RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: 4 liters of a 20 percent solution of alcohol in water are mixed with 5 liters of a 10 percent alcohol in water solution. What is the percentage of alcohol in the new solution?
A.14.4%
B.14.8%
C.15.2%
D.15.6%
Answer: A.14.4%
Explanation: The total amount of alcohol is 0.2(4) + 0.1(5) = 1.3 liters.
The percentage is 1.3 / 9 = 13 / 90 which is about 14.4%
The answer is A.
Question: Amit and Ian paint a wall in alternating shifts. First Amit paints alone, then Ian paints alone, then Amit paints alone, etc. During each of his shifts, Amit paints 1/2 of the remaining unpainted area of the wall, while Ian paints 1/3 of the remaining unpainted area of the wall during each of his shifts. If Amit goes first, what fraction of the wall's area will remain unpainted after Amit has completed his 3th shift?
A.1/17
B.1/54
C.1/81
D.1/162
Answer: A.1/17
Explanation: Fraction of area unpainted after FIRST shift of Amit = 1-(1/2) = 1/2
Fraction of area unpainted after FIRST shift of Ian = (1/2)-(1/3)(1/2) = (2/3)(1/2)
Fraction of area unpainted after SECOND shift of Amit = (1/2)(2/3)(1/2)
Fraction of area unpainted after SECOND shift of Ian = (2/3)(1/2)(2/3)(1/2)
Fraction of area unpainted after THIRD shift of Amit = (1/2)(2/3)(1/2)(2/3)(1/2)=1/18
Answer: option A
Question: Company P had 15 percent more employees in December than it had in January. If Company P had 490 employees in December, how many employees did it have in January?
A. 391
B. 426
C. 410
D. 423
Answer: B. 426
Explanation: D = number of employees in December
J = number of employees in January
J x 1.15 = D
J x 1.15 = 490
J = 490/1.15
J = 49,000/115 = 426
Thus B is the correct answer.
Question: Today is Tuesday. A person wants to meet a lawyer and as that lawyer is busy he asks him to come three days after the before day of the day after tomorrow? On which day the lawyer asks the person to come?
A.Saturday
B.MONDAY
C.TUESDAY
D.WEDNESDAY
Answer: A.Saturday
Explanation: Today is Tuesday
after three days--->Friday
now, (Friday)after before day--->Thursday
then, (Thursday)day after tomorrow--->Saturday
ANSWER:A
Question: Two vessels A and B contain milk and water mixed in the ratio 8:5 and 5:2 respectively. The ratio in which these two mixtures be mixed to get a new mixture containing milk and water in the ratio 9:4
A.2:7
B.5:2
C.3:5
D.5:7
Answer: A.2:7
Explanation: Soln:-
Required Ratio = (5/7−9/13)/(9/13−8/13)
= 2/7
Answer: A
Question: There are 6 magazines lying on a table; 3 are fashion magazines and the other 3 are sports magzines. If 2 magazines are to be selected at random from the 8 magazines, what is the probability that at least one of the fashion magazine will be selected?
A.4/5
B.8/9
C.4/6
D.1/2
Answer: A.4/5
Explanation: 1- (3c2/6c2) = 1-1/5 = 4/5
Answer : A
Question: A certain sum of money at simple interest amounted Rs.850 in 10 years at 3% per annum, find the sum?
A.651.85
B.652.85
C.653.85
D.654.85
Answer: C.653.85
Explanation: 850 = P [1 + (10*3)/100]
P = 653.85
Answer: C
Question: 800 students took the test on English and Maths. 35% students failed in english and 45% failed in maths. 40% of those who passed in maths also passed in english, then how many students failed in both ?
A.162
B.138
C.16
D.38
Answer: C.16
Explanation: Passed in english = 65%
Passed in maths = 55%
Passed in both = 40% of 55% = 2/5 * (55%) = 22%
Passed in (English + Maths - Both + Neither) = 100%
65 + 55 - 22 + Neither = 100
Neither = 100 - 98 = 2% = 0.02 * 800 = 16
Answer: C
Question: 3 women and a few men participated in a chess tournament. Each player played two matches with each of the other players. If the number of matches that men played among themselves is 78 more than those they played with the women, how many more men than women participated in the tournament?
