RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: A survey of n people in the town of Eros found that 50% of them preferred Brand A. Another survey of 150 people in the town of Angie found that 60% preferred Brand A. In total, 55% of all the people surveyed together preferred Brand A. What is the total number of people surveyed?
A.50
B.100
C.150
D.300
Answer: D.300
Explanation: It is simply a weighted average question. Since the given average of 50% and 60% is 55% (right in the middle), it means the number of people surveyed in Eros (n) is same as the number of people surveyed in Angie.
So n = 150
Total = 150 + 150 = 300
Answer (D)
Question: What is the are of an equilateral triangle of side 16 cm?
A.63√6 cm2
B.64√4 cm2
C.64√3 cm2
D.62√3 cm2
Answer: D.62√3 cm2
Explanation: Area of an equilateral triangle
= √3/4 S2
If S = 16, Area of triangle
= √3/4 * 16 * 16
= 64√3 cm2;
Answer:D
Question: The length of a train and that of a platform are equal. If with a speed of 90 k/hr, the train crosses the platform in one minute, then the length of the train (in meters) is?
A.288
B.277
C.208
D.750
Answer: D.750
Explanation: Speed = [90 * 5/18] m/sec = 25 m/sec; Time = 1 min. = 60 sec.
Let the length of the train and that of the platform be x meters.
Then, 2x/60 = 25 è x = 25 * 60 / 2 = 750
Answer:D
Question: If the sides of a cube are in the ratio 4:3. What is the ratio of their diagonals?
A.4:3
B.4:0
C.3:3
D.4:6
Answer: A.4:3
Explanation: a1:a2 = 4:3
d1:d2 = 4:3
Answer: A
Question: A family consists of grandparents, parents and three grand children. The average age of the grandparents is 67 years, that of the parents is 40 years and that of the grandchildren is 6 years. What is the average age of the family?
A.28 4â„7 years
B.31 5â„7 years
C.33 1â„7 years
D.27 1â„2 years
Answer: C.33 1â„7 years
Explanation: Required average = (67Ã—2+40Ã—2+6Ã—3/2+2+3)
=232/7
= 33 1â„7 years
Answer C
Question: 80% of the population of a village is 64000. The total population of the village is?
A.26799
B.24000
C.80000
D.29973
Answer: C.80000
Explanation: X * (80/100) = 64000
X = 800 * 100
X = 80000
Answer: C
Question: In the xy-plane, a line has slope 5 and x-intercept 3. What is the y-intercept of the line?
A.-15
B.-3
C.0
D.3
Answer: A.-15
Explanation: Let the line be represented by a general equation y=mx+b, where m = slope (5) and b=y intercept. We are also given the value of x-intercept 3.
Theory : y intercept represents the point on the line where the x=0, and x intercept represents the point on the line where the y=0.
Putting these values in the equation : 0 = 5*3 + b => b = -15. Hence A.
Question: What is the greatest prime factor of 1+2+3+。。。+60?
A.59
B.61
C.31
D.37
Answer: B.61
Explanation: find the sum from direct formula = n(n+1)/2 = 60(60+1)/2 = 30*61...
61 is a PRIME number, so ans is 61..
B is the answer
Question: Three dice are rolled. The number of possible outcomes in which at least one dice shows 5 is
A.215
B.36
C.125
D.91
Answer: D.91
Explanation: Required number of possible outcomes
= Total number of possible outcomes – Number of possible outcomes in which 5 does not appear on any dice. (hence 5 possibilities in each throw)
= 6(3) – 5(3) = 216 – 125 = 91
Answer D
Question: S is the set of all fractions defined by the formula n/(n + 1), where n is a positive integer less than 20. What is the product V of all the fractions that are in S?
A.1) 1/20
B.2) 1/21
C.3) 1/2
D.4) 19/40
Answer: A.1) 1/20
Explanation: 1/2 * 2/3 * 3/4 * ... 19/20
= 1/20
Answer - A
Question: A trader has 50 kg of pulses, part of which he sells at 14% profit and rest at 6% loss. On the whole his loss is 4%. How much quantity is sold at 14% profit and that at 6% loss?
