mathewhe/aqua_rat huggingface dataset:
Question: The time it took car P to travel 150 miles was 2 hours less than the time it took car R to travel the same distance. If car P’s average speed was 10 miles per hour greater than that of car R, what was car R’s average speed, in miles per hour?
(A) 23
(B) 50
(C) 60
(D) 70
(E) 80
Rationale: Let speed of car R be=x
Then speed of car P= x+10
A/Q,
(150/x)-(150/(x+10))=2
Solving for x=23 miles\hr.
A
Answer: (A) 23
Question: What sum of money will produce Rs.70 as simple interest in 3 years at 3 1/2 percent?
(A) 667
(B) 500
(C) 266
(D) 288
(E) 211
Rationale: 70 = (P*3*7/2)/100
P = 667
Answer: A
Answer: (A) 667
Question: In a group of 100 adults, 80 percent of the women are left-handed. If there are 12 right-handed women in the group, how many men are in the group?
(A) 48
(B) 52
(C) 54
(D) 60
(E) 40
Rationale: 12 left-haded women compose 100-80=20% (or 1/5) of all women, so there are total of 5*12=60 women --> 100-60=40men.
Answer: E.
Answer: (E) 40
Question: For what values of k will the pair of equations (3x + 4y)/2 = 6 and kx + 12y = 30 does not have a unique solution?
(A) 12
(B) 9
(C) 3
(D) 7.5
(E) 2.5
Rationale: we have 2 equations
1. (3x + 4y)/2 = 6 --> 3x + 4y = 12 -- > 9x + 12y = 36
2. kx + 12y = 30
substract 1-2, we get (9-K)x = 6
i.e. x = 6/(9-k)
then, by looking at options, we get some value of x except for B. When we put k=9, x becomes 6/0 and hence answer is B
Answer: (B) 9
Question: A person borrows Rs. 5000 for 2 years at 4% p.a. simple interest. He immediately lends it to another person at 6p.a for 2 years. Find his gain in the transaction per year.
(A) Rs. 112.50
(B) Rs. 125
(C) Rs. 150
(D) Rs. 167.50
(E) Rs. 175
Rationale: Gain in 2 years
= Rs.[(5000 x (25/4)	x(2/100))-((5000 x 4 x 2)/100)]
= Rs. (625 - 400)
= Rs. 225.
Gain in 1 year = Rs.(225/2)
= Rs. 112.50
ANSWER :A
Answer: (A) Rs. 112.50
Question: After successive discounts of 20%, 10% and 5% a certain good is sold for Rs. 6600. Find the actual price of the good.
(A) s. 6000
(B) s. 9000
(C) s. 10800
(D) s. 9649
(E) s. 9980
Rationale: Let actual price was 100.
After three successive discount this will become,
100 ==20% discount => 80 ==10% discount => 72 ==5% discount = 68.4
Now Compare,
68.4 = 6600
1 = 6600/68.4
100 = (6600*100)/68.4 = Rs. 9649.
Answer: Option D
Answer: (D) s. 9649
Question: Pipes A and B can fill a cistern in 8 and 24 minutes respectively. They are opened an alternate minutes. Find how many minutes, the cistern shall be full?
(A) 22
(B) 12
(C) 88
(D) 99
(E) 27
Rationale: 1/8 + 1/24 = 1/6
6 * 2 = 12
Answer:B
Answer: (B) 12
Question: A person jogged 10 times along the perimeter of a rectangular field at the rate of 12 kilometers per hour for 30 minutes. If field has a length that is twice its width, find the area of the field in square meters.
(A) 29,000 square meters
(B) 16,000 square meters
(C) 20,000 square meters
(D) 32,000 square meters
(E) 45,000 square meters
Rationale: Let us first find the distance d jogged
distance = rate ? time = (12 km / hr) ? 30 minutes
= (12 km/hr) ? 0.5 hr = 6 km
The distance of 6 km corresponds to 10 perimeters and therefore 1 perimeter is equal to
6 km / 10 = 0.6 km = 0.6 ? 1000 meters = 600 meters
Let L and W be the length and width of the field. The length is twice the width. Hence
L = 2 W
The perimeter is 600 meters and is given by
2 (L + W) = 600
Substitute L by 2 W
2 (2 W + W) = 600
Simplify and solve for W
4 W + 2 W = 600
6 W = 600
W = 100
Find L
L = 2 W = 200
Find the area A of the rectangle
A = L * W = 200 * 100 = 20,000 square meters
correct answer C
Answer: (C) 20,000 square meters
Question: Hillary and Eddy are climbing to the summit of Mt. Everest from a base camp 5,000 ft from the summit. When they depart for the summit at 06:00, Hillary climbs at a rate of 800 ft/hr with Eddy lagging behind at a slower rate of 500 ft/hr. If Hillary stops 1000 ft short of the summit and then descends at a rate of 1,000 ft/hr, at what time do Hillary and Eddy pass each other on her return trip?
