RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: When Professor Wang looked at the rosters for this term's classes, she saw that the roster for her economics class (E) had 20 names, the roster for her marketing class (M) had 28, and the roster for her statistics class (S) had 18. When she compared the rosters, she saw that E and M had 9 names in common, E and S had 7, and M and S had 10. She also saw that 4 names were on all 3 rosters. If the rosters for Professor Wang's 3 classes are combined with no student's name listed more than once, how many names will be on the combined roster?
A.30
B.44
C.42
D.46
Answer: B.44
Explanation: Total # of students 20+28+18-(9+7+10)+4=44.
Answer: B.
Question: The combined salaries of three brothers is $270,000. Mr. Big earns twice what Mr. Small earns, and Mr. Middle earns 1 1/2 times what Mr. Small earns. What is the smallest salary of the three brothers?
A. 45,000
B. 60,000
C. 55,000
D. 30,000
Answer: B. 60,000
Explanation: Mr. Small = x;
Mr. Middle = 3/2*x;
Mr. Big = 2x.
x + 3/2*x + 2x = 270 --> x=60
Answer: B
Question: If Jake loses 29 pounds, he will weigh twice as much as his sister. Together they now weigh 99 pounds. What is Jake's present weight, in pounds?
A. 69
B. 135
C. 139
D. 147
Answer: A. 69
Explanation: J = Jake’s current weight, in pounds
S = Sister’s current weight, in pounds
We are told that “If Jake loses 8 pounds, he will weigh twice as much as his sister.We put this into an equation:
J – 29 = 2S
J = 2S + 29 (Equation 1)
Next, we are told that “Together they now weigh 89 pounds.” We can also put this into an equation.
J + S = 89 (Equation 2)
To solve this equation, we can substitute 2S + 8 from Equation 1 for the variable J in Equation 2:
2S + 29 = 89-S
3S = 60
S = 20
J + 20 = 89
J = 69
Answer: A
Question: The value of x + x(xx) when x = 1 is:
A.5
B.8
C.2
D.1
Answer: C.2
Explanation: x + x(xx)
Put the value of x = 1 in the above expression we get,
=1 + 1(1)
= 1 + 1(1)
= 1 + 1
= 2 CORRECT ANSWER : C
Question: What profit percent is made by selling an article at a certain price, if by selling at 2/3rd of that price, there would be a loss of 30%?
A.5%
B.29%
C.10%
D.80%
Answer: A.5%
Explanation: SP2 = 2/3 SP1
CP = 100
SP2 = 70
2/3 SP1 = 70
SP1 = 105
100 --- 5 => 5%
Answer: A
Question: A sum of Rs.312 was divided among 100 boys and girls in such
a way that each boy gets Rs.3.60 and each girl Rs.2.40.
A.45
B.49
C.52
D.60
Answer: D.60
Explanation: Let number of boys = x
Then number of girls = (100-x)
3.60x +2.40(100-x) = 312 ¡ê 1.2x
= 312 - 240
= 72 ¡ê x = 60
answer :D
Question: How many integers are divisible by 3 between 20! and 20! + 20 inclusive?
A.6
B.7
C.8
D.9
Answer: B.7
Explanation: B - 7
20! is divisible by 3
There are 6 numbers between 10! and 10!+20 that are divisible by 3.
Hence 7
Question: The average age 8 members of a committee are the same as it was 2 years ago, because an old number has been replaced by a younger number. Find how much younger is the new member than the old number?
A.14 years
B.16 years
C.18 years
D.12 years
Answer: B.16 years
Explanation: 2 * 2
= 16
Answer:B
Question: If an object travels 200 feet in 2 seconds, what is the object's approximate speed in miles per hour? (Note: 1 mile = 5280 feet)
A.68
B.54
C.21
D.48
Answer: A.68
Explanation: 1 mile = 5280 feet
=> 1 feet = 1/5280 miles
If the object travels 200 feet in 2 sec
then it travels 200/2 * 60 * 60 feet in 1 hour (1 hr = 60 min * 60 sec)
= 3600 * 100 feet in 1 hour
= 360000 feet in 1 hr
= 360000/5280 miles in 1 hour
= 36000/528 miles/hr ~ 68 miles/hr
Answer - A
Question: A part of certain sum of money is invested at 9% per annum and the rest at 12% per annum, if the interest earned in each case for the same period is equal, then ratio of the sums invested is?