A.5 kg, 45 kg
B.15 kg, 35 kg
C.10kg, 40 kg
D.None of these
Answer: A.5 kg, 45 kg
Explanation: Solution:
ratio of quantity sold at 14% profit and 6% loss,
= 2:18 = 1:9
Hence, pulses sold at 14% profit,
= (50*1)/10 = 5 kg
At 6% Wheat sold at loss = 45 kg.
Answer: Option A
Question: A,B and C can do a piece of work in 6,8 and 12 days respectively. In how many days would all of them complete the same job together?
A.5 2/3 days.
B.3 2/3 days.
C.2 2/3 days.
D.4 2/3 days.
Answer: C.2 2/3 days.
Explanation: Explanation:
A,B and C can do the work in 6,8 and 12 days respectively. Therefore,
part done by A in 1 day =1/6
part done by B in 1 day = 1/8
part done by C in 1 day = 1/12
part done by A,B and C in 1 day = 1/6+1/8+1/12
=9/24
Net job can be done by A,B,C together in 1 day =24/9 =2 2/3 days.
Answer: Option C
Question: A football team plays games only against the other five teams in its league and always in the following order: Smith, Jones, Glen, Fader, and Gary . If the team’s final game of the season is against Fader, which of the following could be the number of games in the team’s schedule?
A.18
B.52
C.24
D.72
Answer: C.24
Explanation: IMO 'C' is the answer.
Matches will be in multiples of 5x+4. The answer that satisfies this condition is C
Question: If a monkey can climb 6 meter & slip down 3 meter in alternate minutes, than how much time can be taken by the monkey to climb up to a height of 60 meter.
A.36 min
B.37 min
C.38 min
D.39 min
Answer: B.37 min
Explanation: In 1st min it climb 6m and in 2nd min it slips 3m,
so it final displacement is 3m in 2min.
now for 51m it has taken 34 min.
in 35 min it goes to 57m.
in 36 min come down to 54 m.
in 37 min it goes to 60
ANSWER:B
Question: Kiran travels from A to B by car and returns from B to A by cycle in 7 hours. If he travels both ways by car he saves 3 hours. What is the time taken to cover both ways by cycle?
A.10 hours
B.17 hours
C.19 hours
D.16 hours
Answer: A.10 hours
Explanation: Let the time taken to cover from A to B in car and cycle be x hours and y hours respectively.
x + y = 7 --- (1) ; 2x = 4 --- (2)
solving both the equations, we get y = 5
So, time taken to cover both ways by cycle = 2y hours = 10 hours.
Answer: A
Question: The value of 99^(95/99) x 99 is:
A.9989
B.9896
C.9890
D.9809
Answer: B.9896
Explanation: (100 – 4/99) x 99 = 9900 – 4
= 9896.
ANSWER:B
Question: A man can row his boat with the stream at 6 km/h and against the stream in 4 km/h. The man's rate is?
A.1 kmph
B.6 kmph
C.8 kmph
D.9 kmph
Answer: A.1 kmph
Explanation: DS = 6
US = 4
S = ?
S = (6 - 4)/2 = 1 kmph
Answer: A
Question: A company has a hierarchical system where for every 10 workers, there is one team lead, and for every 3 teams leads, there is one supervisor. If the company has 13 supervisors, how many workers does it have?
A.140
B.321
C.390
D.500
Answer: C.390
Explanation: Some students may initially answer 130 to this question, especially if answering similar problems. However, that would be incorrect, as this is not a straight-forward ratio of 1:3:10.
The ratio of supervisors to team leads is 1:3, and the ratio of team leads to workers is 1:10. Therefore, the ratio of supervisors to workers is 1:30.
Therefore, 13*30=390
Answer: C)
Question: A car covers a distance of 180 km in 10 hrs. What is its speed in mps.
