mathewhe/aqua_rat huggingface dataset:
Question: Balls of equal size are arranged in rows to form an equilateral triangle. the top most row consists of one ball, the 2nd row of two balls and so on. If 19 balls are added, then all the balls can be arranged in the shape of square and each of the sides of the square contain 8 balls less than the each side of the triangle did. How many balls made up the triangle?
(A) 465
(B) 2209
(C) 2878
(D) 1210
(E) 1560
Rationale: As expected, this question boils down to 2 equation,
Consider total number of Balls in Triangle = T and number of balls in last row = x.
1+2+3+...+x = T
x(x+1)/2 = T ----(a)
As mentioned in the question, side of a square will be (x-8) and total number of Balls in square will be (T+19)
(x-8)^2 = T+19 -----(b)
Now the hardest part of the question will be to solve these 2 equations and this looks like time consuming BUT the easy way will be plug and play. Also, we've to find a value of T (from 5 optiosn given below) which can make a square of a a number. One we know this, it will be a cake walk.
We can see that option A fits this criteria in eq (b). Add - 465+19 = 484 = 22^2 = (x-8)^2 Hence, x = 30
Cross check by putting in eq (a) = x(x+1)/2 = T = > 30*31/2=465
Hence, answer is A.
Answer: (A) 465
Question: The average of a couple was 28Yrs when they were married 5Yrs ago.The avg age of
the couple and a child, who was born during the interval, is 23Yrs now. How old is the
child now ?
(A) 2 Yrs
(B) 4 Yrs
(C) 3 Yrs
(D) 1 Yrs
(E) None of these
Rationale: (a+b-5-5)/2=28;
a+b=66;
a+b+c/3=23;
solving both c=3
ANSWER:C
Answer: (C) 3 Yrs
Question: If 8 men can reap 80 hectares in 24 days , then how many hectares can 36 men reap in 30 days?
(A) 127
(B) 237
(C) 287
(D) 450
(E) 281
Rationale: Explanation:
Let the required no of hectares be x. Then
More men, More hectares (Direct proportion)
More days, More hectares (Direct proportion)
Men\: 8:36\\ Days\: 24:30 \end{matrix}\right\} :80:x
\inline \fn_jvn \therefore \inline \fn_jvn 8\times 24\times x=36\times 30\times 80 \inline \fn_jvn \Leftrightarrow \inline \fn_jvn x=\frac{36\times 30\times 80}{8\times 24} \inline \fn_jvn \Leftrightarrow x= 450
Answer: D
Answer: (D) 450
Question: What proximate value should come in place of the question mark (?) in the following question?
6.695 Ã— 1084 + 2568.34 â€“ 1708.34 = ?
(A) 6,000
(B) 12,000
(C) 10,000
(D) 8,096
(E) 9,000
Rationale: ? â‰ˆ 6.7 Ã— 1080 + 2560 â€“ 1700 â‰ˆ 7236 + 860 â‰ˆ 8096
Answer D
Answer: (D) 8,096
Question: The average of first 6 natural numbers is?
(A) 5.2
(B) 3.5
(C) 5.3
(D) 5.9
(E) 5.1
Rationale: Sum of 6 natural no. = 42/2 = 21
Average = 21/6 = 3.5
Answer:B
Answer: (B) 3.5
Question: Twenty four men can do a work in 48 days. How many men are required to complete the work in 12 days?
(A) 85
(B) 46
(C) 50
(D) 96
(E) 60
Rationale: D
96
We have M1 D1 = M2 D2
So, 24 * 48 = M2 * 12 => M2 = 96.
Answer: (D) 96
Question: A train 360 m long is running at a speed of 45 kmph.In what time will it pass a bridge 140 m long?
(A) 40 sec
(B) 42 sec
(C) 45 sec
(D) 48 sec
(E) 49 sec
Rationale: speed of the train 45* 5/18 = 25/2 m/sec
time = (360+140)/25/2
= 500*2/25
=40sec
ANSWER:A
Answer: (A) 40 sec
Question: kumar saves 32% of his monthly salary. If he spends Rs. 27200, then find his savings?
(A) 15400
(B) 14300
(C) 13200
(D) 12800
(E) 9500
Rationale: Answer: Option D
Let the monthly salary of kumar be Rs. x.
