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STAT1+STAT2： there are two approaches
1. Write the values of t from stat1 and then from stat2 and then take the common values
From STAT1 t = 1,5,9,13,17,21,25,29,33
From STAT2 t = 1,4,7,10,13,16,19,22,25,28,31,34
Common values are t = 1,13,25,
2. Equate t = 4k+1 to t=3s+1
We have 4k + 1 = 3s+1
k = 3s/4
since, k is an integer so only those values of s which are multiple of 4 will satisfy both STAT1 and STAT2
so, common values are given by t = 3s + 1 where s is multiple of 4
so t = 1,13,25 (for s=0,4,8 respectively)
Clearly we cannot find a unique reminder when t is divided by 5 as in some cases (t=1) we are getting the reminder as 1 and in some(t=10) we are getting the reminder as 0.
So, INSUFFICIENT
So, answer will be E
Example 2：If p and n are positive integers and p > n, what is the remainder when p^2 - n^2 is divided by 15 ?
(1) The remainder when p + n is divided by 5 is 1.
(2) The remainder when p - n is divided by 3 is 1
Sol:
STAT1 : The remainder when p + n is divided by 5 is 1.
p+n = 5k + 1
but we cannot say anything about p^2 - n^2 just from this information.
So, INSUFFICIENT
STAT2 : The remainder when p - n is divided by 3 is 1
p-n = 3s + 1
but we cannot say anything about p^2 - n^2 just from this information.
So, INSUFFICIENT
STAT1+STAT2：
p^2 - n^2 = (p+n) * (p-n) = (5k + 1) * (3s + 1)= 15ks + 5k + 3s + 1
The reminder of the above expression by 15 is same as the reminder of 5k + 3s + 1 with 15 as 15ks will go with 15.
But we cannot say anything about the reminder as its value will change with the values of k and s.
So INSUFFICIENT
Hence answer will be E
Example 3：If n is a positive integer and r is the remainder when 4 +7n is divided by 3, what is the value of r?
(1) n+1 is divisible by 3
(2) n>20.
Sol:
r is the remainder when 4 + 7n is divided by 3
7n + 4 can we written as 6n + n + 3+ 1 = 3(2n+1) + n +1
reminder of 7n+4 by 3 will be same as reminder of 3(2n+1) +n +1 by 3
3*(2n+1) will go by 3 so the reminder will be the same as the reminder of (n+1) by 3.
STAT1: n+1 is divisible by 3
n+1 = 3k (where k is an integer)
n+1 will give 0 as the reminder when divided by 3
so, 7n+4 will also give 0 as the reminder when its divided by 3 (as its reminder is same as the reminder for (n+1) when divided by 3 => r =0
So, SUFFICIENT
STAT2: n>20.
we cannot do anything by this information as there are many values of n
so, INSUFFICIENT.
Hence, answer will be A
Practice: If x is an integer, is x between 27 and 54?
(1) The remainder when x is divided by 7 is 2.
(2) The remainder when x is divided by 3 is 2.
Sol:
STAT1: The remainder when x is divided by 7 is 2.
x = 7k + 2
Possible values of x are 2,9,16,...,51,...
we cannot say anything about the values of x
so, INSUFFICIENT
STAT2: The remainder when x is divided by 3 is 2.
x = 3s + 2
Possible values of x are 2,5,8,11,...,53,...
we cannot say anything about the values of x
so, INSUFFICIENT
希望以上为大家分享的GMAT数学考点及练习题目分享【英文版】能够对大家有帮助。