A.1:5
B.2:3
C.4:9
D.4:3
Answer: D.4:3
Explanation: Explanation:
12:9
= 4:3
Answer: D
Question: In a throw of dice what is the probability of geÆ«ng number greater than 3
A.1/2
B.1/3
C.1/5
D.1/6
Answer: A.1/2
Explanation: Explanation:
Number greater than 3 is 4, 5, 6, so only 3 number
Total cases of dice = [1,2,3,4,5,6]
So probability = 3/6 = 1/2
Answer: A
Question: A, B and C completed a piece of work, A worked for 6 days, B for 9 days and C for 4 days. Their daily wages were in the ratio of 3:4:5. Find the daily wages of C, if their total earning was Rs.1406?
A.s.109
B.s.108
C.s.100
D.s.95
Answer: D.s.95
Explanation: 3x 4x 5x
6 9 4
18x + 36x + 20x = 1406
74x = 1406 => x = 19
5x = 95 Rs.
Answer:D
Question: The value of x + x(xx) when x = 4 is:
A.8
B.10
C.64
D.14
Answer: C.64
Explanation: x + x(xx)
Put the value of x = 4 in the above expression we get,
4 + 4(4*4)
= 4 + 64
= 68
ANSWER : C
Question: A man traveled a total distance of 1800 km. He traveled one-third of the whole trip by plane and the distance traveled by train is two-thirds of the distance traveled by bus. If he traveled by train, plane and bus, how many kilometers did he travel by bus?
A.660
B.680
C.720
D.760
Answer: C.720
Explanation: total distance traveled = 1800 km.
distance traveled by plane = 600 km.
distance traveled by bus = x
distance traveled by train = 2x/3
x + 2x/3 + 600 = 1800
5x/3 = 1200
x = 720 km
The answer is C.
Question: Find the average of first 40 natural numbers.
A.20.5
B.18
C.19.5
D.19
Answer: A.20.5
Explanation: Exp. Sum of first n natural numbers = n( n+1)/2
So, sum of first 40 natural numbers = 40*41/2 = 820
Required average =820/40 =20.5
Answer:A
Question: The lenght of a room is 5.5 m and width is 4 m. Find the cost of paving the floor by slabs at the rate of Rs. 950 per sq. metre.
A.s. 20,550
B.s. 15,600
C.s. 20,900
D.s. 17,600
Answer: C.s. 20,900
Explanation: Area of the floor = (5.5 Ã— 4) m2 = 22 m2.
Cost of paving = Rs. (950 Ã— 22) = Rs. 20900
Answer: Option C
Question: Employees of a certain company are each to receive a unique 8-digit identification code consisting of the digits 0, 1, 2, 3, 4, 5, 6, and 7 such that no digit is used more than once in any given code. In valid codes, the second digit in the code is exactly twice the first digit. How many valid codes are there?
A.1220
B.1840
C.2160
D.2480
Answer: C.2160
Explanation: There are 6! ways to make codes starting with 12.
There are 6! ways to make codes starting with 24.
There are 6! ways to make codes starting with 36.
The number of codes is 3*6! = 2160.
The answer is C.
Question: A train 140m long is running at 60kmph. In how much time will it pass a platform 260m long?
A.15 seconds
B.24 seconds
C.28 seconds
D.30 seconds
Answer: B.24 seconds
Explanation: Distance travelled = 140 + 260m = 400m
Speed = 60 * 5/8 = 50/3m
Time = 400 * 3/50 = 24 Second
Answer : B
Question: If (2^13)(25^S) = 5(10^m) what is the value of m ?
