RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: June 25, 1982, fell on a Friday. On which day of the week did December 25, 1983, fall?
A. Sunday
B. Monday
C. Tuesday
D. Wednesday
Answer: A. Sunday
Explanation: 6/25/82 - 12/25/83
The date range contains one full year of 365 days plus a partial year. The number of days in the partial year is:
June - 5, July - 31, August - 31, September - 30, October - 31, November - 30, and December - 25.
5 + 31 + 31 + 30 + 31 + 30 + 25 = 183.
183 + 365 = 548 total days in the date range.
Divide by 7 to determine how much the day of the week advances: 548 / 7 = 78 remainder 2.
Since the first date was a Friday, advance the day of the week by 2; the second date fell on a Sunday. The answer is A.
Question: A train crosses a platform of 120 m in 15 sec, same train crosses another platform of length 180 m in 18 sec. then find the length of the train?
A.167m
B.180m
C.187m
D.287m
Answer: B.180m
Explanation: Length of the train be ‘X’
X + 120/15 = X + 180/18
6X + 720 = 5X + 900
X = 180m
Answer:B
Question: Two trains travelling in the same direction at 40 and 22 kmph completely pass off another in 1 minute. If the length of the first train is 125 m, what is the length of the second train?
A.387 m
B.287 m
C.175 m
D.187 m
Answer: C.175 m
Explanation: RS = 40 – 22 = 18 * 5/18 = 5 mps
T = 60 sec
D = 5 * 60 = 300 m
125
--------
175 m
Answer: C
Question: One fourth of a solution that was 10 percent gram flour by weight was replaced by a second solution resulting in a solution that was 16 percent gram flour by weight. The second solution was what percent gram flour by weight ?
A.34%
B.24%
C.22%
D.18%
Answer: A.34%
Explanation: EQ can be written as ...
let sol be s... so (3/4)s*(.1)+(1/4)s*t=s*(.16).... we get t(% of gram flour in 2nd sol)=34%=A
Question: How many numbers between 101 and 250, exclusive are divisible by three?
A.34
B.41
C.50
D.83
Answer: C.50
Explanation: Numbers upto 250 divisible by 3 is 250/3 = 83
Numbers upto 101 divisible by 3 is 101/3 = 33
Total number of numbers between 101 and 250 that are divisible by 3 is 83 - 33 = 50
ANSWER:C
Question: Solve:-
111 x 111 x 111 + 555 x 555 x 555 = ?(111 x 111 - 111 x 555 + 555 x 555)
A.888
B.666
C.555
D.988
Answer: B.666
Explanation: Given Exp. = (a3 + b3) = (a + b) = (111 + 555) = 666 (a2 - ab + b2)
Answer B
Question: Each of the dogs in a certain kennel is a single color. Each of the dogs in the kennel either has long fur or does not. Of the 45 dogs in the kennel, 28 have long fur, 17 are brown, and 8 are neither long-furred nor brown. How many long-furred dogs are brown?
A.26
B.19
C.11
D.8
Answer: D.8
Explanation: No of dogs=45
Long fur=28
Brown=17
Neither long fur nor brown=8
Therefore, either long fur or brown=45-8=37
37=28+17-Both
Both=8
Answer D
Question: If K is the sum of reciprocals of the consecutive integers from 3 to 8, inclusive, then K is closest in value to which of the following?
A.1.2
B.1/10
C.1/8
D.1/6
Answer: A.1.2
Explanation: 1/3 + 1/4 + 1/5 + 1/6 + 1/7 + 1/8
=0.33+0.25+0.20+0.16+ 0.14+0.12=1.2
A
Question: A student got twice as many sums wrong as he got right. If he attempted 36 sums in all, how many did he solve correctly ?
A.12
B.16
C.18
D.24
Answer: A.12
Explanation: Explanation:
Suppose the boy got x sums right and 2x sums wrong.
Then, x + 2x = 36 3x = 36 x = 12.