A.40 m/s
B.5 m/s
C.20 m/s
D.15 m/s
Answer: B.5 m/s
Explanation: Explanation:
Distance = Speed x Time
Speed = (180/10) = 18 kmph
Spees in mps = 18 x 5/18 = 1 x 5 = 5 mps.
Answer: Option B
Question: A fraction bears the same ratio to 1/27 as 3/7 does to 5/9. The fraction is?
A.1/23
B.1/35
C.1/25
D.1/13
Answer: B.1/35
Explanation: Let the fraction be x. Then,
x:1/27 = 3/7 : 5/9
x × 5/9 = 1/27 × 3/7
x × 5/9 = 1/9 × 1/7
x × 5/9 = 1/63
x × 5 = 9/63
5x = 1/7 = 1/35
B
Question: If the tens digit of positive integer x is 5 and the tens digit of positive integer y is 5, how many possible values of the tens digit of 2(x+y) can there be?
A.2
B.3
C.4
D.5
Answer: C.4
Explanation: We only need to consider the tens and ones digits of x and y, and the last two digits can be represented as 50 + p and 50 + q respectively.
2(50+p+50+q)= 200 + 2(p + q)
2(p+q) can range from 0 up to a maximum value of 36 when p=q=9.
Then the tens and ones digits of 2(x+y) can range from 00 up to 36.
There can be 4 possibilities for the tens digit.
The answer is C.
Question: A began business with 1000 and is joined afterwards by B with 6000. When did B join, if the profits at the end of the year are divided equally?
A.8 months
B.9 months
C.10 months
D.2 months
Answer: D.2 months
Explanation: Let B join after x months of the start of the business so that B’s money is invested for (12 – x) months.
∴ Profit ratio is 12 × 1000 : (12 – x) × 6000
or 12 : 6(12 – x)
Since profit is equally divided so
12 = 6(12 – x) or x = 2. Thus B joined after 8 months.
Answer D
Question: The length of a rectangle is increased by 25% and its breadth is decreased by 20%. What is the effect on its area?
A.Remains same
B.5% decrease
C.7% decrease
D.2% decrease
Answer: A.Remains same
Explanation: 100 * 100 = 10000
125 * 80 = 10000
No change
A
Question: Which of the following is equivalent to the pair of inequalities x + 7 > 10 and x - 1 <= 5 ?
A. 2 < x < 16
B. 2 <= x < 4
C. 3 < x <= 6
D. 4 < x <= 8
Answer: C. 3 < x <= 6
Explanation: Solution:
Let’s isolate x in both inequalities, starting with x + 7 > 10.
x + 7 > 10
x > 3
Next we isolate x in the inequality x – 1  5.
x – 1 <= 5
x <= 6
Bringing these two inequalities together we know:
3 < x <= 6
The answer is C.
Question: Ramu bought an old car for Rs. 40000. He spent Rs. 13000 on repairs and sold it for Rs. 64900. What is his profit percent?
A.20
B.22.5
C.18
D.99
Answer: B.22.5
Explanation: Total CP = Rs. 40000 + Rs. 13000 = Rs. 53000 and SP = Rs. 64900
Profit(%) = (64900 - 53000)/53000 * 100 = 22.5%
Answer: B
Question: A room has equal number of men and women. Eight women left the room, leaving twice as many men as women in the room . What was the total number of men and women present in the room initially?
A.32
B.34
C.28
D.30
Answer: A.32
Explanation: Explanation :
Assume that initial number of men = initial number of women = x
2(x-8) = x
=> 2x - 16 = x
=> x = 16
Total number of men and women = 2x = 2 × 16 = 32
Answer : A
Question: On June 1 a bicycle dealer noted that the number of bicycles in stock had decreased by 4 for each of the past 5 months. If the stock continues to decrease at the same rate for the rest of the year, how many fewer bicycles will be in stock on december 1 than were in stock on January 1?
