RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: A sum of money is distributed among A,B,C,D in the proportion of 6:4:8:5. If C gets $3000 more than D, what is the B's share?
A.$2000
B.$6000
C.$1000
D.$4000
Answer: D.$4000
Explanation: Let the shares of A,B,C,D are 6x,4x,8x,5x
8x-5x = 3000
3x = 3000,X=1000
B's share = 4x = $4000
Answer is D
Question: The difference in compound interest earned on a deposit (compounded annually) in year 1 and year 2 is $ 40. Had the interest rate been three times its present value, the difference a would have been how much?
A.40/3
B.40
C.120
D.360
Answer: D.360
Explanation: CASE 1:
Deposit = $x;
Rate of increase = r.
Interest yearned in 1 year = xr. Deposit in 1 year = x + xr.
Interest yearned in 2 year = (x + xr)r.
The difference a= (x + xr)r - xr = xr^2 = 40.
CASE 2:
Deposit = $x;
Rate of increase = 3r.
Interest yearned in 1 year = x(3r). Deposit in 1 year = x + 3xr.
Interest yearned in 2 year = (x + 3xr)3r.
The difference = (x + 3xr)3r - 3xr = 9xr^2. Since from CASE 1 we know that xr^2 = 40, then 9xr^2 = 9*40 = 360.
Answer: D.
Question: A student has to select 3 subject out of 6 subjects M,B,H,U,L. If he has chosen M, what is the probability of B being chosen ?
A.2/5
B.1/5
C.3/5
D.7/5
Answer: A.2/5
Explanation: Explanation :
Out of 6 subjects, one subject M has already been chosen. Ramaining 2 subjects are to be choden from rest (6-1) i.e 5 subjects.
Without restriction, no. of selections = 5C2.
With restriction, no. of selection of B from rest 4 subject = 4C1.
=> Probability
= Selections with restriction / Selections without restriction
= 4C1 / 5C2 .
= 2 / 5.
Hence, the probability of subject B being chosen is 2 / 5.
Answer : A
Question: If a man walks at the rate of 4 kmph, he misses a train by only 6 min. However, if he walks at the rate of 5 kmph he reaches the station 6 minutes before the arrival of the train. The distance covered by him to reach the station is
A.3 km
B.4 km
C.5 km
D.6 km
Answer: B.4 km
Explanation: Let the distance covered be d and time taken to reach the station in time t
d/4 = t+6/60---(1)
d/5 = t-6/60---(2)
(1)-(2) gives
d/4 - d/5 = (6+6)/60
d/20 = 12/60
d = 12*20/60
=4 km
ANSWER:B
Question: If x is equal to the sum of the integers from 40 to 60, inclusive, and y is the number of even integers from 40 to 60, inclusive, what is the value of x + y?
A.1021
B.1041
C.1061
D.1081
Answer: C.1061
Explanation: x = 40 + 41 +...+ 60 = 21(50) = 1050
y = 11
x+y = 1061
The answer is C.
Question: A store reported total sales of $480 million for February of this year. If the total sales for the same month last year was $320 million, approximately what was the percent increase in sales?
A.2%
B.17%
C.50%
D.65%
Answer: C.50%
Explanation: New Value – Old Value)/Old Value x 100
We are given:
February sales this year = 480 million
February sales last year = 320 million
We need to determine the percent increase between sales from last year to sales this year.
Thus, the new value = 480 million and the old value = 320 million. Let’s plug them into our percent change formula.
(New Value – Old Value)/Old Value x 100
[(480 – 320)/320] x 100
= 50%.
The answer is C.
Question: In a river flowing at 2 km/hr, a boat travels 32 km upstream and then returns downstream to the starting point. If its speed in still water be 6 km/hr, find the total journey time.
A.10 hours
B.12 hours
C.14 hours
D.16 hours
Answer: B.12 hours
Explanation: Explanation :
speed of the boat = 6 km/hr
Speed downstream = (6+2) = 8 km/hr
Speed upstream = (6-2) = 4 km/hr
Distance travelled downstream = Distance travelled upstream = 32 km
Total time taken = Time taken downstream + Time taken upstream
= (32/8) + (32/4) = (32/8) + (64/8) = (96/8) = 12 hr. Answer : Option B
Question: Two numbers are respectively 20% and 50% more than a third number. What percentage is the first of the second?
