RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: Two persons A and B can complete a piece of work in 30 days and 60 days respectively. If they work together, what part of the work will be completed in 10 days?
A.1/8
B.1/3
C.1/6
D.1/2
Answer: D.1/2
Explanation: A's one day's work = 1/30
B's one day's work = 1/60
(A + B)'s one day's work = 1/30 + 1/60 = 1/20
The part of the work completed in 10 days = 10 (1/20) = 1/2.
Answer:D
Question: A discount electronics store normally sells all merchandise at a discount of 10 percent to 30 percent off the suggested retail price. If, during a special sale, an additional 20 percent were to be deducted from the discount price, what would be the lowest possible price of an item costing $200 before any discount?
A. $112.00
B. $145.60
C. $163.80
D. $182.00
Answer: A. $112.00
Explanation: Since the question is essentially just about multiplication, you can do the various mathstepsin a variety of ways (depending on whichever method you find easiest).
We're told that the first discount is 10% to 30%, inclusive. We're told that the next discount is 20% off of the DISCOUNTED price....
We're told to MAXIMIZE the discount (thus, 30% off the original price and then 20% off of the discounted price). Thatmathcan be written in a number of different ways (fractions, decimals, etc.):
30% off = (1 - .3) = (1 - 30/100) = (.7) and the same can be done with the 20% additional discount...
The final price of an item that originally cost $200 would be.....
($200)(.7)(.8) =
($200)(.56)=112
Final Answer:
A
Question: If Sharon's weekly salary increased by 16 percent, she would earn $348 per week. If instead, her weekly salary were to increase by 15 percent, how much would she earn per week?
A. $374
B. $382
C. $345
D. $392
Answer: C. $345
Explanation: (348/116)115 =345
In this case long division does not take much time.
(348/116)=3
3*115=345(300+45)
Answer C
Question: If a * b = a + b/ab , find the value of 5 * (5 * -2) :
A.-3
B.-10
C.-1.66
D.3/5
Answer: B.-10
Explanation: (5 * -2) = (5 x (-2))/(5 + (-2)) = -10/3
So, 5 * (5 * -2) = 5 * (-10/3) = (5 * (-10/3))/(5 + (-10/3))
= (-50/3) * (3/5)
= -10.
ANSWER:B
Question: If x>y>0, which of the following must be true:
I. x^2>y^2
II. x^3 > y^3
III. x<y
A.I and II
B.II only
C.III only
D.II and III
Answer: A.I and II
Explanation: Assuming x and y to be integers
X=3,Y=2
X^2=3^2=9
Y^2=2^2=4
So I is true
Now lets look at option III because if option 3 is true E is the answer or else A
As per question X>Y>0 Hence |X| >Y
So OA=A
Question: X and Y can do a piece of work in 20 days and 12 days respectively. X started the work alone and then after 4 days Y joined him till the completion of the work. How long did the work last?
A.5 days
B.10 days
C.11 days
D.20 days
Answer: B.10 days
Explanation: Work done by X in 4 days =1/20	x 4 = 1/5
Remaining work = (1 -1/5) = 4/5
(X + Y)'s 1 day's work = 1/20+1/12 = 8/60 = 2/15
Now,	2/15 work is done by X and Y in 1 day.
So,4/5work will be done by X and Y in	15/2	x 4/5= 6 days.
Hence, total time taken = (6 + 4) days = 10 days.
ANSWER:B
Question: Krishan and Nandan jointly started a business. Krishan invested three times as Nandan did and invested his money for double time as compared to Nandan. Nandan earned Rs. 4000. If the gain is proportional to the money invested and the time for which the money is invested then the total gain was?
A.28,029
B.28,199
C.28,299
D.28,000
Answer: D.28,000
Explanation: Explanation:
3:1
2:1
------
6:1
1 ----- 4000
7 ----- ? => Rs.28,000
Answer: D
Question: What is the units digit of 23^3 * 17^2 * 39^2?