A. 8
B. 12
C. 20
D. 44
Answer: D. 44
Explanation: Jan 1 = C
Feb 1 = C - 4
March 1 = C - 8
April 1 = C - 12
May 1 = C - 16
June 1 = C - 20
July 1 = C - 24
Aug 1 = C - 28
Sept 1 = C - 32
Oct 1 = C - 36
Nov 1 = C - 40
Dec 1 = C - 44
Difference between stock on December 1 than were in stock on January 1 will be -
C - ( C - 44 )= 44
Hence answer will be (D)
Question: If you are given $4, and the amount doubles every day, how much money will you have after 8 days?
A.$256
B.$512
C.$1024
D.$65536
Answer: D.$65536
Explanation: 4^8=65536
The answer is D.
Question: Fill in the blanks:
3 3 5 4 4 ? 5
A.2
B.7
C.8
D.3
Answer: D.3
Explanation: D
3
Number of letters in one, two, three, four, five, six, seven and so on.
Question: A reduction of 50% in the price of oil enables a house wife to obtain 5kgs more for Rs.800, what is the reduced price for kg?
A.s.42
B.s.46
C.s.40
D.s.80
Answer: D.s.80
Explanation: 800*(50/100) = 400 ---- 5
? ---- 1 => Rs.80
Answer: D
Question: How many digits are used to number a book containg 300 pages.
A.694
B.792
C.698
D.784
Answer: B.792
Explanation: Explanation:
Number of digits in 1 digit numbers = 1 to 9 = 9
Number of digits in 2 digit numbers = 10 to 99 = 90 (2) = 180
Number of digits in 3 digit numbers = 100 to 300 = 201 (3) = 603
Total = 792
Answer: Option B
Question: A towel, when bleached, was found to have lost 20% of its length and 10% of its breadth. The percentage of decrease in area is
A.28%
B.30%
C.32%
D.38%
Answer: A.28%
Explanation: Let original length = x and original breadth = y.
Decrease in area
= xy - 80 x x 90 y
100 100
= xy - 18 xy
25
= 7 xy.
25
Decrease % = 7 xy x 1 x 100 % = 28%.
25 xy
A)
Question: A train travels at the rate of 10 miles/hr for the first hour of a trip, at 20 miles/hr for the second hour, at 30 miles/hr for the third hour and so on. How many hours will it take the train to complete a 210-mile journey? Assume that the train makes no intermediate stops.
A.6
B.6.5
C.7
D.7.5
Answer: A.6
Explanation: A train travels at the rate of 10 miles/hr for the first hour of a trip, at 20 miles/hr for the second hour, at 30 miles/hr for the third hour and so on. How many hours will it take the train to complete a 210-mile journey? Assume that the train makes no intermediate stops.
I think the easiest way to solve this problem would be simply to count the number of miles it travels per hour (and in total)
Hour miles/hour Total miles
1 10 10
2 20 30
3 30 60
4 40 100
5 50 150
6 60 210
It takes a total of nine hours to cover the 210 mile distance.
ANSWER: A 6
Question: A and B can do a piece of work in 3 days, B and C in 4 days, C and A in 6 days. How long will C take to do it?
A.27
B.29
C.24
D.28
Answer: C.24
Explanation: 2c = 1/4 + 1/6 – 1/3 = 1/12
c = 1/24 => 24 days
Answer: C
Question: find two integers, neither of which ends in a zero, and whose product is exactly 1,000,000
A.64 and 15,625
B.60 and 15,625
C.64 and 15,620
D.64 and 15,635
Answer: A.64 and 15,625
Explanation: 1,000,000=10^6
=10x10x10x10x10x10
=(2x5)x(2x5)x(2x5)x(2x5)x(2x5)x(2x5)
=(2^6)x(5^6)
= 64x15625
so the numbers are 64 and 15,625
ANSWER:A
Question: P is four times as fast as Q and working together, they can complete a work in 16 days. In how many days can Q alone complete the work?
A.20 days
B.15 days
C.16 days
D.25 days
Answer: A.20 days
Explanation: P = 4Q
P + Q = 4Q + Q = 5Q
These 5Q people can do the work in 16 days, which means Q can do the work in 80 days.
Hence, P can do the work in 20 days.