A.25%
B.60%
C.80%
D.55%
Answer: C.80%
Explanation: Required answer = (100+x)/(100+y)*100 = 120*100/150 = 80%
Answer is C
Question: If n is a natural number, then (6n2 + 6n) is always divisible by?
A.6 only
B.6 and 12 both
C.12 only
D.6 or 12 only
Answer: B.6 and 12 both
Explanation: (6n2 + 6n) = 6n(n + 1), which is always divisible by 6 and 12 both, since n(n + 1) is always even.
B)
Question: what should be the rate of interest to become a sum five times of itself in 8 years?
A.50
B.40
C.30
D.20
Answer: A.50
Explanation: let the sum x,after 8 years it should 5x.4x is the interest.
4x=x*r*8/100
r=4*100/8=50%
answer A
Question: If the average (arithmetic mean) of a and b is 115, and the average of b and c is 160, what is the value of a − c?
A.−220
B.−100
C.−90
D.135
Answer: C.−90
Explanation: Question: a - c = ?
(a + b)/ 2 =115 ===> a + b = 230
(b + c)/2 = 160 ===> b + c = 320
(a + b) - (b + c) = 230 - 320 ===> a + b - b - c = - 90 ===> a - c = - 90
Answer: C
Question: x<3y<0 which of the following is the greatest?
A.x+2y
B.-2x+y
C.3x-y
D.-(2x+2y)
Answer: D.-(2x+2y)
Explanation: Plugging in -1 for both x and y we get
A. x+2y =-3
B. -2x+y =1
C. 3x-y =-2
D. -(2x+2y) =4
E. x-y =0
Answer: D
Question: If i walk with 30 miles/hr i reach 1 hour before and if i walk with 20 miles/hr i reach 1 hour late.Find the distance between 2 points and the exact time of reaching destination is 11 am then find the speed with which it walks.
A.120 MILES
B.130 MILES
C.140 MILES
D.150 MILES
Answer: A.120 MILES
Explanation: LET ORIGINAL SPEED BE V AND TIME TAKEN BE T...
AS DISTANCE BETWEEN TWO POINTS IS CONSTANT,
30*(T-1)=20*(T+1)=V*T
HENCE, V=24MILE/HR
T=5 HRS
DISTANCE BETWEEN TWO POINTS IS 120 MILES
ANSWER:A
Question: A man by motorcycle goes from Delhi to Bharatpur , a distance of 192 km, at an average speed of 32 kmph. Another man starts from Delhi by car 2.5 h after the motorcyclist starts and reaches Bharatpur half an hour late. What is the ratio of person on the motorcycle to the person going by car ?
A.1:2
B.2:3
C.10:27
D.5:4
Answer: B.2:3
Explanation: A man by motorcycle goes from Delhi to bharatpur
The time take by the motorcyclist = 192/32 = 6 hours
Another man start from Delhi be car after 2.5 hour the man starts = 6 - 2.5 = 3.5
and the man on can reaches half and hour late which is = 3.5 + .5 = 4
Thus, the ratio between motorcycle to car is 4:6
or, 2:3.
ANSWER:B
Question: A, B and C can do a piece of work in 4 days, 6 days and 8 days respectively. How long will they taken, if all the three work together?
A.2
B.4
C.5
D.1 11/13
Answer: D.1 11/13
Explanation: 1/4 + 1/6 + 1/8 = 13/24 => 24/13 => 1 11/13 days
Answer: D
Question: A man sitting in a train which is traveling at 50 kmph observes that a goods train, traveling in opposite direction, takes 9 seconds to pass him. If the goods train is 150 m long, find its speed.
