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If a positive integer m is divided by d, the remainder is 5 MEANS m=dq+5
(1) When \(\frac{m}{3}\) is divided by d, the remainder is 15. So, \(\frac{m}{3}=xd+15.....m=3xd+45\) equating values of m....\(dq+5=3xd+45.......d(q-3x)=40\). All of the variables are integers, so d and q-3x must be factors of 40, and should have their product as 40. So, d can be any factor of 40 but greater than 15 as we know remainder in one case is 15.. Thus d can be 20 or 40
Re: If a positive integer m is divided by d, the remainder is 5. What is
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10 Dec 2019, 03:27
Unsure of my answer but here goes my reasoning.
Question statement analysis gives
m = kd + 5 where k is an integer greater than or equal to 0. Since divisor is alway greater than the remainder, d > 5.
Statement 1 analysis: (m/3)/d = qd + 15
Dividing "m/3" by d is same as multiplying m/3 by 1/d. Thus the statement tells us that "m" divided by "3d" gives a remainder of 15. Again, since divisor is greater than the remainder, the above statement implies 3d>15 which means d>5.
We already knew this from the question statement analysis. Thus, statement 1 is insufficient.
Statement 2 analysis:
D>20
No info on m or d hence insufficient.
Combining statement 1 & 2 gives us no new information about either m or the range of d except that d>20. Thus we can deduce no concrete value of d. Insufficient.
If a positive integer m is divided by d, the remainder is 5. What is
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10 Dec 2019, 03:35
1
ronak1003 wrote:
Unsure of my answer but here goes my reasoning.
Question statement analysis gives
m = kd + 5 where k is an integer greater than or equal to 0. Since divisor is alway greater than the remainder, d > 5.
Statement 1 analysis: (m/3)/d = qd + 15
Dividing "m/3" by d is same as multiplying m/3 by 1/d. Thus the statement tells us that "m" divided by "3d" gives a remainder of 15. Again, since divisor is greater than the remainder, the above statement implies 3d>15 which means d>5.
We already knew this from the question statement analysis. Thus, statement 1 is insufficient.
Statement 2 analysis:
D>20
No info on m or d hence insufficient.
Combining statement 1 & 2 gives us no new information about either m or the range of d except that d>20. Thus we can deduce no concrete value of d. Insufficient.
The answer is E
You are wrong in the highlighted portion.. say m=45 and d=20.. 45 divided by 20 gives 5 as remainder Now 45/3 or 15 divided by 20 will give remainder as 15. BUT m divided by 3d, that is 45 divided by 3*20 or 60 will give 45 as remainder. so m/3 divided by d and m divided by 3d are different when you are checking the remainders
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If a positive integer m is divided by d, the remainder is 5. What is
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12 Jan 2020, 08:22
m/d = R(5 ) means d>5 and m = d.x + 5 , where x is any integer
1. let m/3 be y ---> y = d.p + 15 where p is any integer . Also , note that d>15 otherwise we cant generate remainder of 15. substitute from stem the value of m
---> dx + 5 = 3dp + 45 d = 40 / ( x- 3p )
Now lets find some values of d so that we can prove this statement insufficient. x = 4 p = 1 so, d = 40 x = 5 p= 1 so, d = 20 Hence , insufficient B--> insufficient
Combined
d = 40 only Sufficient
gmatclubot
If a positive integer m is divided by d, the remainder is 5. What is
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12 Jan 2020, 08:22
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