between 10^6 and 10^7

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sanju09: GMAT Instructor; Posts: 3650; Joined: Wed Jan 21, 2009 4:27 am; Location: India; Thanked: 267 times; Followed by:80 members; GMAT Score:760

between 10^6 and 10^7

by sanju09 » Tue Feb 24, 2009 4:52 am

How many different positive integers exist between 10^6 and 10^7, the sum of whose digits is equal to 2?

A. 6
B. 7
C. 5
D. 8
E. 18

The mind is everything. What you think you become. -Lord Buddha

Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001

www.manyagroup.com

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Source: Beat The GMAT — Problem Solving | Tue Feb 24, 2009 4:52 am

sureshbala: Master | Next Rank: 500 Posts; Posts: 319; Joined: Wed Feb 04, 2009 10:32 am; Location: Delhi; Thanked: 84 times; Followed by:9 members

by sureshbala » Tue Feb 24, 2009 5:24 am

Clearly the number must be a 7 digit number only.

Fixing the first digit as, we can place another 1 in any of the other 6 places available. So we have 6 numbers in this case.

The other possible number is 2 followed by six 0's. (this is what most of you miss out in the exam)

Hence totally 7 numbers are possible.

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DanaJ: Site Admin; Posts: 2567; Joined: Thu Jan 01, 2009 10:05 am; Thanked: 712 times; Followed by:550 members; GMAT Score:770

by DanaJ » Tue Feb 24, 2009 5:36 am

sureshbala wrote:Clearly the number must be a 7 digit number only.

Fixing the first digit as 1, we can place another 1 in any of the other 6 places available. So we have 6 numbers in this case.

The other possible number is 2 followed by six 0's. (this is what most of you miss out in the exam)

Hence totally 7 numbers are possible.

You missed 1.

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sanju09: GMAT Instructor; Posts: 3650; Joined: Wed Jan 21, 2009 4:27 am; Location: India; Thanked: 267 times; Followed by:80 members; GMAT Score:760

by sanju09 » Tue Feb 24, 2009 5:41 am

DanaJ wrote:
sureshbala wrote:Clearly the number must be a 7 digit number only.

Fixing the first digit as 1, we can place another 1 in any of the other 6 places available. So we have 6 numbers in this case.

The other possible number is 2 followed by six 0's. (this is what most of you miss out in the exam)

Hence totally 7 numbers are possible.
You missed 1.

Where, DanaJ?

The mind is everything. What you think you become. -Lord Buddha

Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001

www.manyagroup.com

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ven4gmat: Junior | Next Rank: 30 Posts; Posts: 29; Joined: Sun Feb 08, 2009 11:29 am; Thanked: 3 times

by ven4gmat » Tue Feb 24, 2009 5:43 am

DanaJ wrote:
sureshbala wrote:Clearly the number must be a 7 digit number only.

Fixing the first digit as 1, we can place another 1 in any of the other 6 places available. So we have 6 numbers in this case.

The other possible number is 2 followed by six 0's. (this is what most of you miss out in the exam)

Hence totally 7 numbers are possible.
You missed 1.

I am sure he did not miss any number. We cannot have more than 7 numbers...Can you provide your logic please

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DanaJ: Site Admin; Posts: 2567; Joined: Thu Jan 01, 2009 10:05 am; Thanked: 712 times; Followed by:550 members; GMAT Score:770

by DanaJ » Tue Feb 24, 2009 5:48 am

:))
Really funny, guys... I was saying that he missed "1" in row 2 of his explanation..... You guys thought I was talking about another number...

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sanju09: GMAT Instructor; Posts: 3650; Joined: Wed Jan 21, 2009 4:27 am; Location: India; Thanked: 267 times; Followed by:80 members; GMAT Score:760

by sanju09 » Tue Feb 24, 2009 5:53 am

DanaJ wrote:)
Really funny, guys... I was saying that he missed "1" in row 2 of his explanation..... You guys thought I was talking about another number...

O I C

The mind is everything. What you think you become. -Lord Buddha

Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001

www.manyagroup.com

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