A.20 km/hr
B.10 km/hr
C.15 km/hr
D.18 km/hr
Answer: B.10 km/hr
Explanation: speed of train = 50 kmph = 50*5/18 = 250/18 m/sec
relative speed =(250/18)+x where x is speed of goods train
then
150/((250/18)+x) = 9
solving it, we get
x= 50/18 m/sec = 10 km/hr
ANSWER:B
Question: If x=-2, which of the following is(are) true?
I. x^2=-|x| II |x|=-x III x/-3 = -2/3
A.II only
B.I only
C.III only
D.I,II only
Answer: A.II only
Explanation: I. x^2=-|x| -2^2 = - |-2| Not true
II |x|=-x |-2| =-( -2 ) true
III x/-3 = -2/3 Not true
Answer : A
Question: During a certain two-week period, 70 percent of the movies rented from a video store were comedies, and of the remaining movies rented, there were 5 times as many dramas as action movies. If no other movies were rented during that two-week period and there were A action movies rented, then how many comedies, in terms of A, were rented during that two-week period?
A.A/14
B.5A/7
C.7A/5
D.14A
Answer: D.14A
Explanation: Total movies = 100.
Comedies = 70.
Action + Drama = 30. Since there were 5 times as many dramas as action movies, then Action + 5*Action = 30 --> Action = A = 5.
Comedies = 70 = 14A.
Answer: D.
Question: find the last 3 digit of 443^443.
A.306
B.307
C.308
D.309
Answer: B.307
Explanation: power is 443
=>443/4 rem=3
so,443^3=86938307
last 3 digit=307
ANSWER:B
Question: A man can row downstream at 18 kmph and upstream at 10 kmph. Find the speed of the man in still water and the speed of stream respectively?
A.2
B.9
C.7
D.4
Answer: D.4
Explanation: Let the speed of the man in still water and speed of stream be x kmph and y kmph respectively.
Given x + y = 18 --- (1)
and x - y = 10 --- (2)
From (1) & (2) 2x = 28 => x = 14, y = 4.
Answer:D
Question: A man had a stock of 500 books in his bookshop. He sold 25 on Monday, 50 on Tuesday 30 on Wednesday, 100 on Thursday and 150 on Friday. What percentage of the books were not sold?
A.8%
B.10%
C.29%
D.44%
Answer: C.29%
Explanation: Let N be the total number of books sold. Hence
N = 25 + 50 + 30 + 100 + 150= 355
Let M be the books NOT sold
M = 500 - N = 500- 355 = 145
Percentage
Books not sold / total number of books = 145/500 = 0.29= 29%
correct answer C
Question: If a and b are consecutive integers (b>a), which of the following statements could be false? 1. a+b is an even number. 2. ab is even number 3. (a + b) is always an odd number.
A.II only
B.II,III only
C.I only
D.I,II only
Answer: C.I only
Explanation: odd* even = even
odd+even = odd
Answer : C
Question: In his pocket, a boy has 3 red marbles, 6 blue marbles, and 6 green marbles. How many will he have to take out of his pocket to ensure that he has taken out at least one of each color?
A.12
B.13
C.14
D.15
Answer: B.13
Explanation: The worst case scenario would be that he has taken 6 blue and 6 green, a total of 12 marbles, and still doesn't have 3 distinct colors. But the next draw, marble number 13, will surely be red as only the red marbles are left in his pocket.
The answer is B.
Question: by what least number 4320 be multiplied to obtain a number which is a perfect cube ?
A.25
B.50
C.70
D.30
Answer: B.50
Explanation: Solution
Clearly, 4320 = 23 * 33 * 22 * 5.
to make it a perfect cube, it must be multiplied by 2 * 52 i.e., 50 .
Answer B
Question: If w > a and L < a, which of the following cannot be true?
A. d + L = 14
B. d - L = 7
C. d - L = 1
D. a - w = 9
Answer: D. a - w = 9
Explanation: Is the answer D?
If w>a, then w-a>0 (always positive). The converse would be a-w<0 (always negative). Option D states that a-w=9, which can never be true.
Question: In a garden, there are 12 rows and 14 columns of mango trees. The distance between two trees is 2metres and a distance of one metre is left from all sides of the boundary of the garden. The length of the garden is
A.20m
B.22m
C.24m
D.26m
Answer: D.26m
Explanation: Each row contains 14 plants.