A.20
B.15
C.11
D.10
Answer: D.10
Explanation: Let x be the number of men.
Number of matches men play among themselves is 2*(xC2)
Number of matches men play with women is 2*(3x)
2*(xC2) - 2*(3x) =78
x=13
Difference between men and women is 13-3=10.
ANSWER D
Question: A train 110 meters long is running with a speed of 60 kmph. In what time will it pass a man who is running at 6 kmph in the direction opposite to that in which the train is going?
A.5
B.6
C.7
D.8
Answer: B.6
Explanation: Speed of train relative to man = (60 + 6) km/hr = 66 km/hr
[66 * 5/18] m/sec = [55/3] m/sec.
Time taken to pass the man = [110 * 3/55] sec = 6 sec
Answer: Option B
Question: In the infinite sequence 50, 60, 70, 80, 90, . . . , where each term is 10 greater than the previous term, the 100th term is
A.1330
B.1807
C.1910
D.1040
Answer: D.1040
Explanation: T(n) = a + (n-1) d
Here d =10, a=50, n=100
Solving we get T(n) = 1040.
Answer: D
Question: If C.P. of 26 books is equal to S.P of 30 books , then your gain or loss is ?
A.23 1/3 gain %
B.30 10/23 loss %
C.13 1/3 loss %
D.30 1/3 loss %
Answer: C.13 1/3 loss %
Explanation: Say the cost price of 26 books is $26 so $1 for a book.
The cost of 30 books would be $30, and the selling price of 30 books would be 26$, hence the loss = ($30 - $26)/$30 = ~13.3%.
Answer: C.
Question: Beth received 3/12 of the votes cast in a certian election. What franction of the other votes cast would she have needed in order to have received 1/2 of the votes cast?
A.1/5
B.2/7
C.3/9
D.7/20
Answer: C.3/9
Explanation: Let the total votes be 12. Beth received 3 votes, other votes 12-3=9. In order to have received 1/2 of the votes she needed 6 votes so 3 more, which is 3/9 of the other votes.
Answer: C.
Question: Four barrels of water have an average capacity of 8 gallons. What is the maximum possible capacity of the smallest barrel Y if the median is 10 gallons?
A.1
B.2
C.3
D.4
Answer: B.2
Explanation: Suppose 4 barrels are B1, B2, B3, B4 in ascending capacity.
(B1+B2+B3+B4)/4 = 8
B1+B2+B3+B4=32
median is 10 ....... as the no. of terms are even i.e 4, median = (B2+B3)/2
==> B2+B3 = 20
now we have B1+B4 = 32-20 =12
Only the following possible cases can be there :
1,9,11,11
1,10,10,11
2,10,10,10
Max value of smallest barrel Y= 2
Question: A circular grass lawn of 35 metres in radius has a path 7 metres wide running around it on the outside. Find the area of path.
A.1694 m2
B.1700 m2
C.1598 m2
D.1500 m2
Answer: A.1694 m2
Explanation: Radius of a circular grass lawn (without path) = 35 m
∴ Area = πr2 = π(35)2
Radius of a circular grass lawn (with path)
= 35 + 7 = 42 m
∴ Area = πr2 = π(42)2
∴ Area of path = π(42)2 – π(35)2
= π(422 – 352) = π( 42 + 35)(42 – 35)
Answer A
Question: X starts a business with Rs.45000. Y joins in the business after 3 months with Rs.30000. What will be the ratio in which they should share the profit at the end of the year?
A.1:2
B.2:1
C.1:3
D.3:1
Answer: B.2:1
Explanation: Explanation:
Ratio in which they should share the profit
= Ratio of the investments multiplied by the time period
=45000Ã—12:30000Ã—9=45Ã—12:30Ã—9=3Ã—12:2Ã—9=2:1
ANSWER IS B
Question: In how many ways can three boys can be seated on five chairs?