Answer:A
Question: A gang of 8 boys goes on an tour in 2cars, of which 1can seat 5 & the other only 4. In how many ways can they travel?
A.100
B.121
C.126
D.128
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: If P is a prime number greater than 3, find the remainder when p^2 + 17 is divided by 12.
A.6
B.1
C.0
D.8
Answer: A.6
Explanation: Take any prime number greater than 3 and check -
Say p = 5
So, p^2 + 17 = 25+17 => 42
42/12 will have remainder as 6
Say p = 7
So, p^2 + 17 = 49+17 => 66
66/12 will have remainder as 6
So answer will be (A) 6
Question: If the numerator of a fraction be increased by 12% and its denominator decreased by 2% the value of the fraction becomes 6/7. Thus, the original fraction is:
A.1/4
B.2/4
C.3/4
D.2/3
Answer: C.3/4
Explanation: If original fraction is x/y , then
1.12x/0.98y = 6/7
(8/7)*(x/y)=6/7
x/y =6/8=3/4
ANSWER:C
Question: In a 100 m race, A runs at 8km per hour. If A gives B a start of 9 m and still him by 15 seconds, what is the speed of B ?
A.5.46 km/hr.
B.5.56 km/hr.
C.5.76 km/hr.
D.6.76 km/hr.
Answer: A.5.46 km/hr.
Explanation: Time taken by A to cover 100 m =(60 X 60 / 8000)	x 100 sec = 45 sec.
B covers (100 - 9) m = 91 m in (45 + 15) sec = 60 sec.
B's speed = (91 x 60 x 60)/(60 x 1000)km/hr = 5.46 km/hr.
Answer is A
Question: Jamshid and Irwin decided to make up their own version of basketball. In addition to being able to score 2-point baskets, they created ways to score 5-, 11-, and 13-point baskets. If at halftime the product of the point values of Irwin’s baskets was 2,420, how many 11-point baskets T did Irwin score?
A.0
B.1
C.2
D.3
Answer: C.2
Explanation: First thing I noticed was that all these numbers are prime...
Prime factorization gives the following
Step 1:2*1210
Step 2:2*11*110
Step 4:2*11*11*10
Step 5:2*11*11*2*5
So he scored T=2 11-point baskets in my opinion.
Answer C
Question: X can do a piece of work in 8hours. Y and Z together can do it in 6 hours, while X and Z together can do it in 4 hours. How long will Y alone take to do it?
A.24 HOURS
B.20 HOURS
C.34 HOURS
D.12 HOURS
Answer: A.24 HOURS
Explanation: X's 1 hour work= 1/8
(Y+Z)'s 1 hour work= 1/6
(X+Z)'s 1 hour work= 1/4
(X+Y+Z)'s 1 hour work= (1/8+1/6)=7/24
Y's 1hour's work= (7/24-1/4)= 1/24
Y alone will take 24 hours to do the work.
correct option is A
Question: What approximate value should come in place of (x) in the following question?
139.25 + 223.94 / 4.002 = x
A.250
B.203
C.200
D.195
Answer: D.195
Explanation: Explanation:
Given: 139.25 + 223.94 / 4.002 = x
Approximate 139.25 as 140, 223.94 as 224, 4.002 as 4,
we get, x = 140 + 224 / 4 = 140 + 56 = 196 =>195
ANSWER: D
Question: A man's speed with the current is 20 kmph and speed of the current is 5 kmph. The Man's speed
against the current will be
A.11 kmph
B.10 kmph
C.14 kmph
D.17 kmph
Answer: B.10 kmph
Explanation: Explanation:
Speed with current is 20,
speed of the man + It is speed of the current
Speed in sƟll water = 20 - 5 = 15
Now speed against the current will be
speed of the man - speed of the current
= 15 - 5 = 10 kmph
Answer: B
Question: Number S is obtained by squaring the sum of digits of a two digit number D. If difference between S and D is 27, then the two digit number D is:
A.24
B.54
C.34
D.45
Answer: B.54
Explanation: D = 10x + y
S = 10x^2 + y^2
S-D --> (10x^2 + y^2) - (10x + y) = 27 --> 10x (x-1) + y (y+1) = 27
ANSWER:B
Question: If 17m − n = p, then which of the following represents the average (arithmetic mean) of m, n, and p, in terms of m?