(A) 11.0
(B) 12.0
(C) 13.0
(D) 14.0
(E) 15.0
Rationale: Solution:H stopped 1000 ft before reaching the final point, time taken to reach 4000 ft= 4000/800= 5hrs.
this means she reached there at 11:00.
speed difference between them is 800-500=300 ft/hr
so by the time H stops they have 1500 ft of distance
so now here we use relative speed formula they both are travelling toward each other with speed of 1000 and 500 total 1500 ft/hr and distance bwn them is 1500 ft so time taken to meet = 1 hr from 11:00
means 12:00 is the answer.
B
Answer: (B) 12.0
Question: Two cars, Car1 and Car2 move towards each other from R and Y respectively with respective speeds of 20 m/s and 15 m/s. After meeting each other Car1 reaches Y in 10 seconds. In how many seconds does Car 2 reach R starting from Y?
(A) 15.5 sec
(B) 8.4 sec
(C) 33.6 sec
(D) 31.11 sec
(E) 16.8 sec
Rationale: R--------------------------------------|----------------------------Y
Car A(20mps)------------------------->P<---------------Car B(15mps)
Let 2 cars meet each other at point P in t seconds.
Car1 covers distance= 20t. Car2 covers distance=15t. So, total distance RY= 35t.
From P, Car 1 reaches onto Y in 10 secs. So it covers 15t further.
so, 15t/20 = 10
So t=40/3 sec and total distance = (35*40)/3
Hence Car2 will cover total distance in (35*40)/(3*15) = 31.11 sec approx.
Answer D
Answer: (D) 31.11 sec
Question: An aeroplane covers a certain distance at a speed of 100 kmph in 2 hours. To cover the same distance in 1 hours, it must travel at a speed of?
(A) 100km/hr
(B) 150km/hr
(C) 200km/hr
(D) 250km/hr
(E) 300km/hr
Rationale: Distance = 100*2 = 200 km
Required speed = 200 *1 = 200km/hr
Answer is C
Answer: (C) 200km/hr
Question: If the wheel is 14 cm then the number of revolutions to cover a distance of 1056 cm is?
(A) 22
(B) 29
(C) 23
(D) 12
(E) 13
Rationale: 2 * 22/7 * 14 * x = 1056 => x
= 12
Answer:D
Answer: (D) 12
Question: A train traveling at 100 kmph overtakes a motorbike traveling at 64 kmph in 12 seconds. What is the length of the train in meters?
(A) 400 meters
(B) 120 meters
(C) 1777 meters
(D) 60 meters
(E) None of these
Rationale: Train overtakes a bike means that we are talking about total length of the train. (train's head is close to bike when it started and its tail crosses the bike when it overtakes the bike)
Relative speed= 100-64= 36Km/h = 36000 m/h
time= 12 seconds
Distance= speed*time
36000* 12/3600= 120 meters.
B is the answer.
Answer: (B) 120 meters
Question: A can have a piece of work done in 4 days, B can work two times faster than the A, C can work three times faster than A. How many days will they take to do the work together ?
(A) 3/4 days
(B) 6/7 days
(C) 1/4 days
(D) can't say
(E) none
Rationale: A's 1 day work is 1/6
B's 1 day work is 2/6
C's 1 day work is 3/6
(A+B+C)'s 1 day work(1/6+2/6+3/6) is 7/6
so, they can finish the work in 6/7 days
ANSWER:B
Answer: (B) 6/7 days
Question: A company has two types of machines, type R and type S. Operating at a constant rate a machine of R does a certain job in 36 hours and a machine of type S does the job in 2 hours. If the company used the same number of each type of machine to do job in 12 hours,how many machine R were used?