A.7
B.13
C.15
D.16
Answer: B.13
Explanation: given
2^13 * 25^s = 5 * 10^2
=> 2^13 * 5^(2s) = 2^m * 5^(m+1)
Ans B
on comparing the power of 2 => m=13
Question: A thief steals at a car at 2.30 p.m. and drives it at 40 km/hr. The theft is discovered at 3 p.m. and the owner sets off in another car at 75 km/hr. When will he overtake the thief?
A.6:34 p.m
B.9:34 p.m
C.3:34 p.m
D.2:34 p.m
Answer: C.3:34 p.m
Explanation: :
Suppose the thief is overtaken x hrs after 2.30 p.m.
Then, distance covered by the owner in (x - 1/2) hrs.
40x = 75(x - 1/2) => x = 15/14hrs.
So, the thief is overtaken at 3:34 p.m.'
Answer: C
Question: Carl drove from his home to the beach at an average speed of 80 kilometers per hour and returned home by the same route at an average speed of 70 kilometers per hour. If the trip home took 1/2 hour longer than the trip to the beach, how many kilometers l did Carl drive each way?
A. 350
B. 345
C. 320
D. 280
Answer: D. 280
Explanation: Let us backsolve here.
The answer option has to be divisible by 7 to give us 1/2.
Let us try l=280 km. Time taken will be 3.5 hours and 4 hours.
Hence D is the answer.
Question: How many different letter arrangements can be made from the letters of the word RECOVER?
A.1210
B.5040
C.1260
D.1200
Answer: C.1260
Explanation: Possible arrangements are :
7!/2!×2!=1260 [division by 2 times 2! is because of the repetition of E and R]
Answer C
Question: Mr. Jones sold two pipes at $2.50 each. Based on the cost, his profit one was 30% and his loss on the other was 20%. On the sale of the pipes. Find the amount of his profit or loss?
A.gain 0.25 cents
B.lost 4 cents
C.broke even
D.gained 4 cents
Answer: A.gain 0.25 cents
Explanation: 30 % profit on $ 2.50
= $ 30/100 × 2.50
= $ 0.30× 2.50
= $ 0.75
Similarly, 25 % loss on $ 2.50
= $ 20/100 × 2.50
= $ 0.20× 2.50
= $ 0.50
Therefore, in one pipe his profit is $ 0.75 and in the other pipe his loss is $ 0.50
So profit by amount 0.25 cents
Answer is A.
Question: The average monthly salary of 8 workers and one supervisor in a factory was 430.@SSWhen@SSthe@SSsupervisor@CC@SSwhose@SSsalary@SSwas@SS430.@SSWhen@SSthe@SSsupervisor@CC@SSwhose@SSsalary@SSwas@SS430.Whenthesupervisor,whosesalarywas430. When the supervisor, whose salary was 870 per month, retired, a new person was appointed and then the average salary of 9 people was $$420 per month. The salary of the new supervisor is:
A.233
B.600
C.287
D.780
Answer: D.780
Explanation: Explanation:
Total salary of 8 workers and supervisor together = 9 Ã— 430 = 3870
Now total salary of 8 workers = 3870 âˆ’ 870 = 3000
Total salary of 9 workers including the new supervisor = 9 Ã— 420 = 3780
Salary of the new supervisor = 3780 âˆ’ 3000 = 780
Answer: D
Question: In one hour, a boat goes 19 km along the stream and 5 km against the stream. The speed of the boat in still water (in km/hr) is:
A.2
B.4
C.7
D.12
Answer: D.12
Explanation: Sol.
Speed in still water = 1/2 (19+5) kmph = 12 kmph.
Answer D
Question: A student took 6 courses last year and received an average (arithmetic mean) grade of 100 points. The year before, the student took 5 courses and received an average grade of 40 points. To the nearest tenth of a point, what was the student’s average grade for the entire two-year period?
A.79
B.89
C.95
D.72.72
Answer: D.72.72
Explanation: Let the 6 courses that were taken last year be A1 , A2, A3 , A4 , A5 , A6
A1+A2+A3+A4+A5+A6 = 100*6 = 600
The year before , the 5 courses be B1, B2 , B3 , B4 , B5
B1+B2+B3+B4+B5 = 40*5 = 200
Student's average = (600+200)/11 = 72.72
Answer D
Question: The bankerâ€™s discount on Rs. 1600 at 12% per annum is the same as true discount on Rs. 1680 for the same time and at the same rate. The time is :
A.2 months
B.4 months
C.5 months
D.7 months
Answer: C.5 months
Explanation: Sol.