A.2m −1
B.4m
C.6m
D.m/5
Answer: C.6m
Explanation: 17m - n = p
Add n to both sides:
17m = n + p
Add m to both sides:
18m = n + p + m
Now, divide both sides by 3
6m = (n + p + m)/3 = the average of n, p, and m
C
Question: When positive integer n is divided by 4, the remainder is 1. When n is divided by 7, the remainder is 5. What is the smallest positive integer p, such that (n + p) is a multiple of 35?
A.1
B.2
C.5
D.19
Answer: B.2
Explanation: When positive integer n is divided by 4, the remainder is 1 i.e., n=4x+1
values of n can be one of {1, 5, 9, 13, 17, ...........29, 33, 37..................}
Similarly,
When n is divided by 7, the remainder is 5..i.e., n=7y+5
values of n can be one of {5, 12, 19, 26, 33, 40,........}
combining both the sets we get
n={5,33, ...........}
What is the smallest positive integer p, such that (n + p) is a multiple of 35 or 35x
in case of n=33 p=2
so for min value of p, we take min value of n.
B is the answer.
Question: The radius of a wheel is 22.4 cm. What is the distance covered by the wheel in making 500 resolutions?
A.277 m
B.704 m
C.278 m
D.288 m
Answer: B.704 m
Explanation: In one resolution, the distance covered by the wheel is its own circumference. Distance covered in 500 resolutions.
= 500 * 2 * 22/7 * 22.4 = 70400 cm
= 704 m
Answer: B
Question: The average age of husband, wife and their child 3 years ago was 24 years and that of wife and the child 5 years ago was 20 years. The present age of the husband is
A.31 years
B.40 years
C.50 years
D.55 years
Answer: A.31 years
Explanation: Solution
Sum of the present ages of husband, wife and child	= (24x3+3x3) years
= 81 years.
Sum of the present ages of wife and child	= (20x2+5x2) years
= 50 years.
âˆ´ Husband's present age	= (81 - 50) years
= 31 years.
Answer A
Question: In a store there is a number of people, out of which 1/30 are children, 1/6 are women and the remaining 120 are men. How many children are in the store?
A.50
B.120
C.150
D.5
Answer: D.5
Explanation: Let x be the number of people in the store.
x/30+x/6=6x/30=x/5 is the number of children and women
The number of men is x-x/5=4x/5, that is 4x/5=120. Thus, x=150.
The number of children is 1/30*150=5.
Answer D 5.
Question: An article is bought for Rs.1450 and sold for Rs.1420, find the loss percent?
A.2%
B.4%
C.6%
D.8%
Answer: A.2%
Explanation: 1450 ---- 30
100 ---- ? => 2%
Answer:A
Question: If the LCM of 9, 7, 2, and q is 504, which of the following could be q?
A.7
B.8
C.6
D.9
Answer: B.8
Explanation: Using elimination method, eliminate the option to arrive at 8
if x is replaced by 8 and the LCM is calculated you arrive at 504
B
Question: If x, y, and z are consecutive positive integers greater than 1, not necessarily in that order, then which of the following is (are) true?
I. x > z
II. x+ y > z
III. yz > xz
IV. xy > y + z
A.I only
B.II only
C.II and III only
D.II and IV only
Answer: B.II only
Explanation: lets see the choices..
I. x > z...
we do not know the values or the relative values ... need not be true..