(A) 3/4
(B) 4
(C) 18/19
(D) 9
(E) 12
Rationale: yes there is a typo in the question, I got the same ques on my GMAT PREP last week, and the questions goes as:
A company has two types of machines,type R and type S.Operating at a constant rate a machine of R does a certain job in 36 hours and a machine of type S does the job in 2 hours .If the company used the same number of each type of machine to do job in2 hours,how many machine R were used?
So for a job to be done in 2 hours R = 1/2
R_a(Rate of Machine R) = 1/36
R_s(Rate of Machine S) = 1/2
Lets say x machines are used to attain the desired rate, thus
x/36+x/2 = 1/2 (Desired R =1/2 i.e. to complete the job in 2 hours)
(x+18x)/36 = 1/2
19x/36 = 1/2
x = 18/19.
QA = 18/19 (ANSWER C)
Answer: (C) 18/19
Question: Last year, Company M made q dollars in profit. Half of the profit went to the company’s founder. The rest was split evenly among his Three other partners. In terms of q, how much did each of the other partners receive?
(A) q/4
(B) q/5
(C) q/6
(D) q/7
(E) q/8
Rationale: Profit = q
Profit to company founder = q/2
Profit to other partners = q/2
Number of other partners = 3
Profit to each partner = (q/2)/3 = q/6
Answer: C
Answer: (C) q/6
Question: Barbata invests $2600 in the National Bank at 5%. How much additional money must she invest at 8% so that the total annual income will be equal to 6% of her entire investment?
(A) 1200
(B) 3000
(C) 1300
(D) 3600
(E) 2400
Rationale: Let the additional invested amount for 8% interest be x;
Equation will be;
2600+0.05*2600+x+0.08x = 2600+x+0.06(2600+x)
0.05*2600+0.08x = 0.06x+0.06*2600
0.02x = 2600(0.06-0.05)
x = 2600*0.01/0.02 = 1300
Ans: "C"
Answer: (C) 1300
Question: An agent, gets a commission of 2.5% on the sales of cloth. If on a certain day, he gets Rs. 12.50 as commission, the cloth sold through him on that day is worth
(A) 333
(B) 500
(C) 887
(D) 299
(E) 132
Rationale: Explanation:
Let the total sale be Rs. x.
Then, 2.5%. of x = 12.50 <=> (25/100 * 1/100 * x) = 125/10 <=> x = 500.
Answer: B) 500
Answer: (B) 500
Question: The slant height of a cone is 10 cm and radius of the base is 5cm, find the curved surface of the cone?
(A) 150
(B) 155
(C) 158
(D) 157
(E) 190
Rationale: π * 10 * 5
= 157
Answer:D
Answer: (D) 157
Question: If Bill can buy 3 pairs of jeans and 2 shirts for $69 or 2 pairs of jeans and 3 shirts for $76, how much does one shirt cost?
(A) $10
(B) $12
(C) $13.20
(D) $15
(E) $18
Rationale: 3J + 2S = 69
2J + 3S = 76
----------------
5J + 5S = 145 ----(divide by 5)---> J + S = 29
3J + 2S = J + 2(J + S) = J + 58 = 69 ---> J = 11
3*11 + 2S = 69
33 + 2S = 69
2S = 36
S = 18
Answer: E
Answer: (E) $18
Question: In a certain company, the ratio of male to female employees is 7:8. If 3 more men were hired, this ratio would increase to 8:9. How many male employees are there in the company?
(A) 6
(B) 21
(C) 27
(D) 189
(E) 192
Rationale: Another approach is to use TWO variables.
Let M = present number of males
Let F = present number of females
The ratio of male to female employees is 7:8
So, M/F = 7/8
Cross multiply to get 7F = 8M
If 3 more men were hired, this ratio would increase to 8:9
So, (M+3)/F = 8/9
Cross multiply to get 9(M+3) = 8F
Expand: 9M + 27 = 8F
We now have a system of two equations and two variables:
7F = 8M
9M + 27 = 8F
Solve to get: M = 189 and F = 216
ANSWER:D
Answer: (D) 189
Question: How long does a train 110 m long traveling at 60 kmph takes to cross a bridge of 150 m in length?
(A) sec
(B) sec
(C) sec
(D) sec
(E) sec
Rationale: D = 110 + 150 = 260 m
S = 60 * 5/18 = 50/3
T = 260 * 3/50 = 15.6 sec
Answer: D
Answer: (D) sec
Question: If r + | r | = 0, which of the following must be true?