A.9
B.7
C.5
D.3
Answer: D.3
Explanation: The units digit of 23^3 is the units digit of 3*3*3 = 27 which is 7.
The units digit of 17^2 is the units digit of 7*7 = 49 which is 9.
The units digit of 39^2 is the units digit of 9*9 = 81 which is 1.
The units digit of 7*9*1 = 63 is 3.
The answer is D.
Question: Find the odd man out. 362, 482, 551, 263, 344, 284
A.362
B.482
C.551
D.344
Answer: D.344
Explanation: Explanation :
In all numbers except 344, the product of first and third digits is the middle digit.
Answer : Option D
Question: The ratio, by weight, of coffee to sugar to water in a pot of coffee is 3:1:15. The ratio is then altered so that the ratio of coffee to sugar is halved while the ratio of coffee to water is doubled. If the altered pot of coffee contains 12 grams of sugar, how many grams of water does it contain after alteration?
A.35
B.40
C.45
D.50
Answer: C.45
Explanation: The new ratio of coffee to sugar is 1.5:1
The new ratio of coffee to water is 6:15.
The new ratio of coffee to sugar to water is 6:4:15.
If there are 12 grams of sugar, then there are (15/4)*12=45 grams of water.
The answer is C.
Question: In a certain game of dice, the player’s score is determined as a sum of four throws of a single die. The player with the highest score wins the round. If more than one player has the highest score, the winnings of the round are divided equally among these players. If Jim plays this game against 26 other players, what is the probability of the minimum score that will guarantee Jim some monetary payoff?
A.41/50
B.1/221
C.1/1296
D.1/84
Answer: C.1/1296
Explanation: Toguaranteethat Jim will get some monetary payoff he must score the maximum score of 6+6+6+6=24, because if he gets even one less than that so 23, someone can get 24 and Jim will get nothing.
P(24)=1/6^4=1/1296.
Answer: C.
Question: If each side of a square is increased by 25%, find the percentage change in its area?
A.28.88
B.56.25
C.22.89
D.29.18
Answer: B.56.25
Explanation: let each side of the square be a , then area = a x a
As given that The side is increased by 25%, then
New side = =
New area =
increased area=
Increase %= % = 56.25%
Answer: B
Question: A piece of work can be done by 6 men and 5 women in 6 days or 3 men and 4 women in 10 days. It can be done by 9 men and 15 women in how many days ?
A.3 days
B.4 days
C.5 days
D.6 days
Answer: A.3 days
Explanation: Explanation:
To calculate the answer we need to get 1 man per day work and 1 woman per day work.
Let 1 man 1 day work =x
and 1 woman 1 days work = y.
=> 6x+5y = 1/6
and 3x+4y = 1/10
On solving, we get x = 1/54 and y = 1/90
(9 men + 15 women)'s 1 days work =
(9/54) + (15/90) = 1/3
9 men and 15 women will finish the work in 3 days
Option A
Question: Machine E and machine B are each used to manufacture 660 sprockets. It takes machine E 10 hours longer to produce 660 sprockets than machine B. Machine B produces 10 percent more sprockets per hour than machine E. How many sprockets per hour does machine E produces?
A.6
B.6.6
C.60
D.100
Answer: A.6
Explanation: I think the correct answer is A.
Machine E produces at a speed of E sp/hour and B at a speed of B sp/hour.
so, 660/E=(660/B)+10 and E=1,1 E--->1,1*660=660+11E--->A=6, so answer A is correct
Question: A three-digit code for certain locks uses the digits 0, 1, 2, 3, 4, 5, 6, 7 according to the following constraints. The first digit cannot be 0 or 1, the second digit must be 0 or 1, and the second and third digits cannot both be 0 in the same code. How many different codes are possible?
A.144
B.152
C.90
D.168
Answer: C.90
Explanation: The first digit can be filled in 6 ways
For second digit , it can either be 0 or 1
Case 1 -
If second digit is 1 ,Third digit can take 8 values
number of codes = 6 * 1 * 8 = 48
Case 2 -
If second digit is 0,Third digit can take 7 values ( Third digit can't be zero)
number of codes = 6 * 1 * 7= 42
Total number of codes = 90
Answer C
Question: A basket has 5 apples and 4 oranges. Three fruits are picked at random. The probability that at least 2 apples are picked is -.