II. x+ y > z
we take the worst case that z is the largest and x and y are lowest possible..... so 2+3>4.. 5>4.. always true
III. yz > xz
we do not know the values or the relative values between x and y.. need not be true
IV. xy > y + z
xy-y>z or y(x-1)>z...
again lets take the worst scenario..
we take the worst case that z is the largest and x and y are lowest possible..... so (2-1)3>4.. 3>4.. not true
only ii is true
ANSWER:B
Question: If x and y are positive integers such that x < y and z=x/y, which of the following must be true?
I. z>(x − 1)/(y − 2)
II. z<(x − 1)/(y − 2)
III. z>(x + 1)/(y + 2)
A.I only
B.I and II
C.II and III
D.II only
Answer: C.II and III
Explanation: x < y --> Let x = 2 and y = 3 --> z = 2/3
I. z>(x − 1)/(y − 2) --> 2/3 > 1/1 --> False
II. z<(x − 1)/(y − 2) --> 2/3 < 1/1 --> True
III. z>(x + 1)/(y + 2) --> 2/3 > 3/5 --> True
Answer: C
Question: 24 oz of juice P and 25 oz of juice T are mixed to make smothies X and Y . The ratio of p to T in smothie X is 4 is to 1 and that in Y is 1is to 5.How many ounces of juice P are contained in the smothie X?
A.5
B.10
C.15
D.20
Answer: D.20
Explanation: Easy way to solve this question is start from the answer and then conform the information provided in the question.
we can start from option D i.e 20 ... as a quantity of juice P in X because it is the only one option that gets divided by 4 is 20 ... since in the X the juice P to T ratio is 4:1
this gives us that quantity of juice P in X = 20 therefore quantity of Juice T will be 5 ... hence ratio = 4:1
This will lead to quantity of juice P in X = 4 and quantity of Juice T = 20 ... hence ratio 1:5
if we calculate total Juice P = 24 and total of juice V = 25
it fits because totals are same as what mentioned in the question ...
thus ans is D
Question: Two trains are traveling on parallel tracks in the same direction. The faster train travels at 120 miles per hour, while the slower train travels at 100 miles per hour. At 2 o’clock the faster train is 10 miles behind the slower one. How far apart are the two trains at 6 o'clock?
A.60 miles
B.80 miles
C.110 miles
D.120 miles
Answer: C.110 miles
Explanation: Answer = C. 110 miles
Relational speed = 120 - 100 = 20 miles per hour
In 4 hours, difference = 20 * 4 = 120 miles
Fast train trailing 10 miles, so effective difference = 120 - 10 = 110 miles
Question: Jack took a 3-hour bike ride. In the second hour he travlled 18 miles, which was 20 percent farther than he traveled the first hour. If he traveled 25 percent farther in the third hour than he did in the second hour, how many miles did jose travel during the entire ride?
A.54.0
B.54.9
C.55.5
D.57.0
Answer: C.55.5
Explanation: Let the distance travelled in the first hour be x. Thus, 1.2x = 18 , x = 15. Now, the distance travelled in the 3rd hour = 18+1/4∗18 = The only option ending with a 0.5 in the decimal's place is C.
Correct answer is C
Question: The bankers discount of a certain sum of money is Rs. 72 and the true discount on the same sum for the same time is Rs. 60. The sum due is:
A.Rs. 360
B.Rs. 432
C.Rs. 540
D.Rs. 1080
Answer: A.Rs. 360
Explanation: Sum = (B.D*T.D)/(B.D-T.D)
(72*60)/72-60;
360
ANSWER:A
Question: The train leaves from New York City every 40 minutes from Boardman station. A man told John Watson that the train had left 15 minutes ago and the next train to New York City will leave at 9:40 p.m. At what time, man convey this information to John Watson?