(A) r > 0
(B) r≥0
(C) r < 0
(D) r≤0
(E) r = 0
Rationale: Manipulate the equations:
r + | r | = 0
|r| = -r
-r > 0 OR -r = 0
This means r could be 0 or r is less than 0.
D. r≤0
E. r=0
Answer: D
Answer: (D) r≤0
Question: In the city of San Durango, 90 people own cats, dogs, or rabbits. If 60 people owned cats, 20 owned dogs, 40 owned rabbits, and 18 owned exactly two of the three types of pet, how many people owned all three?
(A) 1
(B) 3
(C) 6
(D) 11
(E) 12
Rationale: Total = C + D + R - (CD + DR + CR) - 2CDR
90 = 60 + 20 + 40 - (18) - 2x
x = 6
So, answer will be C
Answer: (C) 6
Question: For any number s, s* is defined as the greatest positive even integer less than or equal to s. What is the value of 5.2 – 5.2*?
(A) 0.2
(B) 1.2
(C) 1.8
(D) 2.2
(E) 4.0
Rationale: Since s* is defined as the greatest positive even integer less than or equal to s, then 5.2* = 4 (the greatest positive even integer less than or equal to 5.2 is 4).
Hence, 5.2 – 5.2* = 5.2 - 4 = 1.2
Answer: B.
Answer: (B) 1.2
Question: If the volume of two cubes are in the ratio 8:1, the ratio of their edges is:
(A) 2:1
(B) 3:2
(C) 3:5
(D) 3:7
(E) None of these
Rationale: Explanation:
Let the edges be a and b of two cubes, then
a3/b3=8/1
=>(a/b)3=(2/1)3
a/b=2/1
=>a:b=2:1
Option A
Answer: (A) 2:1
Question: Solve the quickfire maths brain teaser âˆš25% = ?
(A) 30%
(B) 40%
(C) 50%
(D) 19%
(E) 29%
Rationale: âˆš25%
=> âˆš25/âˆš100
=> 5/10
=> 50/100
=> 50%
C
Answer: (C) 50%
Question: The simple interest accrued on an amount Rs.10,000 at the end of two years is same as the compound interest on Rs.8,000 at the end of two years. The rate of interest is same in both the cases. What is the rate of interest?
(A) 58%
(B) 90%
(C) 80%
(D) 50%
(E) 54%
Rationale: Given that Rs.10,000 is invested in S.I for two years and Rs.8,000 in C.I for two years
=> C.I - S.I
=> 8,000 { [1 + r/100]2 - 1} = (10,000)2r /100
=> 8{ 1 + 2r/100 + r2 / (100)2 - 1} = r/5
=> 16r/100 + 8r2/(100)2 = 20r/100
=> 4r/10 = 8r2/(100)2
=> 8[r/100]2 - 4r/100 = 0
=> r/100 {8r/100 -4} = 0
=> r = 0% of 50%
Since r!= 0%, r =50%
Answer: D
Answer: (D) 50%
Question: 3 candidates in an election and received 1000, 2000 and 4000 votes respectively. What % of the total votes did the winning candidate got in that election?
(A) 45%
(B) 50%
(C) 57.14%
(D) 60%
(E) 65.12%
Rationale: Total number of votes polled = (1000 + 2000 + 4000) = 7000
So, Required percentage = 4000/7000 * 100 = 57.14%
C
Answer: (C) 57.14%
Question: 1/(3-2√2)=?
(A) 9+4√5
(B) 9-4√5
(C) 3+2√2
(D) 9-2√5
(E) 4+9√5
Rationale: This question requires us to rationalize (fix) the denominator.
For more on this technique, seehttps://www.gmatprepnow.com/module/gmat ... video/1044
Given: 1/(3-2√2)
Multiply top and bottom by the CONJUGATE of 3-2√2, which is 3+2√2
So, 1/(3-2√2) = (1)(3+2√2)/(3-2√2)(3+2√2)
= (3+2√2)/(1)
= 3+2√2
=
C
Answer: (C) 3+2√2
Question: I flew my tiny seaplane to visit my mother. On the flight up, I flew at 110 mph. On the way home, I flew 72 mph. What was my average speed for the trip?
