RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: Given two sets A = {1,1,2,2,7,7} and B = {0,1}, if one number is chosen from each set at random, what is the probability that the sum of both numbers is an even number
A.1/5
B.1/6
C.1/2
D.1/3
Answer: C.1/2
Explanation: One way to look at it:
The number from set A can be ANYTHING.
The number selected from set B will determine whether the sum is odd or even.
For example, if a 2 is selected from set A, we need a 0 from set B to get an even sum.
If a 7 is selected from set A, we need a 1 from set B to get an even sum.
And so on.
So, P(sum is even) = P(select ANY number from set AANDselect the number from set B that makes the sum even)
= P(select ANY number from set A)xP(select the number from set B that makes the sum even)
= 1x1/2
= 1/2
= C
Question: Of the three-digit integers greater than 700, how many have distinct digits?
A. 216
B. 82
C. 80
D. 45
Answer: A. 216
Explanation: Three digit number can have only following 3 patterns:
A. all digits are distinct;
B. two digits are alike and third is different;
C. all three digits are alike.
We need to calculate B. B=Total - A - C
Total numbers from 700 to 999 = 299 (3-digit numbers greater than 700);
A. all digits are distinct = 3*9*8=216
Answer: A
Question: Find the compound interest on $ 10,000 in 2 years at 4% per annum, the interest being compounded half-yearly
A.824
B.824.36
C.824.32
D.824.24
Answer: C.824.32
Explanation: Principal = $ 10000; Rate = 2% per half-year; Time = 2 years = 4 half-years.
Amount = $ [10000 * (1+(2/100))4] = $(10000 * (51/50) * (51/50) * (51/50) * (51/50))
= $ 10824.32.
:. C.I. = $ (10824.32 - 10000) = $ 824.32.
Answer C.
Question: There are n cities. What is the number of airlines that connected 5 different cities (airline from city A to city B is different with airline from city B to city A)?
A.n(n-1)
B.n(n+1)
C.n(n-1)/2
D.n(n-3)
Answer: D.n(n-3)
Explanation: First of all, the possible number of airlines is n. Then, the possible number of airlines departing from one city to another becomes (n-4). Hence, the answer is n(n-4), which makes A an answer choice.
D
Question: What is the probability that a two digit number selected at random is a multiple of 3 and not a multiple of 5 ?
A.1/15
B.2/15
C.4/15
D.7/15
Answer: C.4/15
Explanation: Explanation :
Since every third number starting from 10 will be divisible by 3, so total number of numbers divisible by 3 are 90/3 = 30
Numbers which are divisible by 3 and 5 both are numbers which are multiple of 15.
For the range 10 to 99, 15 is the first number divisible by 15 and 90 is the last number.
So total number of numbers divisible by 15 are: (90-15)/15 + 1 = 5 + 1 = 6
Number of numbers which are divisible by 3 are 30 and number of numbers which are divisible by 3 and 5 both are 6. So number of numbers divisible by 3 and not by 5 are: 30-6=24
So total probability = 24/90 = 4/15
Answer : C
Question: The sale price of a trolley bag including the sale tax is Rs. 280. The rate of sale tax is 12% . If the shopkeeper has made a profit of 25%, the cost price of the trolley bag is:
A.Rs 200
B.Rs 220
C.Rs 260
D.Rs 280
Answer: A.Rs 200
Explanation: Explanation :
112% of S.P. = 280
S.P. = Rs.(280x 100/112) = Rs.250.
C.P. = Rs (100/125x 250) = Rs 200
Answer : A
Question: How many factors of 990 are odd numbers greater than 1?
A.13
B.14
C.15
D.16
Answer: C.15
Explanation: When factorized, 990 has 5 prime factors. Of these prime factors 4 are odd and 1 is even. Hence total number of odd factors is 2*2*2*2(16), which includes 1. The total number of odd factors greater than 1 are 15.(option C)
Question: For some integer p, p^2 - 5 is divisible by all of the following EXCEPT
A.30
B.38
C.41
D.29
Answer: A.30
Explanation: Hint: p^2-5 (p is an integer) is never multiple of 3 (try to prove this), hence 30 is out.