A.6:15 PM
B.7:15 PM
C.8:15 PM
D.9:15 PM
Answer: C.8:15 PM
Explanation: Solution
Time of John Watson last missed the train = 8:40 PM - 40 min = 8:00 PM As this information has been given to John Watson 15 minutes after the train has already left, the man gave the information at 8:00 p.m. + 15 min = 8:15 PM
Answer C
Question: In order to obtain an income of Rs. 15000 from 80% stock at Rs. 200, one must make an investment of
A.Rs.30000
B.Rs.37000
C.Rs.37500
D.Rs.40000
Answer: C.Rs.37500
Explanation: Explanation :
Market Value = Rs. 200.
Required Income = Rs. 15000.
Here face value is not given. Take face value as Rs.100 if it is not given in the question
To obtain Rs.80 (ie,80% of the face value 100), investment = Rs.200
To obtain Rs.15000, investment = 200/80Ã—15000=Rs.37500
Answer : Option C
Question: emblem is coded as 216;
crude is coded as 125
hi will be ?
A.243
B.64
C.8
D.32
Answer: C.8
Explanation: coding follows (no. of letters)^3
emblem = 216 = 6^3
crude = 125 = 5^3
hi = 2^3 =8
ANSWER:C
Question: A bowl contains equal numbers of red, orange, green, blue, and yellow candies. Kaz eats all of the green candies and half of the orange ones. Next, he eats half of the remaining pieces of each color. Finally, he eats red and yellow candies in equal proportions until the total number of remaining candies of all colors equals 24% of the original number. What percent of the red candies remain?
A.12.5%
B.16.7%
C.22.5%
D.27.5%
Answer: C.22.5%
Explanation: Let x be the original number of each color so there are a total of 5x candies.
Kaz eats all of the green candies and half of the orange ones.
There are 0 green candies and 0.5x orange candies remaining.
He eats half of the remaining pieces of each color.
There are 0.25x orange candies, and 0.5x each of red, yellow, and blue candies.
He eats red and yellow candies in equal proportions.
orange+blue+red+yellow = 0.75x + red + yellow = 1.2x
red + yellow = 0.45x
red = 0.225x, since red = yellow.
The answer is C.
Question: Three pieces of timber 48 m, 56 m and 72 m long have to be divided into planks of the same length, What is the greatest possible length of each plank ?
A.8 m
B.4 m
C.2 m
D.6 m
Answer: A.8 m
Explanation: Answer
Greatest possible length of each plank = H.C.F of 48, 56, 72 = 8 m
Correct Option: A
Question: A dice is rolled 3times & sum of 3 no.'sappearing on the uppermost face is 15. The chance that the first roll was four is?
A.2/113
B.3/115
C.1/108
D.2/213
Answer: C.1/108
Explanation: Sol. Total number of favorable outcomes n(S) . e . 216 Combinations of outcomes for getting sum of 15 on uppermost face = (4, 5, 6) (5, 4, 6) (6, 5, 4) (5, 6, 4), (4, 6, 5), (6, 4, 5), (5, 5, 5), (6, 6, 3), (6, 3, 6) (3, 6, 6) Now outcomes on which first roll was a four, n(E) = (4, 5, 6), (4, 6, 5) P(E) n(E) 2 1 Pt') = n(S) = 216 = 1/108
C
Question: A professional stock trader just signed her new yearly contract with her employer. She will receive a 6% raise over last year's pay for her base pay, plus the chance to earn a performance bonus of up to $3,000. Last year, she earned no performance bonus. This year, assuming that she earns the full performance bonus, her new pay will be effectively an 8% raise. What will her new pay be assuming that she earns the full performance bonus.
A.162,000
B.173,000
C.180,000
D.213,000
Answer: A.162,000
Explanation: let x = last year's pay
this year's pay + 3,000 = this year's effective pay
(1+.06)*x + 3,000 = (1+.08)*x
1.06x + 3,000 = 1.08x
3,000 = .02x
150,000 = x
thus the new pay effectively is (1+.08)*150,000 = 162,000
A
Question: Set B consists of 19 elements. The average of set B is L. If a new element is added to the set and the average grows by K, what is the value of the new element?