68% of x = 27200
=> x = (27200 * 100)/68 = 40000
His savings = 32/100 * 40000 = 12800.
Answer: (D) 12800
Question: When a whole no. n is divided by 4,we will get 3 as remainder. What will be the remainder if 2n is divided by 4?
(A) 1
(B) 4
(C) 2
(D) 6
(E) 7
Rationale: Let n ÷ 4 = p , remainder = 3
=> n = 4p + 3
2n = 2(4p + 3)
= 8p + 6
= 8p + 4 + 2
= 4(2p + 1) + 2
Hence, if 2n is divided by 4, we will get 2 as remainder.
C
Answer: (C) 2
Question: Sn = n^2 + 5n + 94 and K = S6 – S5 + S4 – S3 - S2 + S1. What is the value of K?
(A) 67
(B) 20
(C) 45
(D) 41
(E) 36
Rationale: I used brute force for this question:
S6: 36+30+94=160
S5: 25+25+94=144
S4: 16+20+94=130
S3: 9+15+94=118
S2: 4+10+94=108
S1: 1+5+94=100
S6-S5+S4-S3+S2-S1= 16+12-8=20
Answer B
Answer: (B) 20
Question: A total of x tourists were transported by bus to a certain museum. If there were y tourists on each bus, which of the following expresses the number of buses used?
(A)  xy
(B)  x/y
(C)  y/x
(D)  x - y
(E)  y^2
Rationale: IMHO (B) x/y as well !
Number of buses used = Total number of tourists / Number of tourists per bus => x/y
PS : In case of any doubt , plug in some numbers
Total number of tourists transported by bus = 500
Number of tourists per bus = 10
No of buses required = 500/10
Answer: (B)  x/y
Question: John bought a total of 16 Mangoes and Oranges. Each Mango costs 80 cents and each orange costs 60 cents. If the average price of the 16 mangoes and oranges that John originally purchased was 65 cents, then how many oranges needs to return to raise the average price of his purchase to 72 cents?
(A) 4
(B) 5
(C) 6
(D) 7
(E) 10
Rationale: Let number of mangoes be x, number of oranges be 16-x
0.80x +(16-x)0.60/16 = 0.65
solving for x, we get x = 4 --> Mangoes 4, Oranges 12
Now, number of oranges to be returned be y
0.80*4 + (12-y)*0.60/16-y = 0.72
solving for y, y = 10
Ans:E
Answer: (E) 10
Question: To mail a package, the rate is 10 cents for the first pound and 5 cents for each additional pound. Two packages weighing 4 pounds and 6 pounds, respectively can be mailed seperately or combined as one package. Which method is cheaper and how much money is saved?
(A) Combined, with a saving of 15 cents
(B) Combined, with a saving of 10 cents
(C) Combined, with a saving of 5 cents
(D) Separately, with a saving of 5 cents
(E) Separately, with a saving of 15 cents
Rationale: 4 pounds cost = 10+3*5 = 25
6 pounds cost = 10+5*5 = 35
Total = 60
10 pounds cost = 10+ 9*5 =55
Answer : C
Answer: (C) Combined, with a saving of 5 cents
Question: The probability of Sam passing the exam is 1/5. The probability of Sam passing the exam and Michael passing the driving test is 1/6. What is the probability of Michael passing his driving test?
(A) 5/6.
(B) 1/2.
(C) 1/3.
(D) 2/3.
(E) 2/5
Rationale: 1/5 *1/m= 1/6 , 1/m = 5/6
Answer A
Answer: (A) 5/6.
Question: If the compound interest on an amount of Rs. 29000 in two years is Rs. 9352.5, what is the rate of interest?
(A) 11
(B) 9
(C) 15
(D) 18
(E) 25
Rationale: let interest rate be x.
(2x+(x^2)/100)*(1/100)*29000 = 9352.5
x = 15
ANSWER:C
Answer: (C) 15
Question: Rs.8000 become Rs.8487.20 in a certain interval of time at the rate of 3% per annum of C.I. Find the time?
