Compare Quantity A and Quantity B, using additional information centered above the two quantities if such information is given, and select one of the following four answer choices:
(A) Quantity A is greater.
(B) Quantity B is greater.
(C) The two quantities are equal.
(D) The relationship cannot be determined from the information given.
(A) Quantity A is greater.
(B) Quantity B is greater.
(C) The two quantities are equal.
(D) The relationship cannot be determined from the information given.
N = 1323*1325*1327*1329
Quantity A : Rem[N/13] + 1
Quantity B : Rem[N/11]
where Rem[A/B] is defined as the remainder obtained when A is divided by B.
Correct Answer: C
Explanation
The solution to this question becomes very simple with the understanding of a simple concept involving remainders.
If N = x1 * x2 * x3 * ……… * xn
And if Rem[x1/k] = r1
Rem[x2/k] = r2 and so on…..
Then, Rem[N/k] = Rem[(r1 * r2 * r3* ………..* rn)/k]
This can be continued recursively until we are left with a single remainder.
Now, in this question, N = 1323*1325*1327*1329
Quantity A: k = 13
Therefore, Rem[1323/13] = 10
Rem[1325/13] = 12
Rem[1327/13] = 1
Rem[1329/13] = 3
Hence, Rem[N/13] = Rem[(10*12*1*3)/13]
= Rem[360/13]
= 9
Similarly, Quantity B: k = 11
Therefore, Rem[1323/11] = 3
Rem[1325/11] = 5
Rem[1327/11] = 7
Rem[1329/11] = 9
Hence, Rem[N/11] = Rem[(3*5*7*9)/11]
= Rem[945/11]
= 10
Or, to illustrate how this can be used recursively,
Rem[N/11] = Rem[(3*5*7*9)/11]
= Rem{[Rem(27/11)*Rem(35/11)]/11}
= Rem{[5*2]/11}
= Rem[10/11]
= 10