Given that R is positive three-digit integer, what is the hundreds digit of R?
1. The hundreds digit of 3R is 8
2. (R+1) results in a number with the hundreds digit of 9.
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Hundreds digit of R?
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Statement 1:
Hundreds digit of 3R is 8.
THink of it this way 3*(some 3 digit numbers) = X8XX
Possible Cases;
3R can be between 801-897 (R between 267-299
(or) 3R can be between 1800 - 1899 (R between 600 - 633)
(or) 3R can be between 2802-2898 ( R between 934 - 966)
Hundreds place can be 2 or 6 or 9
Statement 2:
R+1 results in a number with hundreds digit 9.
The number can be 899 -> R+1 = 900
(or) 901 -> R+1 = 902 and so on.
the hundreds digit can be 8 (or) 9
Combined, we have only cases of 934-966 possible. So hundreds digit will be 9. C IMO
Hundreds digit of 3R is 8.
THink of it this way 3*(some 3 digit numbers) = X8XX
Possible Cases;
3R can be between 801-897 (R between 267-299
(or) 3R can be between 1800 - 1899 (R between 600 - 633)
(or) 3R can be between 2802-2898 ( R between 934 - 966)
Hundreds place can be 2 or 6 or 9
Statement 2:
R+1 results in a number with hundreds digit 9.
The number can be 899 -> R+1 = 900
(or) 901 -> R+1 = 902 and so on.
the hundreds digit can be 8 (or) 9
Combined, we have only cases of 934-966 possible. So hundreds digit will be 9. C IMO
Last edited by shankar.ashwin on Tue Nov 22, 2011 2:49 am, edited 1 time in total.
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Given that R is positive three-digit integer, what is the hundreds digit of R?
Let R = ABC => R = 100A + 10B + C
Let R = ABC => R = 100A + 10B + C
If the hundreds digit of 3R is 8, R can be 266<R<300 or 599<R<634 or 933<R<967 and the hundreds digit of R can be 2 or 5 or 91. The hundreds digit of 3R is 8
R = 899 or R = 9xx i.e. The hundreds digit of R can be 8 or 92. (R+1) results in a number with the hundreds digit of 9.
The hundreds digit is 9, Sufficient!From 1 and 2
Anil Gandham
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How did you so quickly find out the ranges? It took quite sometime for me to get that.shankar.ashwin wrote:Statement 1:
Hundreds digit of 3R is 8.
THink of it this way 3*(some 3 digit numbers) = X8XX
Possible Cases;
3R can be between 801-897 (R between 267-299
(or) 3R can be between 1800 - 1899 (R between 600 - 633)
(or) 3R can be between 2802-2898 ( R between 934 - 966)
Hundreds place can be 2 or 6 or 9
Statement 2:
R+1 results in a number with hundreds digit 9.
The number can be 899 -> R+1 = 900
(or) 901 -> R+1 = 902 and so on.
the hundreds digit can be 8 (or) 9
Combined, we have only cases of 934-966 possible. So hundreds digit will be 9. C IMO
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I am guessing you did it the same way I did, you're given R is a 3 digit number.gmatIntent wrote:
How did you so quickly find out the ranges? It took quite sometime for me to get that.
If R=1000, 3R = 3000.
So we are looking at options < 3000
Possible cases, 800-899 | 1800-1899 | 2800-2899
After this, we just need to divide the range by 3, since R is an integer chose 3R such that its a multiple of 3 (801 and not 800 and so on)
This is one of those questions in which you look at options and know its a C/E question, so immediately start using both statements together you can do it faster.
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Thanksshankar.ashwin wrote:I am guessing you did it the same way I did, you're given R is a 3 digit number.gmatIntent wrote:
How did you so quickly find out the ranges? It took quite sometime for me to get that.
If R=1000, 3R = 3000.
So we are looking at options < 3000
Possible cases, 800-899 | 1800-1899 | 2800-2899
After this, we just need to divide the range by 3, since R is an integer chose 3R such that its a multiple of 3 (801 and not 800 and so on)
This is one of those questions in which you look at options and know its a C/E question, so immediately start using both statements together you can do it faster.