A.30
B.40
C.60
D.80
Answer: C.60
Explanation: There are three boys.
The first boy can sit in any of the five chairs (5 ways).
5
Now there are 4 chairs remaining. The second boy can sit in any of the four chairs (4 ways).
5 4
Now there are 3 chairs remaining. The third boy can sit in any of the three chairs (3 ways).
5 4 3
Hence, total number of ways in which 3 boys can be seated on 5 chairs
=5×4×3=60
ANSWER C 60
Question: The radius of a wheel is 22.4 cm. What is the distance covered by the wheel in making 600 resolutions?
A.844.8 m
B.704 m
C.774 m
D.714 m
Answer: A.844.8 m
Explanation: In one resolution, the distance covered by the wheel is its own circumference. Distance covered in 600 resolutions.
= 600 * 2 * 22/7 * 22.4 = 84480 cm
= 844.8 m
Answer:A
Question: We have a 630 ml of mixture of milk and water in the ratio 7:2. How much water must be added to
make the ratio 7:3?
A.70 ml
B.60 ml
C.80 ml
D.50 ml
Answer: A.70 ml
Explanation: Explanation :
concentration of water in mixture1 = 2/9 (Since the ratio of milk and water = 7:2) ---item(1)
concentration of water in pure water= 1 ---item(2)
Now the above mentioned items are mixed to form a mixture2 where milk and water ratio = 7: 3
=>concentration of water in mixture2 = 3/10
By the rule of alligation, we have
concentration of water
in mixture1 : 2/9 concentration of water
in pure water : 1
Mean concentration
3/10
1 - 3/10 = 7/10 3/10 - 2/9 = 7/90
=> Quantity of mixture1 : Quantity of water = 7/10 : 7/90 = 1/10 : 1/90 = 1 : 1/9
Given that Quantity of mixture1 = 630 ml
=> 630 : Quantity of water = 1 : 1/9
⇒Quantity of water = 630×19=70 ml
Answer : Option A
Question: How many 5 letter words ( with or without meaning) can be formed using all the following 5 letters P,Q,R,V,and T so that letter P is to the left of letter R?
A.90
B.60
C.120
D.144
Answer: B.60
Explanation: Two positions can be selected out of 5 positions in 5C2 ways = 10 ways.
And the remaining 3 letters can be placed in 3 posions in 3! Ways = 6 ways.
So the final Answer = number of ways letters P and R can be arranged x number
of ways the other 3 letters can be arranged
Final Answer = 10 x 6 = 60 ways
B
Question: If s and t are positive integers such that s/t = 17.14, which of the following could be the remainder when s is divided by t ?
A.20
B.45
C.49
D.23
Answer: C.49
Explanation: s/t= 17.14
s = 17.14t
s = (17 + 0.14)t
s = 17t + (14/100)t
s = 17t + (7/50)t
So remainder will be multiple of 7. The only multiple of 7 is 49.
Ans. C
Question: A 300 m long train crosses a platform in 39 sec while it crosses a signal pole in 24 sec. What is the length of the platform?
A.389 m
B.350 m
C.187.5 m
D.299 m
Answer: C.187.5 m
Explanation: Speed = 300/24 = 25/2 m/sec.
Let the length of the platform be x meters.
Then, (x + 300)/39 = 25/2
=> x = 187.5 m.
Answer:C
Question: How much interest will $8,000 earn in 9 months at an annual rate of 6%?
A.$250
B.$350
C.$360
D.$550
Answer: C.$360
Explanation: Soln:-
9 months = 3/4 of year;
6% = 6/100=3/50;
$8,000(principal)*3/50(interest rate)*3/4(time)=$360.
ANSWER:C
Question: Today is Monday. After 61 days, it will be:
A.Wednesday
B.Saturday
C.Tuesday
D.Thursday
Answer: B.Saturday
Explanation: Each day of the week is repeated after 7 days.
So, after 63 days, it will be Monday.