(A) 6 years
(B) 8 years
(C) 9 years
(D) 3 years
(E) 2 years
Rationale: 8487.20 = 8000(34/30)N
(34/30)^2 = (34/30)N => N = 2
At the end of three years what will be the comp.Answer: E
Answer: (E) 2 years
Question: My watch gains 5 min every hour. How many degrees the second hand moves in every min?
(A) 300
(B) 350
(C) 390
(D) 400
(E) 450
Rationale: Gain 5 min
every 1 hr
degrees moves ==>390
ANSWER C
Answer: (C) 390
Question: Three candidates contested an election and received 1136, 7636 and 14000 votes respectively. What percentage of the total votes did the winning candidate get?
(A) 46%
(B) 61%
(C) 74%
(D) 63%
(E) 68%
Rationale: B
14000/(1136 + 7636 + 14000) = 61%.
Answer: (B) 61%
Question: At the end of year 1998, Shepard bought nine dozen goats. Henceforth, every year he added p% of the goats at the beginning of the year and sold q% of the goats at the end of the year where p > 0 and q > 0. If Shepard had nine dozen goats at the end of year 2002, after making the sales for that year, which of the following is true?
(A) p = q
(B) p < q
(C) p > q
(D) p = q/2
(E) None of these
Rationale: Explanation :
The number of goats remain the same. If the percentage that is added every time is equal to the percentage that is sold, then there should be net decrease.
The same will be the case if the percentage added is less than the percentage sold.
The only way the number of goats remain the same if p>q.
Answer : C
Answer: (C) p > q
Question: A can do a certain job in 25 days which B alone can do in 20 days. A started the work and was joined by B after 10 days. The number of days taken in completing the wotk were ?
(A) 14 2/3kmph
(B) 15 2/3kmph
(C) 16 2/3kmph
(D) 17 2/3kmph
(E) 18 2/3kmph
Rationale: Explanation:
Work done by A in l0 days = (1/25) *10 = 2/5
Remaining work = 1 - (2/5) = 3/5
(A+B)s 1 days work = (1/25) + (1/20) = 9/100
9/100 work is done by them in 1 day.
hence 3/5 work will be done by them in (3/5)*(100/9)
= 20/3days.
Total time taken = (10 + 20/3) = 16*(2/3) days
Option C
Answer: (C) 16 2/3kmph
Question: Suppose there is an outlet which is pouring water at a constant rate and is able to fill a swimming pool in nine hours. There is another outlet that is able to fill the pool in five hours. If we open both the outlets and let them pour the water together How many hours will it take to fill the pool ?
(A) 3.11 hours
(B) 2.21 hours
(C) 3.21 hours
(D) 4.21 hours
(E) 5.21 hours
Rationale: total work=1/9+1/5=14/45 so reqired time=45/14
=3.21 hours
ANSWER:C
Answer: (C) 3.21 hours
Question: Carol is three times Alice’s age but only twice as old as Betty. Alice is twenty-four years younger than Carol. How old is Betty?
(A) 26
(B) 19
(C) 22
(D) 18
(E) 24
Rationale: Beyond the obvious Algebra approach to this question, it can also be solved by TESTing THE ANSWERS.
We're told 3 facts about the relative ages of 3 people:
1) Carol's age is 3 times Alice's age
2) Carol's age is 2 times Betty's age
3) Carol is 24 years older than Alice
We're asked for BETTY'S age.
From the answer choices and the information provided, Carol can't be that old (The difference of 12 years = 3 times; that relationship can only occur when the numbers are relatively small). Since Carol is TWICE Betty's age, Betty is clearly younger than Carol, so we'll TEST a smaller answer first.
IF....
Betty = 18
Then Carol = 2(18) = 36
Then Alice = 36 - 24 = 12 AND 36/3 = 12
All of these values mesh perfectly with the facts and with one another, so Betty MUST be 18
D
Answer: (D) 18
Question: If the sides of a triangle are 9 cm, 16 cm and 19 cm, what is its area?
(A) 69
(B) 72
(C) 75
(D) 89
(E) 93
Rationale: The triangle with sides 9 cm, 16 cm and 19 cm is right angled, where the hypotenuse is 19 cm.
Area of the triangle = 1/2 * 9 * 16 = 72 cm2
Answer: Option B
Answer: (B) 72
Question: Three candidates contested an election and received 5000, 22000 and 34800 votes respectively. What percentage of the total votes did the winning candidate get ?