A.a) L(1 + K / 5)
B.b) L * (K/100) - 20L
C.c) 20L(1+K/100)
D.d) 20(1+K/100)-19L
Answer: A.a) L(1 + K / 5)
Explanation: Let's assume the value of new element to bea. So converting the word problem into equation,
(19*L + a) / (19 + 1) = L + k ==> after solving the equation we will get a (value of newly added element) = L + 20K
But according to the answer options, problem writer wanted to conveyk% percent rise in average value.
If we consider this case than resulting equation will be,
(19*L + a) / ( 19+1 ) = L + (K/100)*L ==> 19L + a = 20 [ L + KL/100]
==> a= 20L + KL/5 -19L
==> a= L + KL/5 , which is equivalent to option [A]
Question: Which is a better investment 12% stock at 200 or 7 2/3 stock at 150?
A.12% stock at 200
B.Cannot be compared, as the total amount of investment is not given
C.7 2/3 stock at 150
D.Both are equally good
Answer: A.12% stock at 200
Explanation: Let investment in each case be Rs. (200 x 150).
Income in 1st case = Rs.12 x 200 x 150/200	= Rs. 1800.
Income in 2nd case = Rs.23 x 200 x 150/(3*150)= Rs. 1533.3
Clearly, 12% stock at 200 is better.
ANSWER:A
Question: What is the probability of flipping a fair coin three times and the coin landing on heads on exactly one flip?
A.3/8
B.5/8
C.7/8
D.1/8
Answer: A.3/8
Explanation: Probability = (Favorable combination)/(Total combination)
Favorable combination = (HTT, TTH, THT) ==> 3
Total combination = 8 (2^3)
Probability = (3)/(8)
(A)
Question: The area of a triangle will be when a = 1m, b = 2m, c = 3m, a, b, c being lengths of respective sides?
A.3
B.9
C.0
D.4
Answer: A.3
Explanation: S = (1 + 2 + 3)/2
= 3
Answer:A
Question: If all the 6 are replaced by 9, then the algebraic sum of all the numbers from 1 to 100 (both inclusive) varies by how much?
A.330
B.360
C.380
D.400
Answer: A.330
Explanation: unit place increased by 3. So 6,16,26,....96. Total 10*3 = 30 increased.
ten's place increased by 30. So 60,61,...69. Total 10*30 = 300 increased.
So total varies = 300 + 30= 330.
ANSWER:A
Question: The average (arithmetic mean) of eight numbers is 43.1. If the sum of half of these numbers is 158.4, what is the average of the other half?
A.12.8
B.24.2
C.46.6
D.72.1
Answer: C.46.6
Explanation: arithmetic mean = sum / total numbers
sum = 43.1 * 8 = 344.8
sum of half of these numbers is 158.4. So, 4 numbers sum is 158.4. Rest 4 numbers sum = 344.8-158.4 = 186.4
Arithmetic mean of the 4 nos = 186.4/4 = 46.6
Hence, C is the answer.
Question: The average of the two-digit numbers, which remain the same when the dibits inter-change their positions, is
A.23
B.39
C.55
D.28
Answer: C.55
Explanation: Explanation:
Average = (11 + 22 + 33 + 44 + 55 + 66 + 77 + 88 + 99) / 9
=( (11 + 99) + (22 + 88) + (33 + 77) + (44 + 66) + 55) / 9
= (4 * 110 + 55)/9 = 495 / 9 = 55.
Answer: C
Question: Running 3/4th of his usual rate, a man is 15min late. Find his usual time in hours ?
A.6/4 hrs
B.3/4 hrs
C.9/4 hrs
D.3/4 hrs
Answer: B.3/4 hrs
Explanation: Explanation:
Walking at 3/4th of usual rate implies that time taken would be 4/3th of the usual time. In other words, the time taken is 1/3rd more than his usual time
so 1/3rd of the usual time = 15min
or usual time = 3 x 15 = 45min = 45/60 hrs = 3/4 hrs.