ANSWER:A
Question: A man's speed with the current is 8km/hr and the speed of the current is 20km/hr. The current's speed against the man is:
A.3 km/hr
B.4 km/hr
C.5 km/hr
D.7 km/hr
Answer: B.4 km/hr
Explanation: Man's rate in still water = (20 - 8) km/hr = 12 km/hr.
Current's rate against the current = (12 - 8) km/hr = 4 km/hr
B
Question: If one-seventh of a number exceeds its eleventh part by 100 then the number is…
A.770
B.870
C.1825
D.1925
Answer: D.1925
Explanation: let no be :x
1/7x-1/11x=100
4x/77=100
x=7700/4=1925
ANSWER:D
Question: In a class there are 22 boys and 20 girls. In how many ways can a boy and a girl be selected?
A.288
B.500
C.440
D.266
Answer: C.440
Explanation: We can select one boy from 22 boys in 22 ways.
We select one girl from 20 girls in 20 ways
We select a boy and girl in 22 * 20 ways i.e.,
= 440 ways.
Answer: C
Question: The length of a room is 5.5 m and width is 3.75 m. What is the cost of paying the floor by slabs at the rate of $500 per sq. metre.
A.$10312.50
B.$13512.50
C.$16512.50
D.$14512.50
Answer: A.$10312.50
Explanation: Area =5.5×3.75 sq. metre.
Cost for 1 sq. metre. = $500
Hence, total cost
=5.5×3.75×500= $10312.50
A
Question: When you multiply a number by 5 and
then subtract 5, the result is the same as
if you first subtracted 7 from the same
number and then multiplied by 11. What
is the number?
A.A)23
B.B)13
C.C)12
D.D)31
Answer: C.C)12
Explanation: Let x equal the number and then change the words into an equation and solve for x:
5x – 5 = 11(x – 7)
5x – 5 = 11x – 77
72 = 6x
12 = x
correct answer C)12
Question: If x = a!, which of these following values of a is the least possible value (in this list) for which the last 6 digits of the integer x will all be zero?
A.18
B.24
C.29
D.34
Answer: C.29
Explanation: 2*5 will give one 0 at the end. We need 2^6*5^6 to get 6 zeroes at the end.
There are many 2's, so we need to find the first 6 appearances of 5.
These multiples of 5 are: 5, 10, 15, 20, 5*5...which gives us 6.
To have at least 6 zeroes at the end, a => 25.
The answer is C.
Question: The no. of girls in a class are seven times the no. of boys, which value cannever be the of total students?
A.3
B.4
C.8
D.9
Answer: C.8
Explanation: Let the boys are X, then girls are 7X, total = X+7X = 8X
So it should be multiple of 8, 30 is not a multiple of 8.
C
Question: What number should replace the question mark?
105, 87, ?, 52, 35
A.49
B.37
C.70
D.55
Answer: C.70
Explanation: C
70
The sequence progresses -18, -17, -18, -17.
Question: A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 sec. The speed of the train is?
A.11
B.50
C.99
D.88
Answer: B.50
Explanation: Speed of the train relative to man = 125/10 = 25/2 m/sec.
= 25/2 * 18/5 = 45 km/hr
Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr.
x - 5 = 45 => x = 50 km/hr.
Answer: B
Question: The average of six numbers is 3.95. The average of two of them is 3.4, while the average of the other two is 3.85. What is the average of the remaining two numbers ?
A.4.2
B.4.6
C.4.3
D.4.1
Answer: B.4.6
Explanation: Sum of the remaining two number
= (3.95 * 6) - [(3.4 * 2) + (3.85 * 2)]
= 23.70 - (6.8 + 7.7) = 23.70 - 14.5 = 9.20.
Required average = (9.2 / 2) = 4.6.
Answer: B
Question: Three numbers are randomly selected, with replacement, from the set of integers {0, 1, 2, 3, 4, 5, 6, 7}. If the first number selected is w, the second number selected is x, and the third number is y, what is the probability that w < x < y ?