Answer: A
Question: The length of a room is 5.5 m and width is 3.75 m. Find the cost of paving the floor by slabs at the rate of Rs. 1200 per sq. metre.
A.Rs. 15000
B.Rs. 15550
C.Rs. 24750
D.Rs. 16500
Answer: C.Rs. 24750
Explanation: Solution
Area of the floor = (5.5 × 3.75) m2 = 20.625 m2
∴ Cost of paving = Rs. (1200 × 20.625) = 24750. Answer C
Question: How many seconds will a 500 meter long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr
A.25 Seconds
B.28 Seconds
C.30 Seconds
D.35 Seconds
Answer: C.30 Seconds
Explanation: Explanation:
Relative Speed = 63-3 = 60 Km/hr
= 60 *(5/18) = 50/3 m/sec
Time taken to pass the man will be
500âˆ—3/50=30seconds
ANSWER IS C
Question: A number is doubled and 5 is added. If the resultant is trebled, it becomes 105. What is that number?
A.12
B.29
C.27
D.15
Answer: D.15
Explanation: Explanation:
Let the number be x.
Therefore,
3(2x + 5) = 105
6x + 15 = 105
6x = 90
x = 15
ANSWER:D
Question: The Present worth of Rs.2310 due years hence ,the rate of interest being 15% per annum, is :
A.Rs.1440
B.Rs.1750
C.Rs.1680
D.Rs.1840
Answer: C.Rs.1680
Explanation: Explanation:
P.W.=Rs.[100×2310/100+(15×52)]=Rs.1680.
Answer: C
Question: All even numbers from 2 to 98 inclusive, except those ending in 0, are multiplied together what is the rightmost digit (the units digit) of the product?
A.0
B.2
C.4
D.6
Answer: D.6
Explanation: first multifly all numbers ending with 2 those are 2*12*22*32*42.......*92=2^10=4 is last digit
multify all numbers ending with 4=4^10=6 last digit
multify all numbers ending with 6=6^10= 6 last digit
multifly all numbers ending with 8=8^10=4 last digit
so 4*6*6*4=6 last digit
ANSWER:D
Question: A basket contains 5 apples of which one is rotten. If Henry is to select 2 apples from the basket simultaneously and at random what is the probability that the 2 apples selected will include the rotten apple?
A.1/5
B.3/10
C.2/5
D.1/2
Answer: C.2/5
Explanation: Direct probability approach:
P=15∗44+45∗14=25P=15∗44+45∗14=25: probability of {first apple rotten, second apple good} plus the probability of {first apple good, second apple rotten}.
Reverse probability approach:
Again 1- the probability of the opposite event --> P=1−45∗34=25P=1−45∗34=25.
Answer: C
Question: What is the units digit of 29! + 50! + 3! + 3!?
A.0
B.2
C.4
D.6
Answer: B.2
Explanation: For all N greater than 4, the units digit of N! is 0.
The sum of the four units digits is 0 + 0 + 6 + 6 = 12
The units digit is 2.
The answer is B.
Question: If the milk and water ware added in the ratio 5:4 then how much more water should be added so he gets the ratio of 6:7.
A.11/6
B.11/7
C.11/8
D.6/11
Answer: A.11/6
Explanation: let quantity of water should added be x then
A/Q
5/(4+x)= 6/7
=> 35=24+6x
=> x=11/6
ANSWER:A
Question: if 5 tomatoes are worth 8 oranges,5 oranges are worth 4 apples, 7 apples are worth 3 pineapples and 7 pineapples cost rs.203,then he approx price of each tomato is
A.16
B.5
C.19
D.20
Answer: A.16
Explanation: 7 pineapples cost rs.203 means one pineapple cost is 29
7 apples are worth 3 pineapples means 7 apple cost 29*3. 1 Apple cost (29*3)/7
5 oranges are worth 4 apples. 1 orange cost is (29*3*4)/(7*5)
5 tomatoes are worth 8 oranges. 1 tomato cost is (29*3*4*8)/(7*5*5) = 2784/175 = 15.9
ANSWER:A
Question: A school’s annual budget for the purchase of student computers increased by 60% this year over last year. If the price of student computers increased by 20% this year, then the number of computers it can purchase this year is what percent greater than the number of computers it purchased last year?
