What is the greatest number, which will divide 215, 167, and 135 so as to leave the same remainder in each case?
(A) 16
(B) 18
(C) 24
(D) 32
(E) 64
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sanju09
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ajith
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say r is the remainder and k is the numbersanju09 wrote:What is the greatest number, which will divide 215, 167, and 135 so as to leave the same remainder in each case?
(A) 16
(B) 18
(C) 24
(D) 32
(E) 64
215 = a*k +r
167 = b*k+ r
135 = c*k +r
(167-135) = (b-c)*k
32 = (b-c)*k
48 = (a-b)*k
80 = (a-c)*k
since k has to be the maximum k will be the LCM of 32,48 and 80 which is 16
A
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sanju09
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sure!ajith wrote:say r is the remainder and k is the numbersanju09 wrote:What is the greatest number, which will divide 215, 167, and 135 so as to leave the same remainder in each case?
(A) 16
(B) 18
(C) 24
(D) 32
(E) 64
215 = a*k +r
167 = b*k+ r
135 = c*k +r
(167-135) = (b-c)*k
32 = (b-c)*k
48 = (a-b)*k
80 = (a-c)*k
since k has to be the maximum k will be the LCM of 32,48 and 80 which is 16
A
: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
Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001
www.manyagroup.com
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rohan_vus
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I guess you meant you say GCF and not LCMajith wrote:say r is the remainder and k is the numbersanju09 wrote:What is the greatest number, which will divide 215, 167, and 135 so as to leave the same remainder in each case?
(A) 16
(B) 18
(C) 24
(D) 32
(E) 64
215 = a*k +r
167 = b*k+ r
135 = c*k +r
(167-135) = (b-c)*k
32 = (b-c)*k
48 = (a-b)*k
80 = (a-c)*k
since k has to be the maximum k will be the LCM of 32,48 and 80 which is 16
A
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ajith
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Thanks Rohan and Sanju, Yes Indeed! Thankfully it is just a name and I do not need to alter the calculationsrohan_vus wrote:
I guess you meant you say GCF and not LCM
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kstv
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What is the greatest number, which will divide 215, 167, and 135 so as to leave the same remainder in each case?
215 - 167 = 48
167- 135 = 32
G C F of 48 and 32 is 16
Similar to
Find the greatest number which will divide 25, 73 and 97 so as to leave the same remainder in each case.
(1) 12 (2) 18 (3) 24 (4) 32
215 - 167 = 48
167- 135 = 32
G C F of 48 and 32 is 16
Similar to
Find the greatest number which will divide 25, 73 and 97 so as to leave the same remainder in each case.
(1) 12 (2) 18 (3) 24 (4) 32