S.I. on Rs. 1600 = R.D. on Rs. 1680.
âˆ´ Rs. 1600 is the P.W. of Rs. 1680, i.e., Rs. 80 is S.I. on Rs. 1600 at 12%.
âˆ´ Time = [100 * 80 / 1600 * 12] year = 3/7 year = 5 months.
Answer C
Question: Every digit of a number written in binary is either 0 or 1. To translate a number from binary, multiply the nth digit (reading from right to left) by 2^(n-1)
What is the largest prime number (written in binary) that is a factor of both 110000 and 1100000 ?
A. 10
B. 11
C. 101
D. 1011
Answer: B. 11
Explanation: Binary Divison can provide a quick answer if you are comfortable with it.
as option E is the biggest binary number we try with it first :
100010000/ 11 =10000
1000100000/ 11 =100000
so answer is option is B
Question: Each term of a certain sequence is 3 less than the previous term. The first term of this sequence is 23. If the sum of the first n terms of the sequence is n, what is the value of positive integer n?
A.1
B.13
C.15
D.19
Answer: C.15
Explanation: We know that it is a decreasing sequence i.e. the terms keep decreasing till 0 and then negative terms start.
What does this imply?If the sum of the first n terms of the sequence is n
Since number of terms will definitely be positive, we are looking for a positive sum.
19 + 16 + 13 + 10 + 7 + 4 + 1 -2 -5 -7 -10 .... and so on
Note that the first 7 terms are positive and all others negative. Every negative term has greater absolute value than the corresponding positive terms i.e. -2 absolute value is greater than 1 absolute value, -5 absolute value is greater than 4 absolute value, and so on...
Since we have 7 positive terms, we must have less than 7 negative terms to get the sum as positive. If we have 6 negative terms, we will have a total of 13 terms. Of the given options, only 13 is possible and hence it must be the answer.
Answer (C)
Question: A man whose speed is 4.5 kmph in still water rows to a certain upstream point and back to the starting point in a river which flows at 1.5 kmph, find his average speed for the total journey?
A.5
B.4
C.7
D.3
Answer: B.4
Explanation: M = 45
S = 1.5
DS = 6
US = 3
AS = (2 * 6 * 3) /9 = 4
Answer: B
Question: If a company allocates 15 percent of its budget to advertising, 10 percent to capital improvements, and 60 percent to salaries, what fraction of its budget remains for other allocations?
A.4/5
B.3/5
C.3/20
D.1/5
Answer: C.3/20
Explanation: 15 + 10 + 60 = 85% 100 - 85 = 15% to all others
C
Question: If a and d are both integers, a>d, and -3c>19, then the largest value of d would be?
A.-5
B.-6
C.-7
D.-8
Answer: D.-8
Explanation: No, your thinking is incorrect. When we know that a>d and a<-6.33, the largest value of a can be -7 while if a=-7, then largest value of d < -7 will be -8.For negative numbers, -7 > -8 and -8> -10.
You are right in saying that d can take any value less than -7 ---> d could be -8, -9, -10 .... and out of all these values, -8 is the greatest.
Look at the numbers on the number line. For any 2 numbers, the ones on the right are greater than the ones on the left:
.......-11 -10 -9 -8 -7 -6 -5 ..... 0 1 2 3 4 5 6 ... (-11< -10, -10< -8, 4< 5 etc).
So, as per the question if d<a and a = -7 , then d's largest 'possible' value has to be -8.
-10 is smaller than -8=D
Question: A retailer marks her goods in such a way that the profit made by selling 50 articles is equal to the selling price of 20 articles. What is the percentage of profit made by the retailer?