A.33.33%
B.40%
C.42%
D.48%
Answer: A.33.33%
Explanation: If last year, the budget was B and the price of one computer was P, then B/P was the number of purchased computers.
This year, 1.6B/(1.2P) = 4/3(B/P) = 1.33(B/P) computers can be purchased, which is 33.33% greater than the number of computers purchased last year.
Answer A.
Question: An unbiased cubic die is thrown.What is the probabiltiy of getting a multiple of 3 or 4?
A.1/9
B.1/12
C.1/2
D.3/4
Answer: C.1/2
Explanation: Explanation :
Total numbers in a die=6P(mutliple of 3) = 2/6 = 1/3P(multiple of 4) = 1/6P(multiple of 3 or 4) = 1/3 + 1/6 = 1/2
Answer : C
Question: In a class there are 55 pupil, out of them 10 are in debate only and 18 in singing only. Then how many in both?
A.132
B.26
C.17
D.11
Answer: C.17
Explanation: Explanation:Total pupil = 55
Debate + Singing = 10 + 18 = 28
The intersection for two = 55 â€“ 10 â€“ 28 = 17 play both games.
Answer: C
Question: If point A coordinates are (-6, -3) point B coordinates are (8 ,4 ) if C is along the line A-B so that AC = 1/2 CB. What are the coordinates of point C.
A.(-2, - 2/3)
B.(2, -2/3)
C.(2/3, -2)
D.(0, 2)
Answer: B.(2, -2/3)
Explanation: Look at the diagram below:
Line segment.pngSince, AC= 1/2 CB, then AC = 1/3 AB. This implies that point C is closer to A than to B, which on the other hand implies that the x-coordinate of C must be less than (-6+8)/2=0.5. Only D and A fits, but as (0 , 2) is clearly not on line segment AB, then the answer must be B.
Answer: B.
Question: Of the 420 members at a health club, 260 use the weight room and 300 use the pool. If at least 60 of the members do not use either, then the number of members using both the weight room and the pool must be between:
A.200 to 260
B.160 to 260
C.220 to 260
D.220 to 300
Answer: A.200 to 260
Explanation: W=260
P=300
ALL=420
N(NEITHER)=AT LEAST 60
BOTH=?
W+P-BOTH+N=ALL
260+300-BOTH+60=420
BOTH=200
now pay attention to the fact, that both at most can be 260, since W=260
so, the answer is A
Question: A seller of used cars has 10 cars to sell and each of his clients selected 2 cars that he liked most. If each car was selected exactly thrice, how many clients visited the garage?
A.8
B.10
C.15
D.14
Answer: C.15
Explanation: IfNo caris selected more than once then the number of clients = 10/2 =5
But since every car is being selected three times so No. of Clients must be thrice as well =5*3 = 15
Answer: option C
Question: A man sells a car to his friend at 13% loss. If the friend sells it for Rs.54000 and gains 20%, the original C.P.of the car was :
A.Rs.21724.14
B.Rs.31724.14
C.Rs.51724.14
D.Rs.61724.14
Answer: C.Rs.51724.14
Explanation: Explanation:
S.P = Rs.54,000. Gain earned = 20%
C.P = Rs.[100/120Ã—54000]
=Rs. 45000
This is the price the first person sold to the second at at loss of 13%.
Now S.P = Rs.45000 and loss = 13%
C.P. Rs.[100/87Ã—45000]= Rs.51724.14.