After 61 days, it will be Saturday.
Answer: Option B
Question: Line k is in the rectangular coordinate system. If the c-intercept of k is -2, and the y-intercept is 3, which of the following is an equation of line k?
A.-3c + 2y = 6
B.3c + 2y = -6
C.3c - 2y = 6
D.2c - 3y = 6
Answer: A.-3c + 2y = 6
Explanation: This question can be solved in much simpler way.
To find the c intercept
Put y=0 in the equation of the line.
To find the y-intercept
Put c=0 in the equation of the line.
So
Sub c=0 in the answer choices check whether you are getting y=3.
A. -3c + 2y = 6 --- y = 3
B. 3c+ 2y = -6 --- y = -3
C. 3c - 2y = 6 ----- y = -3
D. 2c - 3y = 6 --- y = -2
E. -2c - 3y = 6 --- y =-2
Eliminate answer B,C,D and E.
So the answer is A.
Question: The sale price of an article including the sales tax is Rs. 616. The rate of sales tax is 10%. If the shopkeeper has made a profit of 12%, then the cost price of the article is:
A.Rs. 500
B.Rs. 515
C.Rs. 550
D.Rs. 600
Answer: A.Rs. 500
Explanation: 110% of S.P. = 616
S.P. = (616 * 100)/110 = Rs. 560
C.P = (110 * 560)/112 = Rs. 500
ANSWER:A
Question: In an election between two candidates, one got 60% of the total valid votes, 30% of the votes were invalid. If the total number of votes was 9000, the number of valid votes that the other candidate got, was:
A.2500
B.2520
C.3000
D.3100
Answer: B.2520
Explanation: Explanation :
Number of valid votes = 70% of 9000
= 6300.
Valid votes polled by other candidates = 40% of 6300
(40/1006300)
= 2520.
Harsh Mishra a year ago
0 upvotes
Answer : B
Question: Two numbers are respectively 20% and 25% more than a third number. The percentage that is first of the second is?
A.12
B.687
C.26
D.96
Answer: C.26
Explanation: I II III
120 125 100
125----------120
100-----------? => 96%
Answer:C
Question: A rectangular grassy plot 110 m. by 65 m has a gravel path 2.5 m wide all round it on the inside. Find the cost of gravelling the path at 50 paise per sq. metre
A.s425
B.s780
C.s880
D.s480
Answer: A.s425
Explanation: area of the plot=110m*65m=7150sq.m
area of plot excluding gravel=105m*60m=6300sq.m
area of gravel =7150sq.m-6300sq.m =850sq.m
cost of building it = 850sq.m*50
= 42500p
in Rs =42500/100=Rs425
ANSWER:A
Question: An article is bought for Rs.685 and sold for Rs.900, find the gain percent?
A.33 1/8%
B.33 8/3%
C.33 1/3%
D.31 12/31%
Answer: D.31 12/31%
Explanation: 685 ---- 215
100 ---- ? => 31 12/31%
Answer: D
Question: 1/0.04 is equal to
A.25.5
B.2.5
C.25
D..25
Answer: C.25
Explanation: Explanation:
1/0.04 = (1 * 100)/4 = 100/4 = 25
Option C
Question: A sum of money is to be distributed among A, B, C, D in the proportion of 5 : 2 : 4 : 3. If C gets Rs. 800 more than D, what is B's share?
A.Rs. 1600
B.Rs. 1500
C.Rs. 2000
D.Rs. 2500
Answer: A.Rs. 1600
Explanation: Let the shares of A, B, C and D be Rs. 5x, Rs. 2x, Rs. 4x and Rs. 3x respectively.
Then, 4x - 3x = 800
x = 800.
B's share = Rs. 2x = Rs. (2 x 800) = Rs. 1600.
Answer = A
Question: A radio station has to choose two days of the seven in a week to broadcast a certain program, and that set will repeat each week. The program can be broadcast equally on any of the seven weekdays —- weekdays vs. weekends don’t matter at all —- nor does it matter whether the days the program airs are adjacent or not. Absolutely any two of the seven weekdays can be chosen. How many different two-day combinations of the seven weekdays can be constructed?
