GMAt Prac Probs PS
PS Solution from Forums 2
1. Positive integer n leaves a remainder of 4 after division by 6 and a remainder of 3 after division by 5. If n is greater than 30, what is the remainder that n leaves after division by 30?
(A) 3
(B) 12
(C) 18
(D) 22
(E) 28
How to approach this Problem?
Positive integer n leaves a remainder of 4 after division by 6 --> --> 4, 10, 16, 22, 28, ...
Positive integer n leaves a remainder of 3 after division by 5 --> --> 3, 8, 13, 18, 23, 28, ...
- we have 30 as lcm of 5 and 6 is 30 and we have 28 as the first common integer in the above patterns is 28.
Hence remainder when positive integer n is divided by 30 is 28.
Answer: E.
P.S. n>30 is a redundant information.
2. In the infinite sequence , , ,...., , each term after the first is equal to twice the previous term. If , what is the value of a_1?
A. 4
B. 24/7
C. 2
D. 12/7
E. 6/7 The formula for calculating term would be --> and ;
Given: --> --> .
Answer: E. This is clearly a geometric progression.
The nth term of a GP is given by a1*r(n-1) where r is the ratio between two successive terms
a5 = a1 2^(5-1) = a1 2^4 = 16a1 a2 = a1 2^(2-1) = a1 2^1 = 2a1
a5 - a2 = 12
16a1 - 2a1 = 12
14a1 = 12 a1 = 12/14 a1 = 6/7 Let the therefore, It is given that , that means: ; , therefore
Answer is E.
3 GMATPREP. Two dogsled teams raced across a 300 mile course in Wyoming. Team A finished the course in 3 fewer hours than team B. If team A's average speed was 5 mph greater than team B's, what was team B's average mph?
A. 12
B. 15
C. 18
D. 20
E. 25 Ans. D.-20.
4. 268. Working at their respective constant rates, machine A makes 100 copies in 12 minutes and machine B makes 100 copies in 15 minutes. If a number of x machine A and a number of y machine B work simultaneously at their respective rates for 2 hours, what is the total number of copies that they will produce?
(1) x = y.
(2) 5x + 4y = 90.
1. Positive integer n leaves a remainder of 4 after division by 6 and a remainder of 3 after division by 5. If n is greater than 30, what is the remainder that n leaves after division by 30?
(A) 3
(B) 12
(C) 18
(D) 22
(E) 28
How to approach this Problem?
Positive integer n leaves a remainder of 4 after division by 6 --> --> 4, 10, 16, 22, 28, ...
Positive integer n leaves a remainder of 3 after division by 5 --> --> 3, 8, 13, 18, 23, 28, ...
- we have 30 as lcm of 5 and 6 is 30 and we have 28 as the first common integer in the above patterns is 28.
Hence remainder when positive integer n is divided by 30 is 28.
Answer: E.
P.S. n>30 is a redundant information.
2. In the infinite sequence , , ,...., , each term after the first is equal to twice the previous term. If , what is the value of a_1?
A. 4
B. 24/7
C. 2
D. 12/7
E. 6/7 The formula for calculating term would be --> and ;
Given: --> --> .
Answer: E. This is clearly a geometric progression.
The nth term of a GP is given by a1*r(n-1) where r is the ratio between two successive terms
a5 = a1 2^(5-1) = a1 2^4 = 16a1 a2 = a1 2^(2-1) = a1 2^1 = 2a1
a5 - a2 = 12
16a1 - 2a1 = 12
14a1 = 12 a1 = 12/14 a1 = 6/7 Let the therefore, It is given that , that means: ; , therefore
Answer is E.
3 GMATPREP. Two dogsled teams raced across a 300 mile course in Wyoming. Team A finished the course in 3 fewer hours than team B. If team A's average speed was 5 mph greater than team B's, what was team B's average mph?
A. 12
B. 15
C. 18
D. 20
E. 25 Ans. D.-20.
4. 268. Working at their respective constant rates, machine A makes 100 copies in 12 minutes and machine B makes 100 copies in 15 minutes. If a number of x machine A and a number of y machine B work simultaneously at their respective rates for 2 hours, what is the total number of copies that they will produce?
(1) x = y.
(2) 5x + 4y = 90.