A.25/42
B.9/20
C.10/23
D.41/42
Answer: A.25/42
Explanation: Total fruits = 9
Since there must be at least two apples,
(⁵C₂ * ⁴C₁)/⁹C₃ + ⁵C₃/⁹C₃ = 25/42.
ANSWER:A
Question: Bilal and Ahmed play the following game with n sticks on a table. Each must remove 1,2,3,4, or 5 sticks at a time on alternate turns, and no stick that is removed is put back on the table. The one who removes the last stick (or sticks) from the table wins. If Bilal goes first, which of the following is a value of n such that Ahmed can always win no matter how Bilal plays?
A.7
B.10
C.11
D.12
Answer: D.12
Explanation: If the number of sticks on a table is a multiple of 6, then the second player will win in any case (well if the player is smart enough).
Consider n=6, no matter how many stick will be removed by the first player (1, 2, 3 ,4 or 5), the rest (5, 4, 3, 2, or 1) can be removed by the second one.
The same for n=12: no matter how many sticks will be removed by the first player 1, 2, 3 ,4 or 5, the second one can remove 5, 4, 3, 2, or 1 so that to leave 6 sticks on the table and we are back to the case we discussed above.
Answer: D.
Question: There are five different models that are to appear in a fashion show. Two are from Europe, two are from South America, and two are from North America. If all the models from the same continent are to stand next to each other, how many ways can the fashion show organizer arrange the models?
A.96
B.48
C.64
D.24
Answer: A.96
Explanation: Since we have 3 continental pairs (EU, SA, NA), these 3 pairs have 3*2*1 = 6 Combinations. Within each pair, you have however 2 different ways to put them together for each of the pair (2*2*2*2= 16). So we have 6*16 =96.
Please correct me if im wrong.
Answer A.
Question: 81, 64, 27, 16...
A.12
B.4
C.9
D.3
Answer: C.9
Explanation: 81/3 = 27
64/4 = 16
27/3 = 9
ANSWER: C
Question: Marginal cost is the cost of increasing the quantity produced (or purchased) by one unit. If the fixed cost for n products is $12,000 and the marginal cost is $200, and the total cost is $16,000, what is the value of n?
A. 20
B. 50
C. 60
D. 80
Answer: A. 20
Explanation: Total cost for n products = fixed cost for n products + n*marginal cost --> $16,000 = $12,000 + n * $200 --> n = 20.
Answer: A.
Question: A train 125 m long passes a man, running at 8 km/hr in the same direction in which the train is going, in 10 sec. The speed of the train is?
A.53
B.50
C.60
D.79
Answer: A.53
Explanation: Speed of the train relative to man = 125/10 = 25/2 m/sec.
= 25/2 * 18/5 = 45 km/hr
Let the speed of the train be x km/hr. Then, relative speed = (x - 8) km/hr.
x - 8 = 45 => x = 53 km/hr.
Answer: Option A
Question: A shop owner sells 110 eraser and gains SP of 22 metres. Find the gain %?
A.25%
B.35%
C.27%
D.23%
Answer: A.25%
Explanation: Gain=22 orangesTotal 110 orangesCP 110-22=88(22/88)*100=25%Ans A
Question: What number is 75 more than three-fourth of itself?
A.138
B.225
C.300
D.324
Answer: C.300
Explanation: 3/4x+75= x
That means 75=1/4x
x= 75*4= 300
C is the answer
Question: The cash difference between the selling prices of an article at a profit of 4% and 6% is Rs 3. The ratio of two selling prices is
A.51:52
B.52:53
C.53:54
D.54:55
Answer: B.52:53
Explanation: Explanation:
Let the Cost price of article is Rs. x
Required ratio =
104% of x/ 106% of x
=104/106=52/53=52:53
Option B
Question: If c and d are both negative and cd < d^2, which of the following must be true?