Correct Option : C
Question: Three people each took 6 tests. If the ranges of their scores in the 6 practice tests were 17, 28 and 35, 42 what is the minimum possible range in scores of the three test-takers?
A.a 17
B.b) 28
C.c) 35
D.d) 45
Answer: D.d) 45
Explanation: It is finding the minimum range between all their scores, if all test taker scores are between 0 and maximum range we will have:
A- 0 and 17
B- 0 and 28
C- 0 and 35
D-0 and 42
therefore the minimum range is 42, it cant be any lower however you play with the numbers.
D
Question: A room 5.44m long and 3.74m broad is to be paved with square tiles. The least number of square tiles required to cover the floor is:
A.176
B.192
C.184
D.162
Answer: A.176
Explanation: Area of the room= 544*374 sq.cm
Size of largest square tile= HCF of 544 cm & 374cm
Area of 1 tile= 34*34 sq.cm
Therefore, number of tiles= (544*374/34*34)= 176
ANSWER:A
Question: A textile manufacturing firm employees 125 looms. It makes fabrics for a branded company. The aggregate sales value of the output of the 125 looms is Rs 5,00,000 and the monthly manufacturing expenses is Rs 1,50,000. Assume that each loom contributes equally to the sales and manufacturing expenses are evenly spread over the number of looms. Monthly establishment charges are Rs 75000. If one loom breaks down and remains idle for one month, the decrease in profit is:
A.13000
B.7000
C.10000
D.2800
Answer: D.2800
Explanation: Explanation :
Profit = 5,00,000âˆ’(1,50,000+75,000) =Rs. 2,75,000.
Since, such loom contributes equally to sales and manufacturing expenses.
But the monthly charges are fixed at Rs 75,000.
If one loan breaks down sales and expenses will decrease.
New profit :-
=>500000Ã—(124/125)âˆ’150000Ã—(124/125)âˆ’75000.
=>Rs 2,72,200.
Decrease in profit
=>2,75,000âˆ’2,72,200
=>Rs. 2,800.
Answer : D
Question: P, Q and R started a business by investing Rs.120000, Rs.135000 and Rs.150000 respectively. Find the share of each, out of the annual profit of Rs.56700.
A.17850, 18900, 21000
B.16800, 18900, 21000
C.17850, 18900, 22000
D.18900, 17850, 21000
Answer: B.16800, 18900, 21000
Explanation: P : Q : R = 120000:135000:150000
=120:135:150=24:27:30=8:9:10
Share of P
=56700×8/27=2100×8=16800
Share of Q
=56700×9/27=2100×9=18900
Share of R
=56700×10/27=2100×10=21000
Answer is B.
Question: What least number must be subtracted from 427398 so that remaining no.is divisible by 14
A.3
B.5
C.6
D.7
Answer: C.6
Explanation: Explanation:
On dividing 427398 by 14 we get the remainder 6, so 6 should be subtracted
Answer: Option C
Question: The average of 10 numbers is calculated as 15. It is discovered later on that while calculating the average, one number namely 36 was wrongly read as 26. The correct average is?
A.28
B.27
C.16
D.29
Answer: C.16
Explanation: 10 * 15 + 36 – 26
= 160/10
= 16
Answer:C
Question: The areas, in kilometers squared, of some countries are given below. USA: 9,629,091, Russia: 18,098,242, China: 9,598,094, Canada: 9,984,670, the UK: 242,400 and India: 3,287,263.
What is the difference between the areas of Russia and China?
A.5,476,811 kilometers squared
B.8,500,148 kilometers squared
C.9,843,123 kilometers squared
D.1,878,965 kilometers squared
Answer: B.8,500,148 kilometers squared
Explanation: he difference between the areas of Russia and China is given by
18,098,242 - 9,598,094 = 8,500,148 kilometers squared
correct answer B
Question: On a scale that measures the intensity of a certain phenomenon, a reading of n+1 corresponds to an intensity that is 10 times the intensity corresponding to a reading of n. On that scale, the intensity corresponding to a reading of 8 is how many times as great as the intensity corresponding to a reading of 3?