(A) 56.31
(B) 45%
(C) 75.20%
(D) 86%
(E) 95.15%
Rationale: Explanation :
Total number of votes polled = (5000+ 22000 + 34800)
= 61800.
Required percentage = (34800/ 61800) X100
= 56.31%.
Answer : A
Answer: (A) 56.31
Question: By selling an article at Rs.500, a profit of 25% is made. Find its cost price?
(A) 400
(B) 267
(C) 287
(D) 480
(E) 811
Rationale: SP = 500
CP = (SP)*[100/(100+P)]
= 500 * [100/(100+25)]
= 500 * [100/125] = Rs.400
Answer: A
Answer: (A) 400
Question: A group of college friends plan to rent a house together for x dollars per month, which is to be shared equally among them. If four, rather than six people rent the house together, how many more dollars, in terms of x, will each person have to pay for rent per month?
(A) x/4
(B) x/6
(C) x/12
(D) x/10
(E) x/24
Rationale: If 6 people share the rent, each person would pay x/6.
If 4 people share the rent, each person will pay x/4.
The extra amount each person pays is x/4 - x/6 = 3x/12 - 2x/12 = x/12
The answer is C.
Answer: (C) x/12
Question: For any integer p, *p is equal to the product of all the integers between 1 and p, inclusive. How many prime numbers are there between *9 + 3 and *9 + 9, inclusive?
(A)  None
(B)  One
(C)  Two
(D)  Three
(E)  Four
Rationale: Generally *p or p! will be divisible by ALL numbers from 1 to p. Therefore, *9 would be divisible by all numbers from 1 to 9.
=> *9+3 would give me a number which is a multiple of 3 and therefore divisible (since *9 is divisible by 3)
In fact adding anyprimenumber between 1 to 9 to *9 will definitely be divisible.
So the answer is none (A)!
Supposing if the question had asked for prime numbers between *9 + 3 and *9 + 11 then the answer would be 1. For *9 +3 and *9 + 13, it is 2 and so on...
A
Answer: (A)  None
Question: The average monthly salary of 8 workers and one supervisor in a factory was 430.@SSWhen@SSthe@SSsupervisor@CC@SSwhose@SSsalary@SSwas@SS430.@SSWhen@SSthe@SSsupervisor@CC@SSwhose@SSsalary@SSwas@SS430.Whenthesupervisor,whosesalarywas430. When the supervisor, whose salary was 870 per month, retired, a new person was appointed and then the average salary of 9 people was $$430 per month. The salary of the new supervisor is:
(A) 870
(B) 600
(C) 287
(D) 771
(E) 191
Rationale: Explanation:
Total salary of 8 workers and supervisor together = 9 Ã— 430 = 3870
Now total salary of 8 workers = 3870 âˆ’ 870 = 3000
Total salary of 9 workers including the new supervisor = 9 Ã— 430 = 3870
Salary of the new supervisor = 3870 âˆ’ 3000 = 870
Answer: A
Answer: (A) 870
Question: A rectangular park 60 m long and 40 m wide has two concrete crossroads running in the middle of the park and rest of the park has been used as a lawn. If the area of the lawn is 2109 sq. m, then what is the width of the road?
(A) 2.91 m
(B) 3 m
(C) 5.82 m
(D) 4.32 m
(E) None of these
Rationale: Area of the park = (60 x 40) m2 = 2400 m2.
Area of the lawn = 2109 m2.
Area of the crossroads = (2400 - 2109) m2 = 291 m2.
Let the width of the road be x metres. Then,
60x + 40x - x2 = 291
x2 - 100x + 291 = 0
(x - 97)(x - 3) = 0
x = 3.
Answer: Option B
Answer: (B) 3 m
Question: Lionel left his house and walked towards Walt's house, 48 miles away. Two hours later, Walt left his house and ran towards Lionel's house. If Lionel's speed was 3 miles per hour and Walt's 4 miles per hour, how many miles had Lionel walked when he met Walt?