A.c < d < c^2 < d^2
B.c < d < d^2 < c^2
C.d < c < c^2 < d^2
D.c^2 < d^2 < d < c
Answer: C.d < c < c^2 < d^2
Explanation: Because cd <d^2 and both are negative, I thought c < d. So I crossed off answers c), d), and e).
And because c < d , c^2 < d^2
ans C
Question: The ages of Ashley and Mary are in the ratio 4:7. The sum of their ages is 22. Find the age of Mary.
A.11yrs
B.12yrs
C.13yrs
D.14yrs
Answer: D.14yrs
Explanation: a:m=4:7
let the ages of a & m be x &22-x
x/22-x=4/7
x=8
a=8yrs
m=14yrs
ANSWER:D
Question: How much time will take for an amount of Rs. 400 to yield Rs. 81 as interest at 4.5% per annum of simple interest?
A.4 1/2 years
B.6 1/2years
C.7 1/2years
D.12 1/2years
Answer: A.4 1/2 years
Explanation: Time = (100 * 81) / (400 * 4.5) = 4 1/2years
ANSWER:A
Question: After replacing an old member by a new member, it was found that the average age of five numbers of a club is the same as it was 3 years ago. What is the difference between the ages of the replaced and the new member?
A.2 years
B.4 years
C.8 years
D.15 years
Answer: D.15 years
Explanation: Sol.
Age decrease = (5 × 3) years = 15 years.
So, the required difference = 15 years.
Answer D
Question: Tough and Tricky questions: Functions. Let a be a positive integer. Let n#a equal n^(2a) if a is odd and n^(3a) if a is even. Then (2#3) + (2#3) – (3#3) is equal to
A.64
B.82
C.128
D.729
Answer: D.729
Explanation: Answer:
3^6 + 3^6 - 3^6 = 3^6 = 729
ANs D
Question: What is the area of a square field whose diagonal of length 20 m?
A.300 sq m
B.250 sq m
C.200 sq m
D.400 sq m
Answer: C.200 sq m
Explanation: d2/2 = (20 * 20)/2 = 200
ANSWER:C
Question: In an election only two candidates contested. A candidate secured 70% of the valid votes and won by a majority of 172 votes. Find the total number of valid votes?
A.430
B.570
C.480
D.520
Answer: A.430
Explanation: Let the total number of valid votes be x.
70% of x = 70/100 * x = 7x/10
Number of votes secured by the other candidate = x - 7x/100 = 3x/10
Given, 7x/10 - 3x/10 = 172 => 4x/10 = 172
=> 4x = 1720 => x = 430.
ANSWER:A
Question: If a * b * c =(√(a + 2)(b + 3)) / (c + 1), find the value of 6 * 15 * 1.
A.8
B.5
C.2
D.3
Answer: C.2
Explanation: 6 * 15 * 1 = (√(6 + 2)(15 + 3) )/ (1 + 1)
= (√8 * 18) / 2
= (√144) / 2
= 12 / 6 = 2
Answer is C.
Question: A certain school implemented a reading program for its students, with the goal of getting each student to read 6 books per month year-round. If the school has c classes made up of s students in each class, how many books will the entire student body read in one year?
A.20cs
B.cs/2
C.72cs
D.(2cs)/12
Answer: C.72cs
Explanation: Ans: C
Solution: simple multiplication s students , c classes , 6 books/ month= 72 books a year
total number of books = 72cs
Question: Circular gears L and R start to rotate at the same time at the same rate. Gear L makes 20 complete revolutions per minute and gear R makes 40 revolutions per minute. How many seconds after the gears start to rotate will gear R have made exactly 6 more revolutions than gear L?
A.a) 6
B.b) 8
C.c) 10
D.d) 12
Answer: A.a) 6
Explanation: Gear L -- 20 rotations per 60 seconds -- 2 rotation per 6 seconds.
Gear R -- 40 rotations per 60 seconds -- 4 rotations per 6 seconds.