Leaving 2 corner plants, 12 plants in between have (12 x 2) metres & 1 metre on each side is left.
Length = (24 + 2) m = 26m.
ANSWER:D
Question: Given a spinner with four sections of equal size labeled T, B, C, and D, what is the probability of NOT getting an T after spinning the spinner two times?
A.15/16
B.9/16
C.1/2
D.1/4
Answer: B.9/16
Explanation: The probability of NOT getting an T after spinning the spinner two times is 3/4*3/4=9/16 (so getting any of the remaining 3 letters out of 4).
Answer: B.
Question: From the integer n, if n*n*n*n is odd, then what is true from below options?
A.n is odd
B.n*n is even
C.n is odd and n*n is even
D.n is even
Answer: A.n is odd
Explanation: n is odd
Option A
Question: What percentage of numbers from 1 to 70 have 1 or 9 in the unit's digit?
A.12 %
B.16 %
C.18 %
D.20 %
Answer: D.20 %
Explanation: Clearly, the numbers which have 1 or 9 in the unit's digit, have squares that end in the digit 1. Such numbers from 1 to 70 are 1, 9, 11, 19, 21, 29, 31, 39, 41, 49, 51, 59, 61, 69.
Number of such number =14
Required % = (14/70)x100 % =20 %
answer : D
Question: If xy not equal 0 and x^2*y^2 -xy = 42, which of the following could be y in terms of x?
I. 1/2x
II. -7/x
III. 6/x
A.II
B.III
C.IV
D.II and III
Answer: D.II and III
Explanation: x2y2 â€“ xy = 6
x2y2-xy-42 = 0
(xy-6)(xy+7)=0
xy = 6 or xy=-7
y = 6/x or y = -7/x
II and III only
D
Question: 2001+1015
A.8390
B.3016
C.2808
D.3890
Answer: B.3016
Explanation: B
Question: A train running at the speed of 60 km/hr crosses a pole in 6 seconds. What is the length of the train?
A.186 m
B.100 m
C.872 m
D.150 m
Answer: B.100 m
Explanation: Speed=(60 * 5/18) m/sec = (50/3) m/sec Length of the train
= (Speed x Time) = (50/3 * 6) m
= 100 m.
Answer: B
Question: A man invests 1/3rd of his income at 7%, 1/4th at 8% and the remainder of his income at 10%. If the annual profit is Rs 561. What was the initial capital?
A.Rs 66098
B.Rs 6608
C.Rs 6628
D.Rs 6600
Answer: D.Rs 6600
Explanation: Explanation:
Let initial amount that the man invests be A
Let x be the capital
=> Profit on 1st investment + Profit on 2nd investment + Profit on 3rd investment
=> S.I. = P X R X T
=> Remainder of capital = 1 - 1/3 - 1/4 = 5/12x (x being the capital)
=> a*1/3 *7/100 + 1/4 *a * 8/100 + 5x/12*a* 10/100 = 561
Therefore, a = 6600
ANSWER: D
Question: A and B’s salaries together amount to Rs. 4,000. A spends 95% of his salary and B spends 85% of his. If now their savings are the same, what is A’s salary?
A.2777
B.1500
C.3000
D.2776
Answer: C.3000
Explanation: (5/100) A = (15/100) B
A = 3B
A + B = 4000
4B = 4000 => B = 1000
A = 3000
Answer C
Question: 123 : 36 : : 221 : ?
A.52
B.69
C.72
D.25
Answer: D.25
Explanation: (1+2+3)^2 = 36
(2+2+1)^2 = 25
ANSWER:D
Question: At 1:20 PM, Train X departed from Station A on the road to Station B. At 1:30 PM, Train Y departed Station B on the same road for Station A. If Station A and Station B are p miles apart, Train X’s speed is r miles per hour, and Train Y’s speed is s miles per hour, how many hours after 1:00 PM, in terms of p, r, and s, do the two trains pass each other?