(A) 12
(B) 16
(C) 20
(D) 24
(E) 28
Rationale: In the first 2 hours Lionel at the rate of 3 miles per hour covered distance=rate*time=3*2=6 miles. So, the distance between him and Walt was 48-6=42 miles when Walt left his house. Now, their combined rate to cover this distance was 3+4=7 miles per hour, hence they will meet (they will cover that distance) in time=distance/rate=42/7=6 hours. Total time that Lionel was walking is 2+6=8 hours, which means that he covered in that time interval distance=rate*time=3*8=24 miles.
Answer: D.
Answer: (D) 24
Question: The average weight of 5 person's increases by 4 kg when a new person comes in place of one of them weighing 50kg. What is the weight of the new person?
(A) 70
(B) 86.5
(C) 80
(D) 88.5
(E) 75
Rationale: Total increase in weight =5 × 4=20
If x is the weight of the new person, total increase in weight = x−50
=> 20= x - 50
=> x = 20+50= 70
ANSWER:A
Answer: (A) 70
Question: The least perfect square, which is divisible by each of 21,36 and 66 is
(A) 213444
(B) 214344
(C) 214434
(D) 213443
(E) None of these
Rationale: L.C.M. of 21, 36, 66 = 2772.
Now, 2772 = 2 x 2 x 3 x 3 x 7 x 11
To make it a perfect square, it must be multiplied by 7 x 11.
So, required number = 22 x 32 x 72 x 112 = 213444
Answer A
Answer: (A) 213444
Question: X, Y and Z contract a work for Rs. 1100. X and Y together are to do 7/11 of the work. C’s share is:
(A) Rs.366.6
(B) Rs.400
(C) Rs.600
(D) Rs.800
(E) Rs.900
Rationale: (A + B) : C = 7/11 : 4/11 = 7 : 4.
Therefore, C’s share = Rs. 1100 * 4/11
= Rs.400.
ANSWER:B
Answer: (B) Rs.400
Question: What is the units digit of 63^3 * 17^3 * 49^3?
(A) 1
(B) 3
(C) 5
(D) 7
(E) 9
Rationale: The units digit of 63^3 is the units digit of 3*3*3 = 27 which is 7.
The units digit of 17^3 is the units digit of 7*7*7 = 343 which is 3.
The units digit of 49^3 is the units digit of 9*9*9 = 729 which is 9.
The units digit of 7*3*9 = 189 is 9.
The answer is E.
Answer: (E) 9
Question: What is the present worth of Rs. 176 due in 2 years at 5% simple interest per annum?
(A) 288
(B) 160
(C) 120
(D) 277
(E) 6123
Rationale: Let the present worth be Rs. x. Then,
S.I. = (176 - x)
(x * 5 * 2) / 100 = (176 - x)
10x = 17600 - 100x
110x = 17600 => x = 160.
Answer: B
Answer: (B) 160
Question: If log 27 = 1.431, then the value of log 9 is:0.934
B.	0.945
C.	0.954
D.	0.958
(A) 0.934
(B) 0.945
(C) 0.954
(D) 0.958
(E) 0.964
Rationale: log 27 = 1.431
log (3^3 ) = 1.431
3 log 3 = 1.431
log 3 = 0.477
log 9 = log(3^2 ) = 2 log 3 = (2 x 0.477) = 0.954.
Answer is C.
Answer: (C) 0.954
Question: There are 28 girls in hostel whose average age is decreased by 2 months, when one girl 18 yrs is replaced by a new boy.Find the age of new girl.
(A) 1 year
(B) 1 year 2 months
(C) 4 years 8 months
(D) 3 years
(E) None
Rationale: Total decrease = 28 * 2 = 56 months
= 4 years 8 months
C
Answer: (C) 4 years 8 months
Question: A tap can fill a tank in 2 hours. After half the tank is filled, two more similar taps are opened. What is the total time taken to fill the tank completely?
(A) 1 hr 40 min
(B) 4 hr
(C) 3 hr
(D) 1 hr 20 min
(E) 2 hr 50 min
Rationale: Explanation:
1 tap can fill the tank in 2 hours.
Therefore
1 tap can fill half tank in 1 hours.
3 taps can fill the tank in 2/3 hour.
Therefore
3 taps can fill half tank in 2/6 hour =20 minutes.