A.5/32
B.7/64
C.9/64
D.53/512
Answer: B.7/64
Explanation: The number of ways to select w, x, and y is: 8*8*8=512
The number of ways to choose three different numbers from the set is 8C3=56.
There are six permutations for each group of three different numbers, but only one permutation satisfies w < x < y.
P(w < x < y) = 56/512 = 7/64
The answer is B.
Question: The table below shows the enrollment in various classes at a certain college.
Class | Number of Students
Biology | 60
Physics | 35
Calculus | 40
Although no student is enrolled in all three classes, 15 are enrolled in both Biology and Physics, 10 are enrolled in both Biology and Calculus, and 12 are enrolled in both Physics and Calculus. How many different students are in the three classes?
A.51
B.88
C.90
D.98
Answer: D.98
Explanation: No. of total students = no of students of biology + no of students of physics but not biology + no of students of calculus but not biology and physics
No. of total students = 60 + (35-15) + (40-10-12) = 60+20+18 = 98
Hence, Answer will be D.
Question: For all positive integers n and m, the function A(n) equals the following product:
(1 + 1/2 + 1/2^2)(1 + 1/3 + 3^2)(1 + 1/7 + 7^2)…(1 + 1/p_n + 1/p_n^2), where p_n is the nth smallest prime number, while B(m) equals the sum of the reciprocals of all the positive integers from 1 through m, inclusive. The largest reciprocal of an integer in the sum that B(25) represents that is NOT present in the distributed expansion of A(5) is
A.1/4
B.1/5
C.1/6
D.1/7
Answer: B.1/5
Explanation: For all positive integers n and m,
A(n) = (1 + 1/2 + 1/2^2)(1 + 1/3 + 3^2)(1 + 1/5 + 5^2)…(1 + 1/p_n + 1/p_n^2), where p_n is the nth smallest prime number,
note:i think there's a typo in the above function, A(n) could be (1 + 1/2 + 1/2^2)(1 + 1/3 +1/3^2)(1 + 1/5 +1/5^2)…(1 + 1/p_n + 1/p_n^2)
B(m) = sum of the reciprocals of all the positive integers from 1 through m, inclusive.
A(5), here 5 represents the 5th smallest prime number; the 5th smallest prime number is 11 {2, 3, 5, 7, 11, ...}
A(5) = (1 + 1/2 + 1/2^2)(1 + 1/3 + 3^2)(1 + 1/5 + 5^2)(1 + 1/7 + 1/7^2)(1 + 1/11 + 11^2)
The distributed expansion of A(5) = 1 + 1/2 + 1/3 + 1/4 + 1/5 + 1/6 +1/7 + 1/9+ 1/10 + 1/11 +1/12 + 1/14+ ...
missing numbers are 1/8, 1/13, 1/16, ....
B(25) = (1 + 1/2 + 1/3 + 1/4 + ... + 1/16 + 1/17 + ... + 1/25)
here the largest reciprocal is 1 and the reciprocals are arranged in descending order based on their values
The largest reciprocal that present in B(25) but not in A(5) is 1/5
Answer B
Question: The function f is defined by subtracting 25 from the square of a number and the function d is defined as the square root of one-half of a number. If d(f(x))=10, then which of the following is a possible value of x?
A.-15
B.-5
C.0
D.5
Answer: A.-15
Explanation: f(x) = x^2-25
d(x) = sqrt(x/2) not sqrt(x)/2, because the question clearly says its square root of (half of the number).
d(f(x)) = 10
d(x^2-25) =10
sqrt((x^2-25)/2) = 10
=> (x^2-25)/2 = 100
=>x^2 = 225
=> x = 15 or -15
Answer is A.
Question: At what price must an article costing Rs.47.50 be marked in order that after deducting 5% from the list price. It may be sold at a profit of 25% on the cost price?
A.62.5
B.62.8
C.62.1
D.62.2
Answer: A.62.5
Explanation: CP = 47.50
SP = 47.50*(125/100) = 59.375
MP*(95/100) = 59.375
MP = 62.5
Answer:A
Question: A sales executive was given a target to get annual bonus. He already reached 1/2 of his last year's target. If the target was reduced by 5% this year, what percentage target of the last year's target does he need to reach to get bonus?