A.9
B.15
C.21
D.35
Answer: C.21
Explanation: Pick 2 days out of 7.. 7C2 = 21
Answer : C
Question: How many positive integers H less than 10,000 are such that the product of their digits is 210?
A.24
B.30
C.48
D.54
Answer: D.54
Explanation: 210 is the answer when 2, 3, 5 and 7 are multiplied. 210 can also be arrive using 5,6 and 7 and 1, 5, 6 and 7.
So sum of arrangements of 2357, 567 and 1567. This translates to 4! +3! + 4!, this equals to 24 + 6 + 24 = 54, D is the answer.
Question: A pack of baseball cards consists of 12 outfielder cards and 8 infielder cards. What is the lowest number of outfielder cards that would have to be removed from the pack so that no more than 45 percent of the pack would be outfielder cards?
A.4
B.5
C.6
D.7
Answer: C.6
Explanation: let the number of O card to be removed=X
then remaning cards=12-X
now this 12-X cards should count less than 45% of toatal Ocards
12-X<.45*12
X<12-5.4
X<6.6
X=6
Ans C
Question: If a number between 0 and 1/2 is selected at random, which of the following will the number most likely be between
A.0 and 3/20
B.3/9 and 1/2
C.1/5 and 1/4
D.1/4 and 3/10
Answer: B.3/9 and 1/2
Explanation: E. 3/9 and 1/2
Definitely not. I am always happy to explain a given question or issue if I can. However, I sometime donot put my explanation if I am answering first because I want to put others first for their explanation.
Now you have excellent explanantion byscthakur. In fact the question is asking the likelyness of or high chances/probability of having a given number. Hope you already got it. B
Question: A person buys an article at $600. At what price should he sell the article so as to make a profit of 8%?
A.670
B.689
C.648
D.740
Answer: C.648
Explanation: C
648
Cost price = $600
profit = 8% of 600 = $48
Selling price = Cost price + Profit
= 600 + 48 = 648
Question: A truck covers a distance of 550 metres in 1 minute whereas a train covers a distance of 33 kms in 45 minutes. What is the ratio of their speed?
A.3 : 7
B.4 : 7
C.1 : 4
D.3 : 4
Answer: D.3 : 4
Explanation: Explanation:
Speed of the truck = Distance/Time=550/1=550 meters/minute
Speed of the train = Distance/Time=33/45 km/minute = 33000/45 meters/minut
Speed of the truck/Speed of the train = 550/(33000/45) = (550 × 45)/33000 = (55 × 45)/3300
= (11 × 45)/660 = (11×9)/132 = 9/12 = 34
Hence, Speed of the truck : Speed of the train = 3 : 4
Answer: Option D
Question: How much time does a train 150 metres long running at 90 km/hr take to pass a pole?
A.7.9s
B.6s
C.7.5s
D.7.6s
Answer: B.6s
Explanation: Explanation:
90 km/hr = 90 * 5/18 = 25 m/s
Speed = distance/time; v = d/t
25 = 150/t
t = 6s
ANSWER: B
Question: Find the compound interest and the amount on Rs.4000 at 5% per annum for 3 years when C.I is reckoned yearly?
A.s.261.50
B.s.440.50
C.s.630.50
D.s.346.50
Answer: C.s.630.50
Explanation: A = 4000(21/20)3
= 4630.50
= 4000
---------
630.50
ANSWER:C
Question: Karthikeyan arranged a party to celebrate his birth day.20 of his close friends were invited. One friend left before the cake was cut due to an urgent phone call.The big cake was drawing the attention of the party visitors. This cake is to be divided among friends and of course Karthikeyan will get his share. A man eats 3 pieces, a woman eats two pieces and a child eats half a piece of cake. Including Karthikeyan count the number of men,women and children in the party. There are 20 pieces of cake in all.