A.5
B.50
C.10^5
D.5^10
Answer: C.10^5
Explanation: For n=3, consider the intensity to be x.
For n+1 = 4 , we have [intensity*10 ]= 10x
For n+2 = 5 , we have [10x*10 ]= 100x
For n+3 = 6 , we have [100x*10 ]= 1000x
For n+4 = 7 , we have [1000x*10 ]= 10000x
For n+5 = 8 , we have [10000x*10 ]= 100000x
Now , for n = 8 -->100000x = 10^5 x
which is 10^5 times x, the original intensity at n=3
ANSWER:C
Question: If it takes a tub 4 minutes to drain 5/7 of its content, how much more time will it take for the tub to be empty?
A.48 seconds
B.1 minute, 12 seconds
C.1 minute, 36 seconds
D.2 minutes, 14 seconds
Answer: C.1 minute, 36 seconds
Explanation: If 5/7 of tub's content is drained 2/7 th of tub still needs to be drained.
If it takes 4 minutes to drain 5/7 th of tub it takes 4*(7/5) minutes to drain the entire tub and 4*(7/5)*(2/7) min to drain 2/7 th of the tub which is 8/5 minutes or 1 3/5 minutes or 1 minute 36 seconds
So answer is C
Question: if none of the figures 2,4,5,7,8,0 be repeated,how many different numbers of 4 digits can be formed wiyh them.?
A.150
B.200
C.250
D.300
Answer: D.300
Explanation: here 1st place can be filled by five ways(i.e any one from 2,4,5,7,8),and second place will be again in 5 ways (remaining from 6 digits ,6-1=5) and next place in 4 ways ,and again in 3 ways so ans will be 5*5*4*3=300
ANSWER:D
Question: Find the least multiple of 23,which when divided by 18,21 and 24 leaves remainders 7,10 and 13 respectively.
A.3002
B.3013
C.3024
D.3036
Answer: B.3013
Explanation: Solution
Here (18 - 7) = 11, (21 - 10) = 11 and (24 - 13) = 11. L.C.M. of 18,21 and 24 is 504.
Let required number be 504 k - 11.
Least value of k for which (504 k - 11 ) is divisible 23 is k = 6.
So, Required number = 504 × 6 - 11 =3024 - 11 = 3013.
Answer B
Question: In how many ways can the letters of the word AGENDA be rearranged such that the vowels always appear together?
A.6!/2!
B.3!*3!
C.4!/2!
D.(4! *3!)/2!
Answer: D.(4! *3!)/2!
Explanation: In the word ABACUS , there are 3 vowels - 2 A's and E
Number of ways the letters of word AGENDA be rearranged such that the vowels always appear together
= (4! * 3! )/2!
We can consider the the 3 vowels as a single unit and there are 3 ways to arrange them . But since 2 elements of vowel group are identical we divide by 2! .
The entire vowel group is considered as a single group .
Answer D
Question: At a kennel with 80 dogs, 45 of the dogs wear tags and 40 wear flea collars. If 6 of the dogs wear both, then how many of the dogs wear neither a collar nor tags?
A.1
B.6
C.34
D.79
Answer: A.1
Explanation: Dogs wear neither a collar nor tags = 80 - ( 45 + 40 - 6 )
Dogs wear neither a collar nor tags = 80 - 79
Dogs wear neither a collar nor tags = 80 - 79
Hence, answer will be 1
ANSWER:A
Question: The difference between a two-digit number and the number after interchanging the position of the two digits is 36. What is the difference between the two digits of the number?
A.4
B.6
C.3
D.Cannot be determined
Answer: A.4
Explanation: Let the two-digit no. be l0x + y.
Then, (10x + y) – (10y + x) = 36
or, 9(x – y) = 36
or, x – y = 4
Answer A
Question: 3 litre of water is added to 11 litre of a solution containing 42% of alcohol in the water. The percentage of alcohol in the new mixture is?
