Problem Solving

[GMAT math practice question]

What is the remainder when the product of the first 10 prime numbers is divided by 4?

A. 0
B. 1
C. 2
D. 3
E. not defined

What is the remainder when 30 is divided by 4?

One approach:
1. Break the dividend 30 into factors: 30 = 5*6
2. Divide the divisor 4 into each factor: 5/4 = 1 R1, 6/4 = 1 R2
3. Multiple the resulting remainders: 1*2 = 2

Step 3 indicates that 30 divided by 4 will yield a remainder of 2.
This approach can be applied to any problem that asks for the remainder when a large integer or product is divided by a divisor.
Repeat the 3 steps until the value yielded by Step 3 is less than the divisor.

Max@Math Revolution wrote:[GMAT math practice question]

What is the remainder when the product of the first 10 prime numbers is divided by 4?

A. 0
B. 1
C. 2
D. 3
E. not defined

Product of the first 10 prime numbers = 2*3*5*7*11*13*17*19*23*29

Dividing 4 into each of the prime factors above yields the following remainders:
2*3*1*3*3*1*1*3*3*1 = 6*9*9

Dividing 4 into each of the factors in red yields the following remainders:
2*1*1 = 2

Since the result in blue is less than the divisor of 4, the desired remainder is 2.

The correct answer is C.

=>

2, 3, 5, 7, 11, 13, 17, 19, 23 and 29 are the first 10 prime numbers.
Of these, only 2 is an even integer. Their product is an even number, but it is not divisible by 4.
Thus, the product has remainder 2 when it is divided by 4.

Therefore, C is the answer.
Answer: C