A.66.67%
B.33.33%
C.40%
D.25%
Answer: A.66.67%
Explanation: Let Cost Price = x
Profit = y
Selling Price = x+y
50y = 20(x+y)
30y = 20x
Percentage Profit =y/x∗100=20/30∗100=66.667
Answer = A
Question: Mr X, a businessman, had income in the year 1995 such that he earned a profit of 20% on his investment in the business. In the year 1996 his investment was less by 4000 but still had the same income (Income = Investment + Profit) as that in 1995. Thus the per cent profit earned in 1996 increased by 6%. What was his investment in 1995?
A.100000
B.100500
C.84000
D.Data inadequate
Answer: C.84000
Explanation: Let the investment of X in 1995 be x.
∴ Profit = x⁄5
∴ Income = (x + x⁄5) = 6⁄5x
Investment of company X in 1996 would be (x – 4000) From the question,
(x - 4000) × 126⁄100 = 6⁄5x ⇒ x = 84000
Answer C
Question: The Coen family consists of a father, a mother, two children and a dog. A photographer is about to take the family's picture. How many different arrangements (of standing in a row) does the photographer have, if it is known that the Mother insists of standing by her younger Child, as the song says?
A.12
B.24
C.30
D.48
Answer: D.48
Explanation: We need to find the number of arrangements of Father, Mother, Child-1, Child-2, and a Dog, so that M and C2 are always together.
Consider F and M to be one unit, then we would have total of four units: {F}, {C1}, {MC2}, {D}. The number of arrangements of these four units is 4!, but M and C2 within their unit can be arranged in 2 ways: {C2M} or {MC2}, so total number of arrangements is 4!*2=48.
Answer: D.
Question: if 8 people take an hour to complete a piece of work, then how long should 16 people will take to complete the same piece of work?
A.15 min
B.30 min
C.26 min
D.28 min
Answer: B.30 min
Explanation: if 8 people take an hour to complete a piece of work, then
16 people will take 8*60/16 = 30 mins to complete the same piece of work.
ANSWER:B
Question: .04 × ? = .000016.
A.0.0004
B.0.04
C.4
D.0.4
Answer: A.0.0004
Explanation: Solution
Let .04 × x = .000016. Then, x = .000016/.04 = .0016/4 = .0004. Answer A
Question: The true discount on a bill of Rs. 540 is Rs. 90. The banker's discount is:
A.Rs. 60
B.Rs. 108
C.Rs. 110
D.Rs. 112
Answer: B.Rs. 108
Explanation: P.W. = Rs. (540 - 90) = Rs. 450.
S.I. on Rs. 450 = Rs. 90.
S.I. on Rs. 540 = Rs. (90/450)X540	= Rs. 108.
B.D. = Rs. 108.
ANSWER :B
Question: What will be the percentage increase in the area of the cube's surface if each of the cube's edges grows by 40%?
A.95%
B.90%
C.85%
D.96%
Answer: D.96%
Explanation: The question is very easy. My logic is the following:
A surface = 6*a^2
After 40% increase A surface = 6* ((1.4a)^2) = 6*1.96*a^2
The increase in the surface area = (6*1.96*a^2 - 6*a^2)/6*a^2 = (6*a^2(1.96-1))/(6*a^2) = 1.96-1=0.96 = 96%
Answer :D
Question: A no. when divided by the sum of 555 and 445 gives 2times their difference as quotient & 20 as remainder. Find the no. is?
A.122456
B.220020
C.220022
D.235467
Answer: B.220020
Explanation: (555 + 445) * 2 * 110 + 20 = 220000 + 20 = 220020
B
Question: The total age of A and B is 14 years more than the total age of B and C. C is how many years younger than A ?
A.14
B.27
C.21
D.18
Answer: A.14
Explanation: (A+B) - (B+C) = 14
A - C = 14.
C is younger than A by 14 years.
Answer: A
Question: When the integer n is divided by 17, the quotient is x and the remainder is 2. When n is divided by 23, the quotient is y and the remainder is 14. Which of the following is true?
A. 23x + 17y =19
B. 17x –23y = 12
C. 17x +23y =19
D. 14x + 5y = 6
Answer: B. 17x –23y = 12
Explanation: From the problem it follows:
n=17x+2
n=23y+14
So, 17x+2=23y+14
17x-23y=12
The answer is B
Question: If 625^(-x) +5^(-2x) + 5^(-4x) = 15, what is the value of x?