(A) 198 mph
(B) 91 mph
(C) 88 mph
(D) 100 mph
(E) 99 mph
Rationale: (110 mph +72 mph)/2= 91 mph
Correct answer is: B
Answer: (B) 91 mph
Question: A retailer buys a radio for Rs 225. His overhead expenses are Rs 20. He sellis the radio for Rs 300. The profit percent of the retailer is
(A) 22.4%
(B) 50%
(C) 25%
(D) 52%
(E) None of these
Rationale: Explanation:
cost price = (225 + 20) = 245 sell price = 300
gain = (55/245)*100 = 22.4%. Answer: A
Answer: (A) 22.4%
Question: John invested Rs. 3500 in a scheme for 3 years at compound interest rate 4% p.a. How much amount will John get on maturity of the fixed deposit?
(A) s.4000
(B) s.3578
(C) s.3258
(D) s.3990
(E) s.3937.02
Rationale: Amount = [3500 * (1 + 4/100)3]
= 3500 * 26/25 * 26/25 * 26/25
= Rs.3937.02
Answer:E
Answer: (E) s.3937.02
Question: Martins made a part payment of $650 toward buying a brand new washing machine, which represents 15% of the total cost of the washing machine, how much remains to be paid?
(A) $1116.3
(B) $3583.3
(C) $3283.3
(D) $3683.3
(E) $2683.3
Rationale: Explanation:
Let's start with what the total price of the washing machine would be. If 15% is equal to $650 then 100% equals $x. We just have to multiply $650 by 6.67 to get total amount=$4333.3. Out of this amount we then need to deduct the amount already paid which was $650 so we have $4333.3-$650=$3683.3
Answer: Option D
Answer: (D) $3683.3
Question: In a particular 100 meter race, 7 athletes are participating that are numbered 1-7. In how many ways can athlete #4 finish ahead of #2 provided there's no tie among the athletes?
(A) 1240
(B) 1860
(C) 2520
(D) 3220
(E) 4180
Rationale: The total number of ways for the athletes to finish is 7! = 5040.
#4 will be ahead of #2 in exactly half of these possibilities.
5040/2 = 2520
The answer is C.
Answer: (C) 2520
Question: A zinc-copper alloy with 6 kg of pure zinc would contain 90% of zinc. The alloy with 4 kg of 90% zinc alloy contains 84% of zinc. Calculate the weight and percentage of zinc in the zinc-copper alloy.
(A) 2.4 kg or 80%
(B) 4.8 kg or 80%
(C) 3.4 kg or 60%
(D) 7.4 kg or 18%
(E) 1.4 kg or 60%
Rationale: Right Answer Explanation:
x : 6
y : 100
90
10 : 90 – y
(90-y)/6 = 10/x = ………..(1)
In the second case,
x 4
y 90
84
6 84-y
Therefore (84-y)/4 = 6/x ………..(2)
Dividing (1) and (2)
=
540 – 6y = 1260 – 15y
9y = 720
y = 80
x = 60/(90-80) = 60/10 = 6 kg
Quantity of zinc in x = 80% of x
= 0.8 6
= 4.8 kg
Weight and percentage of zinc is 4.8 kg or 80%
B
Answer: (B) 4.8 kg or 80%
Question: The average (arithmetic mean) of 14, 32, and 53 is 3 more than the average of 21, 47, and x. What is x?
(A) 20
(B) 21
(C) 22
(D) 23
(E) 24
Rationale: The average of 14, 32, and 53 is 33.
The average of 21, 47 and x is 30.
Then 21 + 47 + x = 90.
x = 22.
The answer is C.
Answer: (C) 22
Question: A teacher gave the same test to three history classes: D, B, and C. The average (arithmetic mean) scores for the three classes were 65, 80, and 77, respectively. The ratio of the numbers of students in each class who took the test was 4 to 6 to 5, respectively. What was the average score for the three classes combined?
(A) 74
(B) 75
(C) 76
(D) 77
(E) 78
Rationale: Ans : B (75)
lets say class D indeed has 4 children, B has 6 children and C has 5 children.
now, if the average of class D is 65, hence total marks awarded in the class = 65*4=260
Similarly,
class B = 80*6 = 480
class C = 77*5 = 385
total marks provided = D+B+C = 260+480+385 = 1125
avg. marks = 1125 / 15 (total no. of students) = 75=B
Answer: (B) 75
Question: The total of the ages of Amar, Akbar and Anthony is 40 years. What was the total of their ages two years ago ?