A.30%
B.33%
C.35%
D.40%
Answer: B.33%
Explanation: We have a 11 litre solution containing 42% of alcohol in the water.
=> Quantity of alcohol in the solution
=
11
×
42
100
=11×42100
Now 3 litre of water is added to the solution.
=> Total quantity of the new solution = 11 + 3 = 14
Percentage of alcohol in the new solution
=
11
×
42
100
14
×
100
=11×4210014×100
=
11
×
3
100
=
33%
B)
Question: The population of a town is 10000. It increases annually at the rate of 27% p.a. What will be its population after 2 years?
A.14000
B.14400
C.16129
D.14600
Answer: C.16129
Explanation: Formula :
10000 × 127/100 × 127/100 = 16129
Answer : C
Question: Find the no of ways in which 6 toffees can be distributed over 5 different people namely A,B,C,D,E.
A.210
B.211
C.212
D.213
Answer: A.210
Explanation: acc to formula (n+r-1)C (r-1) = (6+5-1)C(5-1)
=10C4 = 210
ANSWER:A
Question: The three competitors in a race have to be randomly chosen from a group of four men and three women. How many different such trios contain at least one woman?
A.10
B.15
C.16
D.31
Answer: D.31
Explanation: The total number of ways to choose three runners 7C3 = 35
The number of trios with only males is 4C3 = 4
The number of trios which include at least one woman is 31.
The answer is D.
Question: What is the sum of all four digit integers formed using the digits 3 ,4 ,5 and 6 (repetition is allowed)
A.1279874
B.1279872
C.1279875
D.1279876
Answer: B.1279872
Explanation: n = 4 * 4 * 4 * 4 = 256
<x> = (6666 + 3333) / 2 = 4999.5
Sum = number of integers x average value
n * <x> = 256 * 4999.5 = 1279872
answer = B
Question: Sum of two numbers is 80. Greater number exceeds by 5 from four times of the smaller. Find the numbers?
A.015
B.28
C.17
D.19
Answer: A.015
Explanation: Explanation:
x + y = 80
x â€“ 4y = 5
x = 65 y = 15
Answer:A
Question: Y invested $1000 in a business and Z invested $3000 in a business. At the end of the year they got $4000 as the profit. Find their share?
A.$1000,$2000
B.$2000,$3000
C.$1000,$3000
D.$2000,$3000
Answer: C.$1000,$3000
Explanation: Y:Z = 1000:3000
Y:Z = 1:3
Y's share = 4000*1/4 = $1000
Z's share = 4000*3/4 = $3000
Answer is C
Question: If the price of petrol increases by 25% and Bill intends to spend only an additional 15% on petrol, by how much % will he reduce the quantity of petrol purchased?
A.A)8%
B.B)7%
C.C)10%
D.D)6%
Answer: A.A)8%
Explanation: Explanation:
Assume that the initial price of 1 Litre petrol = Rs.100 ,Bill spends Rs.100 for petrol,
such that Bill buys 1 litre of petrol
After the increase by 25%, price of 1 Litre petrol = 100 × (100+25)/100 = Rs.125
Since Bill spends additional 15% on petrol,
amount spent by Bill = 100× (100+15)/100 = Rs.115
Hence Quantity of petrol that he can purchase = 115/125 Litre
Quantity of petrol reduced = (1−115/125) Litre
Percentage Quantity of reduction = (1−115125)/1 × 100 = 10/125 × 100 = 105 × 4 = 2 × 4 = 8%
Answer: Option A
Question: A person invested in all Rs. 2600 at 4%, 6% and 8% per annum simple interest. At the end of the year, he got the same interest in all the three cases. The money invested at 4% is?
A.1266
B.2887
C.2668
D.1200
Answer: D.1200
Explanation: Let the parts be x, y and [2600 - (x + y)].