A.-4
B.-1/4
C.0
D.1/4
Answer: A.-4
Explanation: We're told that 625^(-X) + 25^(-2X) + 5^(-4X) = 15. We're asked for the value of X.
Since each of the calculated terms MUST be positive (regardless of what the exponent is), we can use thebasesto our advantage.....
With Answer A, we'd have 625^4, which is MUCH BIGGER than 15 (and we'd be adding to that big number). Eliminate A.
With Answer E, we'd have 625^(-4), which would create a TINY fraction (and we'd add some other fractions to it, so the total would be MUCH TOO SMALL). Eliminate E.
With Answer D, we'd have 625^(-1/4), which will also be a fraction (just not as tiny as the one in answer E), but the total would still be TOO SMALL. Eliminate D.
With Answer C, anything to the '0 power' is 1, so we'd have 1+1+1 = 3. This is not 15. Eliminate C.
A
Question: The average number of shirts with Salman, Ambani and Dalmiya is 60, if all of them reached a shopping mall in Delhi and purchased 3 shirts each of them then average number of shirt each of them now has
A.66
B.63
C.62
D.64
Answer: B.63
Explanation: Required average
= Old average + New average
= 60 + 3 = 63
answer :B
Question: Two students appeared at an examination. One of them secured 9 marks more than the other and his marks was 56% of the sum of their marks. What are the marks obtained by them?
A.42, 33
B.41, 33
C.42, 35
D.41, 35
Answer: A.42, 33
Explanation: Let the marks secured by them be x and (x + 9)
Then sum of their marks = x + (x + 9) = 2x + 9
Given that (x + 9) was 56% of the sum of their marks
=>(x+9) = 56/100(2x+9)
=>(x+9) = 14/25(2x+9)
=> 25x + 225 = 28x + 126
=> 3x = 99
=> x = 33
Then (x + 9) = 33 + 9 = 42
Hence their marks are 33 and 42
A)
Question: If the average (arithmetic mean) of five consecutive negative integers is 2k – 1, what is the difference D between the greatest and least of the five integers?
A.4K
B.4k^2 -4k
C.4-4k
D.4
Answer: D.4
Explanation: (n-2 + n - 1 + n + n + 1 + n + 2)/5 = 2k - 1
=> n = 10k - 5
Greatest = n + 2 = 10k - 5 + 2 = 10k - 3
Least = n - 2 = 10k - 5 - 2
=> Difference D= 10k - 3 - (10k - 7)
= 4
Answer - D
Question: 3 no.'s A, B & C are in the ratio of 12:15:25. If sum of these no.'s is 312, find the ratio between the difference of B & A & the difference of C & B.
A.2 : 5
B.3 : 10
C.4 : 5
D.4 : 7
Answer: B.3 : 10
Explanation: We have, a = 12, b = 15, c = 25 and x = 312.
ax_ 12 X 312
a+b+c 12+15+25
— 72,
bx _ 15 X 312 B — — 90 a +b+c 12 + 15+ 25 cx 25 X 312 And, C =
a+b+c 12 + 15+ 25
...B-A=18 andC-B=60
- 150
Thus, their ratio = 18 : 60 or 3 : 10
B
Question: A man sells 45 lemons for Rs 40 and loses 20%. At how much price should he sell 24 lemons to the next customer to make a 20% profit?
A.32
B.20
C.24
D.16
Answer: A.32
Explanation: Explanation:
Let cost price of lemons be x.
Selling price of lemons becomes CP - loss.
=>SP=x-(20/100)x
=>40=x(80/100)
=>50
So 45 lemons cost Rs 50
Cost of 1 lemon = 50/45 Rs
Cost of 24 lemons = (50/45)*24 =80/3 Rs
Selling Price of 24 lemons =(80/3)+(20/100)(80/3)=Rs 32
ANSWER A
Question: three men invested sum. and their ratio is 5:7:6. profit is 1800.then b's share
A.2000
B.2100
C.700
D.2300
Answer: C.700
Explanation: b's share =7/18*1800=700
ANSWER:C
Question: A group of people participate in some curriculum, 30 of them practice Yoga, 20 study cooking, 15 study weaving, 5 of them study cooking only, 8 of them study both the cooking and yoga, 5 of them participate all curriculums. How many people study both cooking and weaving?