(A) 71
(B) 44
(C) 36
(D) 16
(E) 18
Rationale: Explanation:
Required sum = (40 - 3 x 2) years = (40 - 6) years = 36 years.
Answer: C
Answer: (C) 36
Question: Ram and Shakil run a race of 2000m. First Ram gives Shakil a start of 200m and beats him by 1 minute.Next Ram gives shakil a start of 6 min and is beaten by 1000 meters . Find the time in minutes in which Ram and Shakil can run the race seperately.
(A) 12 , 18
(B) 8 , 10
(C) 18 , 20
(D) 20 , 25
(E) None of these
Rationale: Explanation :
Let speed of ram and shakil be x and y resp.
Case 1 : Ram gives a start of 200m and beats Shakil by 1 minute.
2000/x - 1800/y= -60
2000/x= 1800/y -60---------------------(1)
Case2: Ram gives Shakil a start of 6 min and is beaten by 1000 meters
distance travelled by shakil in 6 minutes= (6*60*y) meters = 360y meters
1000/x = (2000- 360y)/y------------------(2)
Solve equation 1 and 2 to obtain x and y
Answer is x = 8 minutes, y = 10 minutes
Hence (B) is the corret answer.
Answer : B
Answer: (B) 8 , 10
Question: The average temperature of Monday, Tuesday, Wednesday and Thursday was 38∘ and that of Tuesday, Wednesday, Thursday and Friday was 40∘. If the temperature on Monday was 36∘, the temperature of Friday was :
(A) 44∘
(B) 40∘
(C) 38∘
(D) 30∘
(E) None of these
Rationale: Explanation:
M+T+W+Th=(4×38)=152
Monday temperature is 36. So T+W+Th=(152-36)=116
T+W+Th+F=(4×40)=160
F = (160-116)=44∘
Correct Option: A
Answer: (A) 44∘
Question: If 25% of x is 15 less than 15% of 1600, then x is?
(A) 872
(B) 738
(C) 900
(D) 840
(E) 83
Rationale: 25% of x = x/4 ; 15% of 1600
= 15/100 * 1600 = 240
Given that, x/4 = 240 - 15
=> x/4 = 225 => x = 900.
Answer:C
Answer: (C) 900
Question: Three models (K, L, and M) of cars are distributed among three showrooms. The number of cars in each showrooms must be equal and each model must be represented by at least one car in every showroom. There are 19 cars of Model K, 17 cars of Model L, and 15 cars of Model M. What is the maximum number of cars of model K in any showroom ?
(A) 17
(B) 16
(C) 15
(D) 14
(E) 13
Rationale: The total number of cars is 51. So each showroom has 17 cars(since the number of cars in each showrooms should be equal 51/3=17).
Moreover that the number of model K is maximum means that the numbers of model L and M should be minimum. Since each model must be represented by at least one car in every showroom that minimum number should be 1.
So Maximum number of model K is 17-2= 15.
The answer is (C)
Answer: (C) 15
Question: If x and y are integers, and x/y is not an integer then which of the following must be true?
(A) x is odd and y is even
(B) x is odd and y is odd.
(C) x is even and y is odd
(D) x<y
(E) None of the above
Rationale: x and y could be co-primes
Answer could be E
Answer: (E) None of the above
Question: Complete the sequence:
B D H N ?
(A) M
(B) V
(C) S
(D) D
(E) Z
Rationale: B+2=D
D+4=H
H+6=N
B+8=V
B
Answer: (B) V
Question: The circulation for magazine P in 1961 was 4 times the average (arithmetic mean) yearly circulation for magazine P for the years 1962-1970. What is the ratio of the circulation in 1961 to the total circulation during 1961-1970 for magazine P ?
(A) 2/7
(B) 5/7
(C) 3/7
(D) 4/7
(E) 1/7
Rationale: There are 9 years from 1962-1970, inclusive. Let's say the average circulation every year between 1962-1970 inclusive is x.
So the total circulation is 9x from 1962-1970, inclusive.
In 1961, the circulation is 4x.
So total circulation for 1961-1970 is 4x + 9x = 13x.