A.0.5 + (p - 0.5s)/(r + s)
B.(p - 0.5s)/(r + s)
C.0.5 + (p - 0.5r)/r
D.(p - 0.5r)/(r + s)
Answer: D.(p - 0.5r)/(r + s)
Explanation: The distance A is going to cover between 1:00 and 1:30
= .5r
now the distance between the two trains = (p-.5r)
the relative velocity = (r-(-s)) = r+s
From 1:30, time is going to take when they meet = (p-.5r)/(r+s)
so the ans is .5+((p-.5r)/(r+s)) [.5 is added for the time from 1:00 to 1:30]
ans is D
Question: A painter intends to mixed two jars of paint to create a new color. He chooses one paint jar randomly from a display containing 2 red and 3 blue samples, and a second jar is chosen at random from a different display containing 3 red and 2 blue samples. If he plans on mixing the two chosen jars together, what is the probability that when mixed together, the result will be purple paint? (The color purple is created with 1 part red and 1 part blue.)
A.1/5
B.1/3
C.2/3
D.4/5
Answer: B.1/3
Explanation: Painter has two buckets he has to randomly pick from 2 different lists ... Let these Lists be A and B ... He has to choose the first bucket from List A , and the second bucket from List B
FOR THE FIRST BUCKET ...
Red color - 2
Blue color - 2
FOR THE SECOND BUCKET
Red color - 3
Blue color -2
In order to get Purple he has to mix red with blue .. Both the LISTS contain either blue or red , therefore we have two scenarios :
Scenario I - He picks Red color from List A and Blue color from List B
Scenario II - He picks Blue color from List A and Red color from List B
Scenario I - Odds for red color from List A are 1/2 .. and for Blue color from List B are 2 /5 .. Multiplying them (because we have to find the odds that both colors are selected from their respective lists together (this is a AND not an OR problem) we get 1/5
Scenario II - Odds for blue color from List A are 1/2 , and for Red color from List B are 3/5 ... Multiplying them we get 3/10 ...
Both the scenarios are equally possible therefore we must ADD the two (not multiply ) because both of them do not have to hold true together (have to independently) for our desired result to be achieved ...
We get 1/5 + 3/10 = 1/3 (B)
Question: How many three letter words are formed using the letters of the word TIME?
A.12
B.20
C.16
D.24
Answer: D.24
Explanation: Explanation:
The number of letters in the given word is four.
The number of three letter words that can be formed using these four letters is â´Pâ‚ƒ = 4 * 3 * 2 = 24.
ANSWER IS D
Question: The mean of 50 observations was 30. It was found later that an observation 48 was wrongly taken as 23. The corrected new mean is
A.35.2
B.36.1
C.30.5
D.39.1
Answer: C.30.5
Explanation: Sol.
Therefore correct sum
= ( 30 × 50 + 48 – 23)
= 1525.
Therefore correct mean
= 1525 / 50
= 30.5.
Answer C
Question: A man can row 8 kmph in still water. When the river is running at 1.8 kmph, it takes him 2 hour to row to a place and back. What is the total distance traveled by the man?
A.8.2 km
B.6.7 km
C.7.6 km
D.7.4 km
Answer: C.7.6 km
Explanation: M = 8
S = 1.8
DS = 9.8
US = 6.2
x/9.8 + x/6.2 = 1
x = 3.8
D = 2.88 * 2 = 7.6
Answer:C
Question: Two stations A and B are 110 km apart on a straight line. One train starts from A at 8 a.m. and travels towards B at 20 kmph. Another train starts from B at 8 a.m. and travels towards A at a speed of 25 kmph. At what time will they meet?
A.11
B.10
C.8
D.12
Answer: A.11
Explanation: Suppose they meet x hours after 8 a.m.
Distance covered by A in x hours = 20x km.
Distance covered by B in (x - 1) hours = 25(x - 1) km.
Therefore 20x + 25(x - 1) = 110
45x = 135
x = 3.
So, they meet at 11 a.m.
Answer: A
Question: The H.C.F. of two numbers is 10 and the other two factors of their L.C.M. are 11 and 15. The larger of the two numbers is:
A.150
B.300
C.299
D.322
Answer: A.150
Explanation: the numbers are (10 x 11) and (10 x 15).