A.1
B.2
C.3
D.4
Answer: B.2
Explanation: Both cooking and weaving = 20 - (5+8+5) = 2
So, the correct answer is B.
Question: Three candidates contested an election and received 3834 votes, 7606 votes, and 14560 votes respectively. What percentage of the total votes did the winning candidate receive?
A.55%
B.56%
C.57%
D.58%
Answer: B.56%
Explanation: The total number of votes polled = (3834 + 7606 + 14560) = 26000
The winner's percentage = 14560/26000 * 100 = 56%
The answer is B.
Question: (69 - 14 x 3 + 2) / [ 9 x 5 - (5)2] = ?
A.1.45
B.2.75
C.26.5
D.265
Answer: A.1.45
Explanation: Answer
Given expression = (69 - 14 x 3 + 2) / [ 9 x 5 - (5)2]
= (69 - 42 + 2) / (45 - 25)
= 29 / 20
= 1.45
Correct Option: A
Question: What is the lowest positive integer that is divisible by each of the integers 1 through 7, inclusive?
A.420
B.840
C.1,260
D.2,520
Answer: A.420
Explanation: The integer should be divisible by: 2, 3, 4(=2^2), 5, 6(=2*3), and 7. The least common multiple of these integers is LCM=2^2*3*5*7=420.
Answer: A.
Question: In a can, there is a mixture of milk and water in the ratio 4 : 5. If it is filled with an additional 8 litres of milk the can would be full and ratio of milk and water would become 6 : 5. Find the capacity of the can?
A.49
B.44
C.77
D.25
Answer: B.44
Explanation: Let the capacity of the can be T litres.
Quantity of milk in the mixture before adding milk = 4/9 (T - 8)
After adding milk, quantity of milk in the mixture = 6/11 T.
6T/11 - 8 = 4/9(T - 8)
10T = 792 - 352 => T = 44.Answer:B
Question: Let Q represent a set of five distinct prime numbers. If the sum of the numbers in Q is even and x is a member of Q, then what is the least possible value that x can be?
A.1
B.2
C.3
D.5
Answer: B.2
Explanation: Q = p1+p2+p3+p4+p5 = even (and all primes are distinct)
if the least prime is 2 then we have sum of Q = even
Ans. B. 2
Question: A boat crossed a lake from North to South at the speed of 6 km/h, entered a river and covered twice as much distance going upstream at 3 km/h. It then turned around and stopped at the south shore of the lake. If it averaged 5 km/h that day, what was its approximate downstream speed?
A.12
B.15
C.16
D.17
Answer: A.12
Explanation: Another way will be:
Total time for the trip = distance covered in Lake/speed in still water +distance covered upstream/upstream speed + distance covered downstream/downstream speed
If 5D is the total distance, then distance covered in lake = D, distance covered upstream = 2D and distance covered downstream = 2D
=>5D/5 = D/4 + 2D/3 + 2D/x (where x is the downstream speed)
=> 5/5 = 1/6 + 2/3 +2/x (div. both sides by D)
=> 1.0 = .16+.66 +.16/x => x=11.98 ~12
option A
Question: Of all the students in a certain dormitory, 1/2 are first-year students and the rest are second-year students. If 4/5 of the first-year students have not declared a major and if the fraction of second-year students who have declared a major is 4 times the fraction of first-year students who have declared a major, what fraction of all the students in the dormitory are second-year students who have not declared a major?
A.1/15
B.4/5
C.4/15
D.1/5
Answer: D.1/5
Explanation: tot students=x
1st year student=x/2----> non majaor=4/5(x/2)-----> maj=1/5(x/2)
2nd year student=x/2---->maj=4(1/5(x/2))=2/5(x)--->non major=x/2-2/5(x)=1/5(x)
hence 1/5
D