Then,
(x * 4 * 1)/100 = (y * 6 * 1)/100 = {[2600 - (x + y)] * 8 * 1}/100
y/x = 4/6 = 2/3 or y = 2/3 x
So, (x * 4 * 1)/100 = [(2600 - 5/3 x) * 80/100
52x = (7800 * 8) => x = 1200
Money invested at 4% = Rs. 1200.
Answer:D
Question: If two balls are randomly selected from a green urn containing 7 black and 7 white balls and placed into a yellow urn initially containing 5 black and 3 white balls. What is the probability that the yellow urn will contain an equal number of black and white balls after the change?
A.A.2/9
B.B.4/9
C.C.3/13
D.D.1/3
Answer: C.C.3/13
Explanation: To have equal number of black and white balls, the yellow urn must have 5 black and 5 white balls. So the balls we select out of the green urn must be both white.
Probability (first ball is white) = 7/14
Probability(second ball is white) = 6/13
Probability (both balls are white) = (7/14)*(6/13) = 3/13
Answer C
Question: What is the probability of rolling a total of 4 with a single roll of two fair six-sided dice, each with the distinct numbers 1 through 6 on each side?
A.1/12
B.1/6
C.2/7
D.1/3
Answer: A.1/12
Explanation: Totalsample spacefrom two fair six-sided dice is 36.
There are six possible ways to be 7 i.e. (1+3), (2+2), (3+1)
So, total probability is 3/36 or 1/12.
Answer is A.
Question: The age of man is three times the sum of the ages of his two sons. Six years hence,his age will be double of the sum of the ages of his sons.The fatherâ€™s present age is :
A.40 years
B.45 years
C.50 years
D.54 years
Answer: D.54 years
Explanation: Solution
Let the sum of present ages of the two sons be x years.
Then,father's present age = 3x years.
âˆ´ (3x + 6)=2 (x +12) â‡” 3x + 6 = 2x + 24â‡” x =18.
Hence,father's present age = 54 years. Answer D
Question: The average salary of all the workers in a workshop is Rs. 8000. The average salary of 7 technicians is Rs. 14000 and the average salary of the rest is Rs. 6000. The total number of workers in the workshop is
A.20
B.21
C.22
D.28
Answer: D.28
Explanation: Sol.
Let the total number of workers be x. Then,
8000x = (14000 × 7) + 6000 ( x – 7)
‹=› 2000x = 56000
‹=› x = 28.
Answer D
Question: A gang of 8 boys goes on an tour in 2 cars, of which 1 canseat 5 & the other only 4. In how many ways can they travel?
A.110
B.130
C.126
D.135
Answer: C.126
Explanation: There are 8 students and the maximum capacity of the cars together is 9.
We may divide the 8 students as follows
Case I: 5 students in the first car and 3 in the second
Or Case II: 4 students in the first car and 4 in the second
Hence, in Case I: 8 students are divided into groups of 5 and 3 in8C3 ways.
Similarly, in Case II: 8 students are divided into two groups of 4 and 4 in 8C4ways.
Therefore, the total number of ways in which 8 students can travel is:
\inline {\color{Blue}8C_{3}+8C_{4}}=56 + 70= 126
C
Question: A sum of money at simple interest amounts to 815 in 3 years and to 854 in 4 years. The sum is:
A.698
B.387
C.373
D.593
Answer: A.698
Explanation: A
698
S.I. for 1 year = (854 - 815) = 39.
S.I. for 3 years = (39 x 3) = 117.
Principal = (815 - 117) = 698.
Question: What is the are of an equilateral triangle of side 16 cm?
A.64√3
B.64√7
C.64√5
D.64√3
Answer: D.64√3
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: In a certain school, the ratio of boys to girls is 5 to 13. If there are 80 more girls than boys, how many boys are there?
A.27
B.36
C.45
D.50
Answer: D.50
Explanation: The ratio of b to G is 5:13 and the other data point is G are more than boys by 80...
Looking at the ratio we can say that the 8(13-5) extra parts caused this diff of 80. so 1 part corresponds to 80/8=10 and so
5 parts correspond to 5*10 = 50.
D