Ratio of circulation in 1961 to total circulation during 1961-1970 is 4x to 14x or 4/14=2/7
Answer : A
Answer: (A) 2/7
Question: Find the area of a rhombus having each side equal to 13 cm and one of whose diagonal is 24 cm.
(A) 150 sq.cm
(B) 120 sq.cm
(C) 130 sq.cm
(D) 125 sq.cm
(E) 110 sq.cm
Rationale: Let ABCD is a rhombus with diagonals AC and BD which intersect each other at O.
AC = 24 ⇒ AO = 12
Let BO = x and AB = 13 cm (given)
By Pythagorean theorem
c 2 = a 2 + b 2
13 2 = 12 2 + x 2 169 = 144 + x 2
x 2 = 169 – 144
x 2 = 25
x = 5 cm
BO = 5 cm
Diagonal BD = 2 x 5 = 10 cm.
Area = ½ x [ product of diagonals]
= ½ x 24 x 10
Area = 120 sq.cm
Answer is B
Answer: (B) 120 sq.cm
Question: Tickets numbered 1 to 20 are mixed up and then a ticket is drawn at random. What is the probability that the ticket drawn has a number which is a multiple of 3 or 5?
(A) 2/5
(B) 9
(C) 9/5
(D) 1/5
(E) 9/20
Rationale: Here, S = {1, 2, 3, 4, ...., 19, 20}.
Let E = event of getting a multiple of 3 or 5 = {3, 6 , 9, 12, 15, 18, 5, 10, 20}.
P(E) = n(E)/n(S) = 9 /20
Answer: (E) 9/20
Question: In a certain town, there are two times as many people who were born in the town’s state as there are people who were born in another state or country. The ratio of those residents born in the town’s state to the town’s total population is
(A) 1 to 4
(B) 2 to 3
(C) 1 to 2
(D) 3 to 4
(E) 4 to 5
Rationale: Town state: 2 times the whole town or country
then ratio will be 2(times)/3 total(times)
So the answer is 2/3.
B
Answer: (B) 2 to 3
Question: There are 4 people and 4 chairs. In how many different ways people can occupy the chairs?
(A) 12
(B) 15
(C) 24
(D) 36
(E) 120
Rationale: number of ways =4! = 24
Answer is C
Answer: (C) 24
Question: In the xy-coordinate system, line k passes through points (-7m, 0) and (0, 3m). Which of the following is a possible equation of line k?
(A) y = -7/3*x + 3m
(B) y = 3/7*x - 7m
(C) y = 7/3*x + 3m
(D) y = 3/7*x + 3m
(E) y = -3/7*x - 7m
Rationale: The slope of the line is 3m/7m=3/7.
The y-intercept is 3m.
the equation of the line is: y = 3/7*x +3m
The answer is D.
Answer: (D) y = 3/7*x + 3m
Question: Ayesha's father was 34 years of age when she was born while her mother was 30 years old when her brother four years younger to her was born. What is the difference between the ages of her parents?
(A) 6
(B) 8
(C) 5
(D) 1
(E) 2
Rationale: Mother's age when Ayesha's brother was born = 30 years.
Father's age when Ayesha's brother was born = (34 + 4) years = 38 years.
Required difference = (38 - 30) years = 8 years.
Answer:B
Answer: (B) 8
Question: A coin is flipped twice.What is the probability that both flips result in heads given that first flip does?
(A) 1/2
(B) 2
(C) 1
(D) 3/2
(E) 1/3
Rationale: A=First flip lands heads.
B=Second flips is head.
P(b|a)=n(a intersection b)/n(a)
=P(h,h)/P[(h,h),(h,t)]
=1/2
Answer is option A
Answer: (A) 1/2
Question: A shopkeeper sold an book offering a discount of 5% and earned a profit of 33%. What would have been the percentage of profit earned if no discount was offered?
(A) 140
(B) 120
(C) 130
(D) 110
(E) 150
Rationale: Let C.P. be $100.
Then, S.P. = $133
Let marked price be $x. Then, 95/100 x = 133
x = 13300/95 = $140
Now, S.P. = $140, C.P. = $100
Profit % = 40%.
A
Answer: (A) 140
Question: A number exceeds by 15 from its 3/8 part. Then the number is?
(A) A)32
(B) B)24
(C) C)39
(D) D)40
(E) E)45
Rationale: x – 3/8 x = 15
x = 24
ANSWER:B
Answer: (B) B)24