First 6 seconds -- Gear L makes 1 rotation. -- Gear R makes 4 rotations -- Net difference -- 2 rotations
Hence every 6 seconds the difference between the number of rotations of R and L gear is 2 units.
Required net difference should be 6 rotations => 3 (6 seconds later) ==> 18 seconds.
Answer: A
Question: In one hour, a boat goes 11 km along the stream and 3 km against the stream. the sped of the boat in still water (in km/hr) is :
A.3
B.5
C.7
D.9
Answer: C.7
Explanation: Solution
Speed in still water= 1/2(11+3) km/hr= 7kmph. Answer C
Question: Given that X and Y are events such that
Z(X)= 0.02
Z(Y)=0.10
Z(XnY)=0.10
Z(X|Y)=
find Z (X|Y) and Z(X|Y)
A.1/5
B.1/6
C.1/6
D.1/4
Answer: A.1/5
Explanation: Here, X and Y are events
Z(X|Y) = Z(XnY)/Z(Y) = 0.10/0.10= 1
Q(G|H) = Z(XnY)/Z(X) = 0.4/0.02 = 1/5
Answer is A
Question: Patrick purchased 80 pencils and sold them at a loss equal to the selling price of 16 pencils. The cost of 80 pencils is how many times the selling price of 80 pencils?
A. 0.75
B. 1.2
C. 1.8
D. 2.4
Answer: B. 1.2
Explanation: Say the cost price of 80 pencils was $80 ($1 per pencil) and the selling price of 1 pencil was p.
Selling at a loss: 80 - 80p = 16p --> p = 5/6.
(cost price)/(selling price) = 1/(5/6) = 6/5 = 1.2.
Answer: B.
Question: Each of the cucumbers in 100 pounds of cucumbers is composed of 99% water, by weight. After some of the water evaporates, the cucumbers are now 97% water by weight. What is the new weight of the cucumbers, in pounds?
A.2
B.33
C.92
D.96
Answer: B.33
Explanation: Out of 100 pounds 99% or 99 pounds is water and 1 pound is non-water. After somewaterevaporates the cucumbers become 97% water and 3% of non-water, so now 1 pound of non-water composes 3% of cucucmbers, which means that the new weight of cucumbers is 1/0.03=34 pounds.
Answer: B.
Question: Half of 3 percent written as decimal is
A.5
B.0.5
C.0.015
D.0.005
Answer: C.0.015
Explanation: Explanation:
It will be 1/2(3%) = 1/2(3/100) = 3/200 = 0.015
Option C
Question: Out of 40 applicants to a law school, 15 majored in political science, 20 had a grade point average higher than 3.0, and 10 did not major in political science and had a GPA equal to or lower than 3.0. How many E applicants majored in political science and had a GPA higher than 3.0?
A.5
B.10
C.15
D.25
Answer: A.5
Explanation: Total applicants = 40
Political science = 15 and Non political science = 40 - 15 = 25
GPA > 3.0 = 20 and GPA <= 3.0 = 20
10 Non political science students had GPA <= 3.0 --> 15 Non political science students had GPA > 3.0
GPA > 3.0 in political science = Total - (GPA > 3.0 in non political science) E= 20 - 15 = 5
Answer: A
Question: One night a certain hotel rented 2/5 of its rooms, including 2/3 of their air conditioned rooms. If 3/5 of its rooms were air conditioned, what percent of the rooms that were not rented were air conditioned?
A.20%
B.25%
C.33%
D.36%
Answer: C.33%
Explanation: The rooms which were not rented is 3/5
The AC rooms which were not rented is (1/3)*(3/5) = 1/5
The percentage of unrented rooms which were AC rooms is (1/5) / (3/5) = 1/3 = 33%
The answer is C.
Question: A can do a job in 30 days and B can do it in 30 days. A and B working together will finish twice the amount of work in ------- days?
A.14 days
B.26 days
C.30 days
D.31 days
Answer: C.30 days
Explanation: C
1/30 + 1/30 = 1/15
15*2 = 30 days
Question: Find k if 64 ÷ k = 4.