Larger number = (10 x 15) = 150.
ANSWER :A
Question: In the first week of the Year, Mancy saved $1. In each of the next 51 weeks, she saved $1 more than she had saved in the previous week. What was the total amount that Mancy saved during the 52 weeks?
A.$1,326
B.$1,352
C.$1,378
D.$2,652
Answer: C.$1,378
Explanation: In the first week of the Year, Mancy saved $1.If you don't recall the formula, there is one method:
1 + 2 + 3 + 4 + 5 ........ + 26 + 27 + ............ + 48 + 50 + 51 + 52
Sum of 1stlast digit = 1 + 52 = 53
Sum of 2nd2nd last digit = 2 + 51 = 53
Sum of 3rd3rd last digit = 3 + 50 = 53
.
.
.
.
This is repeated 26 times
So, 26 * 53 = 1378
Answer = C
Question: A, B, C rent a pasture. If A puts 10 oxen for 7 months, B puts 12 oxen for 5 months and C puts 15 oxen for 3 months for grazing and the rent of the pasture is Rs. 175, then how much amount should C pay as his share of rent?
A.23
B.45
C.15
D.28
Answer: B.45
Explanation: A : B: C = 10*7 : 12*5 : 15*3 = 2*7 : 12*1 : 3*3 = 14 : 12 : 9
amount that C should pay = 175 * (9/35) = 5*9 = 45
Answer is B
Question: A circle graph shows how the budget of a certain company was spent: 61 percent for salaries, 10 percent for research and development, 6 percent for utilities, 5 percent for equipment, 3 percent for supplies, and the remainder for transportation. If the area of each sector of the graph is proportional to the percent of the budget it represents, how many degrees of the circle are used to represent transportation?
A.18°
B.36°
C.54°
D.72°
Answer: C.54°
Explanation: The percent of the budget for transportation is 100 - (61+10+6+5+3)= 15%
100% of the circle is 360 degrees.
Then (15%/100%)*360 = 54 degrees
The answer is C.
Question: If |x – 9/2| = 5/2, and if y is the median of a set of p consecutive integers, where p is odd, which of the following must be true?
I. xyp is odd
II. xy(p^2 + p) is even
III. x^2y^2p^2 is even
A.II only
B.III only
C.I and III
D.II and III
Answer: A.II only
Explanation: x is in range of 2 and 7 so it can be even or odd
y is median of set of odd integers so it can be even or odd
p is given as odd
using above information only II for sure can be inferred as even.
other two, either can be even or odd
correct response is A.
Question: The difference of 2 digit number & the number obtained by interchanging the digits is 36. What is the difference the sum and the number if the ratio between the digits of the number is 1:2?
A.3
B.8
C.9
D.11
Answer: B.8
Explanation: Let the number be xy.
Given xy – yx = 36.
This means the number is greater is than the number got on reversing the digits.
This shows that the ten’s digit x > unit digit y.
Also given ratio between digits is 1 : 2 => x = 2y
(10x + y) – (10y +x) = 36 => x – y = 4 => 2y – y =4.
Hence, (x + y) – (x – y) = 3y – y = 2y = 8
B
Question: A particular store purchased a stock of turtleneck sweaters and marked up its cost by 20%. During the New Year season, it further marked up its prices by 25% of the original retail price. In February, the store then offered a discount of 18%. What was its profit on the items sold in February?
A.27.5%
B.30%
C.35%
D.23%
Answer: D.23%
Explanation: Assume the total price = 100x
Price after 20% markup = 120x
Price after 25%further markup = 1.25*120x = 150x
Price after the discount = 0.82*150x = 123x
Hence total profit = 23%
Option D
Question: By investing Rs. 1620 in 8% stock, Michael earns Rs. 135. The stock is then quoted at:
A.Rs 96
B.Rs 100
C.Rs 150
D.Rs 160
Answer: A.Rs 96
Explanation: to earn Rs 135 investment = Rs 1620
to earn Rs 8 investment =>1620/135*8=96
ANSWER A
Question: The average of five numbers id 28. If one number is excluded, the average becomes 25. What is the excluded number?