Total time taken=1 hour 20 minutes
Answer: Option D
Answer: (D) 1 hr 20 min
Question: Given that E and F are events such that P(E) = 8, P(F) = 2 and P(E n F) = 8,
find P (E|F) and P(F|E)
(A) 5
(B) 4
(C) 12
(D) 36
(E) 98
Rationale: Here, E and F are events
P(E|F) = P(EnF)/P(F) = 8/8= 1
P(F|E) = P(EnF)/P(E) = 8/2 = 4.
B)
Answer: (B) 4
Question: Two good train each 900 m long, are running in opposite directions on parallel tracks. Their speeds are 45 km / hr and 30 km /hr respectively. Find the time taken by the slower train to pass the driver of the faster one.
(A) 12.2 sec
(B) 24.9 sec
(C) 86.4 sec
(D) 60.2 sec
(E) None
Rationale: Sol.
Relative Speed = (45 + 30) km / hr
= (75 x 5 / 18) m/sec
= (125/6) m/sec.
Distance covered = (900 + 900) m = 1000 m.
Required time = (1800 x 6 / 125) sec = 86.4 sec.
Answer C
Answer: (C) 86.4 sec
Question: A dice has one of the first 7 prime number on each its six sides ,with no two sides having the same number .the dice is rolled 12 times and the results added.the addition is most likely to be closet to
(A) 41
(B) 48
(C) 60
(D) 99
(E) 70
Rationale: if die is rolled then avg score = (2+3+5+7+11+13+17 )/7 = 58/7
so, most likely sum for 10 times = 58/7 * 12 = 99
ANSWER:D
Answer: (D) 99
Question: A train 360 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 140 m long?
(A) 40
(B) 99
(C) 88
(D) 66
(E) 21
Rationale: Speed = 45 * 5/18 = 25/2 m/sec
Total distance covered = 360 + 140 = 500 m
Required time = 500 * 2/25 = 40 sec.Answer: A
Answer: (A) 40
Question: A man has Rs. 416 in the denominations of one-rupee notes, five-rupee notes and ten rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has?
(A) 45
(B) 60
(C) 78
(D) 90
(E) 95
Rationale: Let number of notes of each denomination be x.
Then x + 5x + 10x = 416
16x = 416
x = 26.
Hence, total number of notes = 3x = 78
Answer: Option C
Answer: (C) 78
Question: If 18 is 15 percent of 35 percent of a certain number, what is the number?
(A) 9
(B) 36
(C) 40
(D) 300
(E) 400
Rationale: Let the certain number be x.
=> (15/100)*(40/100)*x = 18;
=> x=300;
Ans is (D).
Answer: (D) 300
Question: The rupee/coin changing machine at a bank has a flaw. It gives 10 ten rupee notes if you put a 100 rupee note and 10 one rupee coins if you insert a 10 rupee note but gives 10 hundred rupee notes when you put a one rupee coin!Sivaji, after being ruined by his rivals in business is left with a one rupee coin and discovers the flaw in the machine by accident. By using the machine repeatedly, which of the following amounts is a valid amount that Sivaji can have when he gets tired and stops at some stage (assume that the machine has an infinite supply of notes and coins):
(A) 53947
(B) 53949
(C) 53946
(D) 53945
(E) 53944
Rationale: Explanation:
The process works like this:
Rs.1 Coin ⇒ 10 × 100 = Rs.1000
Rs.100 ⇒ 10 × 10
Rs.10 ⇒ 1 × 10
Sivaji gets more money when he inserts a rupee coin only. For each rupee coin he gets his money increased by 1000 times. Suppose he inserted 1 rupee coin and got 1000 rupees and again converted this into coins. So he ends up with 1000 coins. Now of this, he inserts one coin, he gets 1000. So he has 1999 with him. Now if he inserts another coin, he has 1998 + 1000 = 2998.
Now each of these numbers are in the form of 999n + 1. So option B can be written as 54 × 999 + 1.
Answer: B
Answer: (B) 53949
Question: Pipe A can fill a tank in 3 hours. Due to a leak at the bottom, it takes 9 hours for the pipe A to fill the tank. In what time can the leak alone empty the full tank?