Answer: B
Question: A tank is filled in eight hours by three pipes A, B and C. Pipe A is twice as fast as pipe B, and B is twice as fast as C. How much time will pipe B alone take to fill the tank?
A.17 hours
B.28 hours
C.19 hours
D.14 hours
Answer: B.28 hours
Explanation: 1/A + 1/B + 1/C = 1/8 (Given)
Also given that A = 2B and B = 2C
=> 1/2B + 1/B + 2/B = 1/8
=> (1 + 2 + 4)/2B = 1/8
=> 2B/7 = 8
=> B = 28 hours.
Answer: B
Question: If a = -2, what is the value of –(a^2 + a^3 + a^4 + a^5)?
A.20
B.-4
C.0
D.4
Answer: A.20
Explanation: if a = -2, then putting values in equation
= -[ (-2)^2 + (-2)^3 + (-2^4) + (-2^5) ]
= -[ 4 - 8 + 16 - 32 ]
= 20
Answer = A = 20
Question: When members of a certain club elected a chairman, each member voted for one of the three candidates. If candidate 1 received three times as many votes as the other two candidates together and candidate 2 received nine more votes than candidate 3, which of the following can be the number of members in the club?
A.24
B.30
C.32
D.36
Answer: D.36
Explanation: Let x denote the number of votes for candidate 1, y the number of votes for candidate 2, and z the number of votes for candidate 3. The stem gives that x=3(y+z) and y=z+9. The number of club members =x+y+z=4(y+z)=4(2z+9)=8z+36. Because z must be a non-negative integer, the club can contain 36, 44, 52, ... members. Among the listed choices only choice D fits.
Answer: D
Question: If x and y are positive integers, and (4x)/(3y) is an integer, which of the following must be true?
I) x is a multiple of 4.
II) y is a multiple of 3.
III) x·y is a multiple of 3.
A.I only
B.II only
C.III only
D.I and II only
Answer: C.III only
Explanation: For (4x)/(3y) to be an integer, x must be a multiple of 3. So, x * y is a multiple of 3.
Hence, C. ( rest two statements may or may not be valid)
ANSWER:C
Question: Heinz produces tomato puree by boiling tomato juice. The tomato puree has only 20% water while the tomato juice has 90% water. How many liters of tomato puree will be obtained from 30 litres of tomato juice?
A.3.75 liters.
B.2.5 liters.
C.8.5 liters.
D.2.6 liters.
Answer: A.3.75 liters.
Explanation: Answer:
Explanation:
In each of the solutions, there is a pure tomato component and some water. So while boiling, water evaporates but tomato not. So we equate tomato part in the both equations.
â‡’â‡’ 10%(30) = 80%(x)
â‡’â‡’ x = 3.75 liters.
Answer:A
Question: The three sides of an acute angled triangle (all in cms) are 12, 19 and g. How many integer values can g take?
A.23
B.22
C.15
D.8
Answer: D.8
Explanation: In acute angle triangles all angles in the triangle should be less than 90.
The maximum length of g can be when it is the hypotenuse of the triangle.
So, g= sqrt(12^2 + 19^2) = 22.5 (approx)
The maximum length of g can be when side of length 12 is the hypotenuse of the triangle.
So, g = sqrt (19^2 - 12^2) = 14.7 (approx)
So, g>14.7 and g<22.5.
Hence, possible values for g can be 15,16,17,18,19,20,21 and 22. Total 8 values.
Answer D.
Question: What will be the cost of building a fence around a square plot with area equal to 25 sq ft, if the price per foot of building the fence is Rs. 58?
A.1160
B.1251
C.1102
D.1352
Answer: A.1160
Explanation: Let the side of the square plot be a ft.
a2 = 25 => a = 5
Length of the fence = Perimeter of the plot = 4a = 20 ft.
Cost of building the fence = 20 * 58 = Rs. 1160.
Answer: A