Tough knewton DS

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bblast: Legendary Member; Posts: 1077; Joined: Mon Dec 13, 2010 1:44 amFollowed by: 33 members; Thanked: 118 times; GMAT Score:710

by bblast » Fri Aug 12, 2011 9:27 am

For the four-digit number A,BCD, where A, B, C, and D all represent unique digits, what is the value of B?

1>A,BCD rounded to the nearest hundred is C,D00.
2>B > C + D

A

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Source: Beat The GMAT — Data Sufficiency | Fri Aug 12, 2011 9:27 am

Frankenstein: Legendary Member; Posts: 1448; Joined: Tue May 17, 2011 9:55 amFollowed by: 53 members; Location: India; Thanked: 375 times

by Frankenstein » Fri Aug 12, 2011 9:45 am

Hi,
From(1):
if cd < 50, abcd when round to nearest 100 will be ab00, which is given as cd00. So, a=c and b=d.
But, it is not possible because a,b,c,d are distinct.
if cd>=50, abcd when rounded (ab+1)00
So, ab+1 = cd
As a cannot be equal to c, c should be a+1.
For this to happen, b should be 9.
sufficient
From(2):
b>c+d
Not sufficient

Hence, A

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mak_mak_mak: Newbie | Next Rank: 10 Posts; Posts: 8; Joined: Wed Apr 07, 2010 11:06 am

by mak_mak_mak » Sat Aug 13, 2011 5:06 am

Hi frankenstein,
I dint really understand this solution.
Can you please elaborate ?

Regards,
Mustu

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Frankenstein: Legendary Member; Posts: 1448; Joined: Tue May 17, 2011 9:55 amFollowed by: 53 members; Location: India; Thanked: 375 times

by Frankenstein » Sat Aug 13, 2011 5:19 am

mak_mak_mak wrote:Hi frankenstein,
I dint really understand this solution.
Can you please elaborate ?

Regards,
Mustu

Hi,
Could you point out where you had problem. Anyway, I think it will be easy to understand if we can use some examples.
Consider: abcd = 4856. So, a=4,b=8,c=5,d=6.
When rounder off to nearest 100 it will be come 4900. So, cd00 = 4900 i.e. c=4,d=9.
In this case, a=4, c=4. But, given that a,b,c,d are all distinct integers. So, this doesn't work
Consider ab = 48, when abcd rounded off the first 2 digits will be become 49, which is 1 greater than 48. So, in most cases the first digit(4) remains same when 1 is added.
The only case in which this first digit changes is when the second digit is 9.
For example, consider 4956. When rounded of it becomes 5000
Here a=4, c=5.
So, only when b=9, ab when added by 1 will give a number whose first digit(c) is different from 'a'.

A better example would be abcd = 5960, which when rounded to nearest hundred becomes 6000(cd00).

Last edited by Frankenstein on Sat Aug 13, 2011 6:41 am, edited 1 time in total.

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GmatKiss: Legendary Member; Posts: 2789; Joined: Tue Jul 26, 2011 12:19 amFollowed by: 43 members; Location: Chennai, India; Thanked: 206 times; GMAT Score:640

by GmatKiss » Sat Aug 13, 2011 6:33 am

what is the value of 4789 when rounded to nearest 100 ?

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bblast: Legendary Member; Posts: 1077; Joined: Mon Dec 13, 2010 1:44 amFollowed by: 33 members; Thanked: 118 times; GMAT Score:710

by bblast » Sat Aug 13, 2011 7:24 am

GmatKiss wrote:what is the value of 4789 when rounded to nearest 100 ?

4800

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GmatKiss: Legendary Member; Posts: 2789; Joined: Tue Jul 26, 2011 12:19 amFollowed by: 43 members; Location: Chennai, India; Thanked: 206 times; GMAT Score:640

by GmatKiss » Sat Aug 13, 2011 8:04 am

so now the value of B becomes 8, and not 9 all the time rite!
Please correct me if am wrong!

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Frankenstein: Legendary Member; Posts: 1448; Joined: Tue May 17, 2011 9:55 amFollowed by: 53 members; Location: India; Thanked: 375 times

by Frankenstein » Sat Aug 13, 2011 8:19 am

GmatKiss wrote:so now the value of B becomes 8, and not 9 all the time rite!
Please correct me if am wrong!

Well, 4789 not a valid example for a number that satisfies the condition:
A,BCD rounded to the nearest hundred is C,D00.

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saketk: Legendary Member; Posts: 608; Joined: Sun Jun 19, 2011 11:16 amFollowed by: 8 members; Thanked: 37 times

by saketk » Sun Aug 14, 2011 10:59 am

=
Hi,

For example, consider 4956. When rounded of it becomes 5000
Here a=4, c=5.
So, only when b=9, ab when added by 1 will give a number whose first digit(c) is different from 'a'.

A better example would be abcd = 5960, which when rounded to nearest hundred becomes 6000(cd00).

4956 (a=4, b=9, c= 5, d= 6) -- when rounded becomes 5000 (format should be CD00). This means now the value of D has changed to 0. Which is wrong.The original value of D is 6.

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Frankenstein: Legendary Member; Posts: 1448; Joined: Tue May 17, 2011 9:55 amFollowed by: 53 members; Location: India; Thanked: 375 times

by Frankenstein » Sun Aug 14, 2011 6:16 pm

saketk wrote: 4956 (a=4, b=9, c= 5, d= 6) -- when rounded becomes 5000 (format should be CD00). This means now the value of D has changed to 0. Which is wrong.The original value of D is 6.

Hi,
I have used that example because someone asked me to explain why b should be 9. Yes, that is not an apt example for the given number. The emphasis was only about the first two digits and the only way 'a' changes when rounded off. So, I have even clearly stated a better example that satisfies all conditions of the question. If you have missed it, you can find it.

A better example would be abcd = 5960, which when rounded to nearest hundred becomes 6000(cd00).

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karthikpandian19: Legendary Member; Posts: 1665; Joined: Thu Nov 03, 2011 7:04 pmFollowed by: 70 members; Thanked: 165 times

by karthikpandian19 » Sat Jun 09, 2012 6:06 am

A simple explanation for this question is:

Statement 1:
ABCD is a 4 digit number when rounded to nearest hundred is CD00. From this observe, that the A (THOUSAND place) is changed which can happen only when B (HUNDRED place) is rounded from value 9. Clearcut....so Statement 1 is sufficient.

Statement 2:
B>C+D, from this equation there are many answers for B, hence not sufficient

So answer is A

bblast wrote:For the four-digit number A,BCD, where A, B, C, and D all represent unique digits, what is the value of B?

1>A,BCD rounded to the nearest hundred is C,D00.
2>B > C + D

A

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ronnie1985: Legendary Member; Posts: 626; Joined: Fri Dec 23, 2011 2:50 amFollowed by: 10 members; Location: Ahmedabad; Thanked: 31 times

by ronnie1985 » Sat Jun 09, 2012 10:15 am

God explanation by bblast

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