A.6 women, 2 men and 12 children
B.7 women, 1 men and 12 children
C.5 women, 1 men and 14 children
D.4 women, 2 men and 14 children
Answer: C.5 women, 1 men and 14 children
Explanation: Let the number of men be m, number of women be w and number of children be c
Total number of pieces = Pieces ate by men + Pieces ate by women + Pieces ate by children
There are 20 total pieces. Also a man eats 3 pieces, a woman eats 2 and children half. Therefore above equation becomes.
20 = 3m + 2w + 1/2c
In the above equation, you have to substitute the values given in options to find which one satisfies the equation.
Option c with m = 1, c = 14 and w = 5 perfectly satisfies the equation as follows
20 = 3(1) + 2(5) + (1/2)(14)
20 = 20 i,e our equation is satisfied perfectly by option c
ANSWER:C
Question: The least number which when divided by 5, 6 , 7 and 8 leaves a remainder 3, but when divided by 9 leaves no remainder, is:
A.1677
B.1683
C.2523
D.3363
Answer: B.1683
Explanation: Explanation :
L.C.M. of 5, 6, 7, 8 = 840.
Required number is of the form 840k + 3
Least value of k for which (840k + 3) is divisible by 9 is k = 2.
Required number = (840 x 2 + 3) = 1683.
ANSWER IS B
Question: Toby is four years younger than Debby. Thrice the sum of the ages of Toby and Debby equals their mother’s age. If the age of the mother is 60, find the ages of Toby and Debby?
A.8 and 12
B.5 and 9
C.6 and 10
D.5 and 10
Answer: A.8 and 12
Explanation: Let the age of Debby be x and Toby be x-4
3 ( x + x-4 ) = 60
x = 12
The ages of Toby and Debby are 8 and 12.
Answer : A
Question: In the youth summer village there are 100 people, 50 of them are not working,25 of them have families and 75 of them like to sing in the shower. What is the largest possible number of people in the village, which are working, that don't have families and that are singing in the shower?
A.100
B.75
C.25
D.50
Answer: D.50
Explanation: total =100
not working =50
having family=25
like to sing in shower = 75
working=100-50=50
not having family = 100-25=75
like to sing in shower = 75
largest possible number is the lowest possible among the above
Thus 50
D
Question: An employee’s annual salary was increased $5,000. If her new annual salary now equals $70,000, what was the percent increase?
A.15%
B.0.77%
C.20%
D.22%
Answer: B.0.77%
Explanation: New annual salary = $70,000
Salary increase = $5,000.
Original salary = $70,000 - $5,000.
= $65,000
%Increase = ($5,000/ $65,000 )*100
=0.77%
Hence B.
Question: Ajay and Vijay have some marbles with them. Ajay told Vijay "if you give me 'x' marbles, both of us will have equal number of marbles". Vijay then told Ajay "if you give me twice as many marbles, I will have 30 more marbles than you would". Find 'x'?
A.4
B.5
C.6
D.8
Answer: B.5
Explanation: If Vijay gives 'x' marbles to Ajay then Vijay and Ajay would have V - x and A + x marbles.
V - x = A + x --- (1)
If Ajay gives 2x marbles to Vijay then Ajay and Vijay would have A - 2x and V + 2x marbles.
V + 2x - (A - 2x) = 30 => V - A + 4x = 30 --- (2)
From (1) we have V - A = 2x
Substituting V - A = 2x in (2)
6x = 30 => x = 5.
ANSWER:B
Question: If $3000 was invested at an annual interest rate of 5.6% compounded annually, which of the following represents the amount the investment was worth after 3 years?
A.3000 (1.056)^3
B.3000 (3+1.056)
C.3000 (1+3(0.056))
D.3000 (1+(0.056)^3)
Answer: A.3000 (1.056)^3
Explanation: the formula is CI=P(1+r/100)^t
in this case i think A is the ans
Question: Working alone, machine X can manufacture 1,000 nails in 12 hours. Working together, machines X and Y can manufacture 1,000 nails in 5 hours. How many hours does it take machine Y to manufacture 800 nails working alone?