A.30
B.40
C.32.5
D.35
Answer: B.40
Explanation: Explanation:
Sum of 5 numbers = 5 × 28
Sum of 4 numbers after excluding one number = 4 × 25
Excluded number
= 5 × 28 - 4 × 25
= 140 - 100 = 40
Answer: Option B
Question: Find the average (arithmetic mean) of x and y if the average of x, y, and 10 is 20 greater than the average of x, y, 10, and 20.
A.115
B.130
C.145
D.160
Answer: C.145
Explanation: consider the statement 30 is 20 greater than 10: 30 = 10 + 20
similarly
the average of x, y, and 10 = (the average of x, y, 10, and 20) + 20
(x+y+10)/3 = (x+y+10+20)/4 + 20
(x+y+10)/3 = (x+y+30)/4 + 80/4
(x+y+10)/3 = (x+y+30+80)/4
(x+y+10)/3 = (x+y+110)/4
cross multiply
4(x+y+10) = 3(x+y+110)
4x+4y+40 = 3x+3y+330
4x-3x + 4y-3y = 330 - 40
x + y = 290
thus
(x+y)/2 = 290/2
(x+y)/2 = 145
thus the average of x and y is 145
C
Question: All of the bonds on a certain exchange are designated by a 3-letter, a 4-letter, or a 5-letter code that is created by using the 26 letters of the alphabet. Which of the following gives the maximum number of different bonds that can be designate with these codes?
A.26(26^3 + 26^4)
B.26(26^3 + 26^5)
C.27(26^3 + 26^5)
D.27(26^3) + 26^5
Answer: D.27(26^3) + 26^5
Explanation: 3-letter codes = 26^3;
4-letter codes = 26^4;
5-letter codes = 26^5;
Total = 26^3 + 26^4 + 26^5 = 26^3(1+26) + 26^5 = 26^3*27 + 26^5.
Answer: D.
Question: I buy coffee from 3 different shops at Rs.150,Rs.140,Rs.130 per kg and mix them in proportion 8:5:3.At what price per kg must I sell the mixture to make a profit of 25%?
A.168.906
B.178.906
C.188.906
D.198.906
Answer: B.178.906
Explanation: total=16x kg, tot cp=2290x
sp should be=2862.5x
so sp/kg=178.906
ANSWER:B
Question: In a game, a person is declared winner, if he gets 4 consecutive tails in five throws of a coin. What is the probability of A to win if he has got a tail in the first throw?
A.1/5
B.1/4
C.1/8
D.1/16
Answer: C.1/8
Explanation: First throw = Tails
For a person to win, the next 3 throws must be tails and the 5th throw can be heads or tails. i.e. TTTTH or TTTTT
So the person can win in 2 ways if the first throw is Tails.
Total number of outcomes for the next 4 throws = 2^4 = 16
Probability = 2/16 = 1/8
Answer: C
Question: For any positive integer n, the sum of the first n positive integers equals n(n+1)/2. What is the sum of all the even integers between 99 and 171?
A.2820
B.3440
C.4860
D.5560
Answer: C.4860
Explanation: 100 + 102 + ... + 170 =
100*36 + (2+4+...+70) =
100*36 + 2*(1+2+...+35) =
100*36 + 2(35)(36)/2 =
100*36 + 35*36 = 135(36) = 4860
The answer is C.
Question: The average age of a class of 39 students is 15 years. If the age of the teacher be included, then the average increases by 3 months. Find the age of the teacher.
A.22
B.25
C.97
D.27
Answer: B.25
Explanation: Answer: 25 y
Explanation:
Average age of 39 students = 15 yrs
Total age of 39 students = 39 × 15 = 585 yrs
Avg age of 39 students + teacher =15+ (3/12) =15.25 years
So the total age of (39 student + 1 teacher) or 40 persons = 40 × 15.25 = 610 years
So age of teacher = 610 – 585 = 25 years
Answer:B