Rationale: On dividing 165826 by 4 we get the remainder 2, so 2 should be subtracted
The answer: (B)
Question: Find the least number must be subtracted from 165826 so that remaining no.is divisible by 4?
Options:
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Reasoning: 125^10 = (5^3)^10 = 5^30
Ans: (E)
Question: What is the greatest positive integer x such that 5^x is a factor of 125^10?
Options:
(A) 5
(B) 9
(C) 10
(D) 20
(E) 30
Rationale: Final number = Initial number + 30%(original number) = 110 + 30%(110) = 110 + 33 = 143.
The answer: (A)
Question: A light has a rating of 110 watts, it is replaced with a new light that has 30% higher wattage. How many watts does the new light have?
Options:
(A) 143
(B) 145
(C) 156
(D) 134
(E) 100
Reasoning: Each group has 8 = 8+8+8 = 24 max
4 people are in 2 groups, subtract 4 people twice as they are counted twice
Each pair of groups has 5 in common, so in addition to the 4 people subtract 1 from each group
Ans: 8+8+8-(2(4)) - 3 = 13
Ans: (B)
Question: Each of three charities in Novel Grove Estates has 8 persons serving on its board of directors. If exactly 4 persons serve on 3 boards each and each pair of charities has 5 persons in common on their boards of directors, then how many distinct persons serve on one or more boards of directors?
A.
B.
C.
D.
E.
Options:
(A) 8
(B) 13
(C) 16
(D) 24
(E) 27
Rationale: 1/3: 1/6: 1/1 = 2:1:6
The answer: (C)
Question: The inverse ratio of 3: 6: 1 is?
Options:
(A) 2:3:7
(B) 2:3:9
(C) 2:1:6
(D) 2:3:6
(E) 2:3:1
Rationale: Distance traveled by Eddy = 900 km
Time taken by Eddy = 3 hours
Average speed of Eddy = 900/3 = 300 km/hour
Distance traveled by Freddy = 300 km
Time taken by Freddy = 4 hours
Average speed of Freddy = 300/4 = 75 km/hour
Ratio of average speed of Eddy to Freddy = 300/75 = 4/1
The answer: (D)

Question: Eddy and Freddy start simultaneously from city A and they travel to City B and City C respectively. Eddy takes 3 hours and Freddy takes 4 hours to complete the journey. If the distance between City A and City B is 900 kms and City A and City C is 300 kms. What is the ratio of their average speed of travel? (Eddy: Freddy)
Options:
(A) 8/3
(B) 3/8
(C) 8/5
(D) 4/1
(E) 5/3
Rationale: On dividing 165826 by 4 we get the remainder 2, so 2 should be subtracted
The answer: (B)
Question: Find the least number must be subtracted from 165826 so that remaining no.is divisible by 4?
Options:
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Reasoning: 125^10 = (5^3)^10 = 5^30
Ans: (E)
Question: What is the greatest positive integer x such that 5^x is a factor of 125^10?
Options:
(A) 5
(B) 9
(C) 10
(D) 20
(E) 30
Rationale: Final number = Initial number + 30%(original number) = 110 + 30%(110) = 110 + 33 = 143.
The answer: (A)
Question: A light has a rating of 110 watts, it is replaced with a new light that has 30% higher wattage. How many watts does the new light have?
Options:
(A) 143
(B) 145
(C) 156
(D) 134
(E) 100
Reasoning: Each group has 8 = 8+8+8 = 24 max
4 people are in 2 groups, subtract 4 people twice as they are counted twice
Each pair of groups has 5 in common, so in addition to the 4 people subtract 1 from each group
Ans: 8+8+8-(2(4)) - 3 = 13
Ans: (B)
Question: Each of three charities in Novel Grove Estates has 8 persons serving on its board of directors. If exactly 4 persons serve on 3 boards each and each pair of charities has 5 persons in common on their boards of directors, then how many distinct persons serve on one or more boards of directors?
A.
B.
C.
D.
E.
Options:
(A) 8
(B) 13
(C) 16
(D) 24
(E) 27
Rationale: 1/3: 1/6: 1/1 = 2:1:6
The answer: (C)
Question: The inverse ratio of 3: 6: 1 is?
Options:
(A) 2:3:7
(B) 2:3:9
(C) 2:1:6
(D) 2:3:6
(E) 2:3:1
Rationale: Distance traveled by Eddy = 900 km
Time taken by Eddy = 3 hours
Average speed of Eddy = 900/3 = 300 km/hour
Distance traveled by Freddy = 300 km
Time taken by Freddy = 4 hours
Average speed of Freddy = 300/4 = 75 km/hour
Ratio of average speed of Eddy to Freddy = 300/75 = 4/1
The answer: (D)

user
Question: Eddy and Freddy start simultaneously from city A and they travel to City B and City C respectively. Eddy takes 3 hours and Freddy takes 4 hours to complete the journey. If the distance between City A and City B is 900 kms and City A and City C is 300 kms. What is the ratio of their average speed of travel? (Eddy: Freddy)
Options:
(A) 8/3
(B) 3/8
(C) 8/5
(D) 4/1
(E) 5/3
assistant
Rationale: On dividing 165826 by 4 we get the remainder 2, so 2 should be subtracted
The answer: (B)
Question: Find the least number must be subtracted from 165826 so that remaining no.is divisible by 4?
Options:
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Reasoning: 125^10 = (5^3)^10 = 5^30
Ans: (E)
Question: What is the greatest positive integer x such that 5^x is a factor of 125^10?
Options:
(A) 5
(B) 9
(C) 10
(D) 20
(E) 30
Rationale: Final number = Initial number + 30%(original number) = 110 + 30%(110) = 110 + 33 = 143.
The answer: (A)
Question: A light has a rating of 110 watts, it is replaced with a new light that has 30% higher wattage. How many watts does the new light have?
Options:
(A) 143
(B) 145
(C) 156
(D) 134
(E) 100
Reasoning: Each group has 8 = 8+8+8 = 24 max
4 people are in 2 groups, subtract 4 people twice as they are counted twice
Each pair of groups has 5 in common, so in addition to the 4 people subtract 1 from each group
Ans: 8+8+8-(2(4)) - 3 = 13
Ans: (B)
Question: Each of three charities in Novel Grove Estates has 8 persons serving on its board of directors. If exactly 4 persons serve on 3 boards each and each pair of charities has 5 persons in common on their boards of directors, then how many distinct persons serve on one or more boards of directors?
A.
B.
C.
D.
E.
Options:
(A) 8
(B) 13
(C) 16
(D) 24
(E) 27
Rationale: 1/3: 1/6: 1/1 = 2:1:6
The answer: (C)
Question: The inverse ratio of 3: 6: 1 is?
Options:
(A) 2:3:7
(B) 2:3:9
(C) 2:1:6
(D) 2:3:6
(E) 2:3:1
Rationale: Distance traveled by Eddy = 900 km
Time taken by Eddy = 3 hours
Average speed of Eddy = 900/3 = 300 km/hour
Distance traveled by Freddy = 300 km
Time taken by Freddy = 4 hours
Average speed of Freddy = 300/4 = 75 km/hour
Ratio of average speed of Eddy to Freddy = 300/75 = 4/1
The answer: (D)

Question: Eddy and Freddy start simultaneously from city A and they travel to City B and City C respectively. Eddy takes 3 hours and Freddy takes 4 hours to complete the journey. If the distance between City A and City B is 900 kms and City A and City C is 300 kms. What is the ratio of their average speed of travel? (Eddy: Freddy)
Options:
(A) 8/3
(B) 3/8
(C) 8/5
(D) 4/1
(E) 5/3