A.6 6/7
B.7 1/3
C.7
D.8 1/5
Answer: A.6 6/7
Explanation: rate of machine x = 1000/12
(1000/12 + y)5=1000
y=350/3
350/3 * t = 800
t=6 6/7
A.
Question: A retailer buys 120 pens at the market price of 36 pens from a wholesaler, if he sells these pens giving a discount of 1%, what is the profit % ?
A.210
B.215
C.212
D.230
Answer: D.230
Explanation: let the market price of each pen be $1
then, Cost Price of 120 pens = $ 36 Selling Price of 120 pens =99% of $120=$ 118.80
profit %=((82.80*100)/36) %=230%
Answer D
Question: Among 7 Numbers the Average of first four numbers is 13 and the average of last four numbers is 15. The sum of last three numbers is 55. The square of the fourth Number is equal to the last number then what is the last number?
A.60
B.52
C.5
D.25
Answer: D.25
Explanation: let the numbers be a,b,c,d,e,f,g
d+e+f+g = 15 * 4 = 60
e+f+g = 55, 60 - 55 = 5
so the fourth number is 5. The square is 25.
the answer is Option D.
Question: If 3 : 12 :: x : 16, then find the value of x
A.2
B.3
C.4
D.5
Answer: B.3
Explanation: Explanation:Treat 3:12 as 3/12 and x:16 as x/16, treat :: as = So we get 3/12 = x/16=> 12x = 48=> x = 4 Option B
Question: The average weight of a group of 30 friends increases by 1 kg when the weight of their football coach was added. If average weight of the group after including the weight of the football coach is 31 kg, what is the weight of their football coach?
A.31 kg
B.61 kg
C.60 kg
D.62 kg
Answer: B.61 kg
Explanation: Explanatory Answer
The new average weight of the group after including the football coach = 31 kg.
As the new average is 1 kg more than the old average, old average without including the football coach = 30 kg.
The total weight of the 30 friends without including the football coach = 30 * 30 = 900.
After including the football coach, the number people in the group increases to 31 and the average weight of the group increases by 1 kg.
Therefore, the total weight of the group after including the weight of the football coach = 31 * 31 = 961 kg.
Therefore, the weight of the football coach = 961 - 900 = 61 kg.
Answer B
Question: If one-third of one-fourth of a number is 15, then three-tenth of that number is
A.35
B.36
C.45
D.54
Answer: D.54
Explanation: Let the number be x. then 1/3 of ¼ of x=15
X=15x12=180
The required number=(3/10)*180=54
ANSWER D 54
Question: Which of the following triples of numbers have the same standard deviation as the numbers x, y and z?
I. x-2, y-2, z-2
II. 0,x-y, z-y
III.x-4, y+5, z-1
A.I only
B.II only
C.I and III only
D.II and I only
Answer: D.II and I only
Explanation: If we add or subtract a constant to each term in a set the standard deviation will not change.
Set {x-2, y-2, z-2} is obtained by subtracting 2 from each term of {x, y, z}.
Set {0, x-y, z-y} is obtained by subtracting s from each term of {x, y, z}.
Set {x-4, y+5, z-1} is totally different from {x, y, z}.
Thus the answer is I and II only.
Answer: D.
Question: The average monthly income of P and Q is Rs. 5050. The average monthly income of Q and R is Rs. 6250 and the average monthly income of P and R is Rs. 5200. The monthly income of P is:
A.3500
B.4000
C.4050
D.5000
Answer: B.4000
Explanation: Explanation:
Let P, Q and R represent their respective monthly incomes. Then, we have:
P + Q = (5050 x 2) = 10100 .... (i)
Q + R = (6250 x 2) = 12500 .... (ii)
P + R = (5200 x 2) = 10400 .... (iii)
Adding (i), (ii) and (iii), we get: 2(P + Q + R) = 33000 or P + Q + R = 16500 .... (iv)
Subtracting (ii) from (iv), we get P = 4000.
P's monthly income = Rs. 4000.
ANSWER IS B