(A) 4.5
(B) 17
(C) 18
(D) 19
(E) 12
Rationale: Let the leak can empty the full tank in x hours 1/3 - 1/x = 1/9
=> 1/x = 1/3 - 1/9 = (3 - 1)/9 = 2/9
=> x = 9/2 = 4.5.
Answer: A
Answer: (A) 4.5
Question: A, B and C invested Rs.6300, Rs.4200 and Rs.10500 respectively, in a partnership business. Find the share of A in profit of Rs.12100 after a year?
(A) Rs.3630
(B) Rs.2840
(C) Rs.3200
(D) Rs.5600
(E) Rs.3000
Rationale: Explanation:
6300:4200:10500
3:2:5
3/10 * 12100 = 3630
ANSWER IS A
Answer: (A) Rs.3630
Question: An intelligence agency decides on a code of 2 digits selected from 0, 1, 2, …, 9. But on the slip on which the code is hand written allows confusion between top and bottom, because there are indistinguishable. Thus, for example, the code 91 could be confused with 16. How many codes are there such that there is no possibility of any confusion?
(A) 90
(B) 80
(C) 40
(D) 50
(E) 89
Rationale: Total digits that can be formed = 10C1 * 10C1 = 100.
The digits that still remain digits when turned upside down are 0, 1, 6, 8 and 9.
So codes that can create confusion are:
01, 06, 08, 09
10, 16, 18, 19
60, 61, 66, 68 (69 would still be 69 when inverted)
80, 81, 86, 89
90, 91, 98, 99 (96 would still be 96 when inverted)
There are 20 such numbers.
Required numbers = 100 - 20 = 80
ANSWER:B
Answer: (B) 80
Question: If the product 4864 x 9 P 2 is divisible by 12, then the value of P is:
(A) 1
(B) 5
(C) 8
(D) 6
(E) 4
Rationale: Explanation:
Clearly, 4864 is divisible by 4.
So, 9P2 must be divisible by 3. So, (9 + P + 2) must be divisible by 3.
P = 1.
ANSWER A
Answer: (A) 1
Question: A man has some hens and cows. If the number of heads be 48 and the number of feet equals 140, then the number of hens will be
(A) 26
(B) 27
(C) 28
(D) 29
(E) 30
Rationale: Let number of hens = h and number of cows = c
number of heads = 48
=> h + c = 48 ---(Equation 1)
number of feet = 140
=> 2h + 4c = 140
=> h + 2c = 70 ---(Equation 2)
(Equation 2) - (Equation 1) gives
2c - c = 70 - 48
=> c = 22
Substituting the value of c in Equation 1, we get
h + 22 = 48
=> h = 48 - 22 = 26
i.e., number of hens = 26
Answer is A.
Answer: (A) 26
Question: If the true discount on s sum due 2 years hence at 14% per annum be Rs. 182, the sum due is:
(A) s. 832
(B) s. 968
(C) s. 1960
(D) s. 2400
(E) s. 2800
Rationale: td=pw*r*t/100 so 182=pw*14*2/100 so pw=650
sum=pw+td..
sum=650+182=832
ANSWER:A
Answer: (A) s. 832
Question: Cuboid volume and Base area are 144 m^3 and 18m^3 respectively.Find the height of a cuboid?
(A) 5m
(B) 12m
(C) 6m
(D) 8m
(E) 10m
Rationale: Height of the cuboid=Volume* Base area
=144/18
=8 metre
Answer is option D
Answer: (D) 8m
Question: A train covers a distance of 12 km in 10 min. If it takes 6 sec to pass a telegraph post, then the length of the train is?
(A) 288
(B) 277
(C) 120
(D) 285
(E) 121
Rationale: Speed = (12/10 * 60) km/hr = (72 * 5/18) m/sec = 20 m/sec.
Length of the train = 20 * 6 = 120 m.
Answer: C
Answer: (C) 120
Question: The average mark of 20 students in a class is 70 years. The average age of 10 students is 65. What is the total mark of remaining 10 students?
(A) 850
(B) 800
(C) 750
(D) 700
(E) 680
Rationale: Sum of the ages of 10 students
= (20 * 70) - (10 * 65) = 1400 - 650 = 750
Required Total marks = 750
Answer: C
Answer: (C) 750