A.8
B.12
C.16
D.25
Answer: C.16
Explanation: Since 64 ÷ k = 4 and 64 ÷ 16 = 4, then
k = 16
correct answer is C)16
Question: If [x] is the greatest integer less than or equal to x, what is the value of [-5.6]+[3.4]+[12.7]?
A. 3
B. 5
C. 7
D. 9
Answer: A. 3
Explanation: You are asked what the closest lesser integer value to [x] is.
[-5.6] = -6.0
[3.4] = 3.0
[12.7] = 12.0
Therefore , answer is: -6.0 + 3.0 + 12.0 = 9.0
Option D.
Question: In how many different number of ways the letters of the word 'ENGINEERING' can be arranged
A.276800
B.277000
C.277200
D.277400
Answer: C.277200
Explanation: 11!/(3! × 3! × 2! × 2! × 1!)
= (11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1)/(3 × 2 × 3 × 2 × 2 × 2 × 1)
= 11 × 10 × 8 × 7 × 5 × 3
= 277200
C)
Question: If W is an integer greater than 6, which of the following must be divisible by 3?
A.W(W+1)(W-4)
B.N(N+2)(N-1)
C.N(N+3)(N-5)
D.N(N+4)(N-2)
Answer: A.W(W+1)(W-4)
Explanation: Now take W = 3k , W = 3k+1 W = 3k+2..put in all the choices. If by putting all the values of W we get it is divisible by 3, then it is correct answer choice.
A is correct. It will hardy take 10 sec per choice as we have to consider only 3k+1 and 3k+2.
Question: The ratio of the volumes of two cubes is 729 : 1331. What is the ratio of their total surface areas?
A.81:121
B.81:122
C.81:129
D.81:120
Answer: A.81:121
Explanation: Ratio of the sides = ³√729 : ³√1331
= 9 : 11
Ratio of surface areas = 92 : 112
= 81:121
Answer: A
Question: 4/x + 3x = 3(x+12)
A.-9
B.-1/3
C.-1/9
D.1/9
Answer: D.1/9
Explanation: We can solve - expand the right side, multiply by x on both sides and then subtract away the 3x^2 terms:
(4/X) + 3x = 3(x+12)
(4/x) + 3x = 3x + 36
4 + 3x^2 = 3x^2 + 36x
4 = 36x
1/9 = x
and to confirm, you can plug that answer back into the original equation to see that it makes the left and right sides equal.
D
Question: The price of a table is marked at $12,000. If successive discounts of 15%, 10% and 5% be allowed, then at what price does a customer buy it?
A.8721
B.2304
C.7720
D.6221
Answer: A.8721
Explanation: A
8721
Actual price = 95% of 90% of 85% of $12000
= 95/100 * 90/100 * 85/100 * 12000 = $8721.
Question: Difference between two numbers is 4, six times of the smaller lacks by 6 from the four times of the greater. Find the numbers?
A.5,9
B.7,9
C.9,8
D.11,12
Answer: A.5,9
Explanation: Explanation:
x – y = 4
4x – 6y = 6
x = 9 y = 5
A)
Question: Tom and Linda stand at point A. Linda begins to walk in a straight line away from Tom at a constant rate of 2 miles per hour. One hour later, Tom begins to jog in a straight line in the exact opposite direction at a constant rate of 8 miles per hour. If both Tom and Linda travel indefinitely, what is the positive difference, in minutes, between the amount of time it takes Tom to cover half of the distance that Linda has covered and the amount of time it takes Tom to cover twice the distance that Linda has covered?
A.50
B.72
C.84
D.90
Answer: A.50
Explanation: A is the answer....
D = TS where D=distance, T=Time and S=Speed
To travel half distance, (2+2T) = 8T ==> T = 1/6 ==> 10 minutes
To travel double distance, 2(2+2T) = 8T ==> 1 ==> 60 minutes
Difference, 50 minutes
A
Question: Two trains, each 100 m long, moving in opposite directions, cross other in 8 sec. If one is moving twice as fast the other, then the speed of the faster train is?
