3,
till 50.How many lockers are closed ?

(a)32 (b) 25 (c) 43 (d) None of these.

Ascent Education
An IIM Alumni Venture
Class for CAT, XAT, GRE, GMAT
http://www.ascenteducation.com

Archives of past CAT questions can be viewed at http://www.ascenteducation.com/india-mba/iim/cat/questionbank/questionbank.shtml

• Hi The answer would be 43 because there are only seven such nos which are perfect squares ie 1,4,9,16,25,36,49.So the Doors with these nos would be open as
Message 3 of 4 , Jun 4, 2004
Hi

The answer would be 43 because there are only seven such nos which
are perfect squares ie 1,4,9,16,25,36,49.So the Doors with these nos
would be open as they have odd no factors,rest all would be closed.

Konik Sood

--- In ascent4cat@yahoogroups.com, "Suprovo Das" <suprovo_2200@y...>
wrote:
> A room has 50 lockers all closed. There are 50 people waiting
outside
> the room.The first person goes in and opens all lockers,the second
> person goes in and closes lockers which are multiple of 2,the third
> person change the state of all the lockers which are multiple of 3,
> till 50.How many lockers are closed ?
>
> (a)32 (b) 25 (c) 43 (d) None of these.
>
>
• hi.. i think the answer is 43.. the logic i put in is that all the perfect squares will be open as they have odd no of factors.. for example: take door no 4
Message 4 of 4 , Sep 8, 2004
hi..

i think the answer is 43.. the logic i put in is that all the perfect squares will be open as they have odd no of factors.. for example: take door no 4  the door will be first open, close, open as it is divisible by 1, 2 and 4. Similarly, take 16 the door will be open, close, open, close, open as it is divisible by 1, 2, 4, 8 and 16.

Now lets take a number that is not a perfect square like 2 the door will be open, close as it is only divisible by 1, 2 .

The perfect squares upto 50 are 1,4,9,16,25,36,49.. i.e 7 so the no of doors closed will be 50-7= 43.

Sabyasachi Sen <sabyasachi.sen@...> wrote:
Suprovo,
First of all the second person closes all the doors with even numbers on them ie (25 , Starting 2 and ending 50)
State after 1st person comes out: 25 closed and 25 open

Next the third person changes the state of all with multiple of 3

Total number of doors divisible by 3 is 16 but this includes the ones divisible by 2 also... So got to check for the number of doors divisible by 6 (lcm of 2 and 3)
Number of doors divisible by 6 is 8
That leaves us with 8 doors that are only divisible by 3 and 8 that are also divisible by 2........

So 8 doors will be closed which are divisible by 3 and 8 doors will be again opened which were closed by the second person......(so 17 will remain closed).

Answer: 8+ 17 = 25 doors closed

Regards
Sabyasachi Sen
National Grid Transco Plc.
Tel: +91-40-55386000 Extn - 6312
Dial Comm: 7122204
Mobile: +91-40-32440560
-----Original Message-----
From: Suprovo Das [mailto:suprovo_2200@...]
Sent: Saturday, May 29, 2004 12:23 AM
To: ascent4cat@yahoogroups.com

A room has 50 lockers all closed. There are 50 people waiting outside
the room.The first person goes in and opens all lockers,the second
person goes in and closes lockers which are multiple of 2,the third
person change the state of all the lockers which are multiple of 3,
till 50.How many lockers are closed ?

(a)32 (b) 25 (c) 43 (d) None of these.

Ascent Education
An IIM Alumni Venture
Class for CAT, XAT, GRE, GMAT
http://www.ascenteducation.com

Archives of past CAT questions can be viewed at http://www.ascenteducation.com/india-mba/iim/cat/questionbank/questionbank.shtml

Ascent Education
An IIM Alumni Venture
Class for CAT, XAT, GRE, GMAT
http://www.ascenteducation.com

Archives of past CAT questions can be viewed at http://www.ascenteducation.com/india-mba/iim/cat/questionbank/questionbank.shtml

Do you Yahoo!?
Win 1 of 4,000 free domain names from Yahoo! Enter now.

Your message has been successfully submitted and would be delivered to recipients shortly.