A.9/20
B.6/12
C.7/5
D.10/20
Answer: A.9/20
Explanation: We have 1/2 and 5% that is 1/20
If we assume the last year's target to be 20
This year's target is 5% less of last year=19
The target reached this year 1/2*20=10
Remaining is 19-10=9
Required 9/20
Answer (A)
Question: Molly's age in 18 years will be four times her age three years ago. What is Molly's present age?
A.6
B.8
C.10
D.12
Answer: C.10
Explanation: Let x be Molly's present age.
x + 18 = 4(x-3)
x = 10
The answer is C.
Question: Some pens are divided among A, B, C and D. A gets twice the number of pens that B gets. C gets the same number of pens as D gets. If A gets 25 pens more than D and the ratio of the number of pens that B and C get is 2:3, then find the number of pens that D gets?
A.16
B.76
C.75
D.88
Answer: C.75
Explanation: Let the number of pens that A, B, C and D get be a, b, c and d respectively.
a:b = 2:1
a = c + 25
b:c = 2:3
a:b:c:d = 4:2:3:3
a, d get 4p, 3p pens
=> 4p - 3p = 25 => p = 25
=> D gets 3p = 3 * 25 = 75 pens.
AnswerC
Question: There are two circles of different radii. The are of a square is 784 sq cm and its side is twice the radius of the larger circle. The radius of the larger circle is seven - third that of the smaller circle. Find the circumference of the smaller circle.
A.18
B.99
C.12
D.07
Answer: C.12
Explanation: Let the radii of the larger and the smaller circles be l cm and s cm respectively. Let the side of the square be a cm.
a2 = 784 = (4)(196) = (22).(142)
a = (2)(14) = 28
a = 2l, l = a/2 = 14
l = (7/3)s
Therefore s = (3/7)(l) = 6 Circumference of the smaller circle = 2∏s = 12∏ cm.
Answer: C
Question: Andrea invested a certain sum of money in a bank that paid simple interest. The amount grew to $340 at the end of 2 years. She waited for another 4 years and got a final amount of $420. What was the principal amount that she invested at the beginning?
A.$350
B.$300
C.$400
D.$375
Answer: B.$300
Explanation: What shall be the rate of interest.? Does that is not required for the calculation?
Not really!
Keep in mind that the interest earned each year will be the same in Simple Interest.
At the end of 2 years, Amount = $340
At the end of 6 years, Amount = $420
This means she earned an interest of $80 in 4 years. Or $20 in each year.
We know that the interest earned each year will be the same.
Therefore she must have earned $40 in 2 years.
Hence Principal Amount = $340 - $40 = $300 Option B
Question: Find the area of a parallelogram with base 24 cm and height 16 cm.
A.298 cm2
B.288 cm2
C.187 cm2
D.384 cm2
Answer: D.384 cm2
Explanation: Area of a parallelogram = base * height
= 24 * 16
= 384 cm2
Answer: D
Question: A “palindromic integer” is an integer that remains the same when its digits are reversed. So, for example, 43334 and 516615 are both examples of palindromic integers. How many 6-digit palindromic integers are both even and greater than 500,000?
A.160
B.200
C.240
D.300
Answer: B.200
Explanation: The first digit and last digit are the same so the 2 possibilities are 6 or 8.
The second and third digits can be any number from 0 to 9.
The total number of palindromic integers is 2*10*10 = 200
The answer is B.
Question: A bag is filled with pennies and nickels in the ratio of 5 to 3. There are 60 nickles in the bag, how many coins are there in that bag?
A.40
B.160
C.65
D.70
Answer: B.160
Explanation: A ratio of pennies to nickels of 5 to 3 means that we can write the number of pennies and nickels in the form
number of pennies = 5x and number of nickels = 3x
But we know the number of nickels, 60. Hence
3x = 60
Solve for x
x = 20
The total number of coins is given by
5x + 3x = 8x = 8 × 20 =160
Answer : B