A.16 km/hr
B.17 km/hr
C.60 km/hr
D.15 km/hr
Answer: C.60 km/hr
Explanation: Let the speed of the slower train be x m/sec.
Then, speed of the train = 2x m/sec.
Relative speed = ( x + 2x) = 3x m/sec.
(100 + 100)/8 = 3x => x = 25/3.
So, speed of the faster train = 50/3 = 50/3 * 18/5 = 60 km/hr.
Answer: C
Question: An investment of $3000 was made in a certain account and earned interest that was compounded annually. The annual interest rate was fixed for the duration of the investment, and after 12 years the $3000 increased to $12000 by earning interest. In how many years after the initial investment was made the $3000 have increased to $24000 by earning interest at that rate?
A.16
B.22
C.20
D.18
Answer: D.18
Explanation: In 12 years the investment quadrupled (from $3,000 to $12,000).
Thus, at the same rate compounded annually, it would need additional 12/2=6 years to double (from $12,000 to $24,000).
Therefore, 12+6=18 years are needed $3,000 to increase to $24,000.
Answer: D.
Question: John bought a shirt on sale for 25% off the original price and another 25 % off the discounted price. If the final price was $15, what was the price before the first discount?
A.$45.10
B.$34.31
C.$28.44
D.$26.66
Answer: D.$26.66
Explanation: let x be the price before the first discount. The price after the first discount is
x - 25%x (price after first discount)
A second discount of 25% of the discounted price after which the final price is 15
(x - 25%x) - 25%(x - 25%x) = 15
Solve for x
x = $26.66
correct answer D
Question: Three taps A, B and C can fill a tank in 12, 15 and 20 hours respectively. If A is open all the time and B and C are open for one hour each alternately, the tank will be full is?
A.8 hrs
B.6 hrs
C.7 hrs
D.3 hrs
Answer: C.7 hrs
Explanation: (A + B)'s 1 hour work = (1/12 + 1/15) = 3/20
(A + C)'s 1 hour work = (1/12 + 1/20) = 2/15
Part filled in 2 hrs = (3/20 + 2/15) = 17/60
Part filled in 6 hrs = 3 * 17/60 = 17/20
Remaining part = 1 - 17/20 = 3/20
Now, it is the turn of A and B and 3/20 part is filled by A and B in 1 hour.
Total time taken to fill the tank = (6 + 1) = 7 hrs.
Answer: C
Question: If x > 3 and y < -3, then which of the following must be true ?
A.x/y > 1
B.x/y < -1
C.x/y < 0
D.x + y > 0
Answer: D.x + y > 0
Explanation: Pick x=3, y = -3
A) x/y > 1 - Incorrect as x/y = -1
B) x/y < -1 - Incorrect as x/y = -1
C) x/y < 0 -Correct. It will hold for all values x > 2 and y < -2 as x/y = -1 < 0
D) x + y > 0 - Incorrect. x + y = 0
E) xy > 0 - Incorrect. XY = -9 which is less than zero.
D should be the answer.
Question: (3X+2)(2X-5)=AX^2+ KX+N;
THEN WHAT IS THE VALUE OF A-N+K?
A.4
B.5
C.6
D.7
Answer: B.5
Explanation: (3x+2)(2x-5)=6x^2-11x-10
So,A=6, K=-11, N=-10
Finally,
A-N+K=6-(-10)+(-11)
=6+10-11
=5
ANSWER:B
Question: when W is divided by 14, the reminder is 0. if W is three more than it value and when divided by 9 its remainder is 0. what is the value of W ?
A.42
B.14
C.28
D.30
Answer: A.42
Explanation: W is divided by 14 so that is multiple of 14 as 14,28,42...
W+3 is divided by 9 the remainder is 0 so it is divisible by 9. Consider from option let us take the number is 42 it is divisible by 14 but 42+3 is divisible by 9 so ans is A