question stringlengths 3 1.14k | choices listlengths 4 4 | answer_index int64 0 3 | answer_text stringlengths 3 221 | source stringclasses 1
value | explanation stringlengths 1 3.68k |
|---|---|---|---|---|---|
Amy has to visit towns B and C in any order. The roads connecting these towns with her home are shown on the diagram. How many different routes can she take starting from A and returning to A, going through both B and C (but not more than once through each) and not travelling any road twice on the same trip? | [
"A.10",
"B.8",
"C.6",
"D.4"
] | 1 | B.8 | aqua_rat | Explanation:
Amy can travel clockwise or anticlockwise on the diagram.
Clockwise, she has no choice of route from A to B, a choice of one out of two routes from B to C, and a choice of one out of two routes from C back to A. This gives four possible routes.
Similarly, anticlockwise she has four different routes.
Total ... |
Incomes of two companies A and B are in the ratio of 5 : 8. Had the income of company A been more by 25 lakh, the ratio of their incomes would have been 5 : 4. What is the income of company B? | [
"A.80 lakh",
"B.50 lakh",
"C.40 lakh",
"D.60 lakh"
] | 2 | C.40 lakh | aqua_rat | Let the incomes of two companies A and B be 5x and 8x respectively.
From the question,
5x+25/8x=5/4 ⇒ 20x + 100 = 40x
∴ x = 5
∴ Income of company B = 8x = 40 lakh
Answer C |
The area of a triangle will be when a = 1m, b = 2m, c = 3m, a, b, c being lengths of respective sides. | [
"A.0 sq m",
"B.2 sq m",
"C.9 sq m",
"D.20 sq m"
] | 0 | A.0 sq m | aqua_rat | S = (1 + 2 + 3)/2 = 3
=> No triangle exists
Answer: A |
P and Q started a business investing Rs. 85,000 and Rs. 30,000 respectively. In what ratio the profit earned after 2 years be divided between P and Q respectively? | [
"A.17:6",
"B.17:0",
"C.17:4",
"D.17:2"
] | 0 | A.17:6 | aqua_rat | P:Q = 85000 : 30000
= 17:6.
Answer: A |
A and B are playing mathematical puzzles. A asks B "which whole numbers, greater than one, can divide all the nine three digit numbers 111,222,333,444,555,666, 777,888 and 999?"
B immediately gave the desired answer. It was :- | [
"A.3, 37 and 119",
"B.3, 37 and 111",
"C.9, 37 and 111",
"D.3, 9 and 37"
] | 1 | B.3, 37 and 111 | aqua_rat | Explanation :
Each of the number can be written as a multiple of 111. And,
The factors of 111 are 3 and 37.
Thus, the desired answer is 3, 37 and 111.
Answer : B |
A 1200 m long train crosses a tree in 120 sec, how much time will I take to pass a platform 700 m long? | [
"A.277 Sec",
"B.190 Sec",
"C.187 Sec",
"D.286 Sec"
] | 1 | B.190 Sec | aqua_rat | L = S*T
S= 1200/120
S= 10 m/Sec.
Total length (D)= 1900 m
T = D/S
T = 1900/10
T = 190 Sec
Answer:B |
Which digits should come in place of @ and # if the number 62684@# is divisible by both 8 and 5? | [
"A.4,0",
"B.0,4",
"C.4,4",
"D.0,0"
] | 0 | A.4,0 | aqua_rat | Explanation :
Since the given number is divisible by 5, so 0 or 5 must come in place of #.
But, a number ending with 5 is never divisible by 8.
So, 0 will replace #.
Now, the number formed by the last three digits is 4@0, which becomes divisible by 8, if @ is replaced by 4.
Hence, digits in place of @ and # are 4 and 0... |
A work which could be finished in 8 days was finished 3 days earlier after 10 more men joined. The number of men employed was? | [
"A.22",
"B.30",
"C.88",
"D.71"
] | 1 | B.30 | aqua_rat | x ------- 8
(x + 10) ---- 6
x * 8 = (x + 10)6
x = 30
\Answer: B |
Each digit in the two-digit number G is halved to form a new two-digit number H. Which of the following could be the sum of G and H | [
"A.153",
"B.159",
"C.137",
"D.121"
] | 1 | B.159 | aqua_rat | let the number be x, now x is halved => x/2..the question asks what is x?
x(number) + x/2 (half of that number) = something
=> 3x/2 = something
=> x = 2 (something) / 3
so the answer choice must be divisible by 3
eliminate C, E right away
check the rest
B satisfies
3x/ 2 = 159
=> x = 106
Verify. 106 + 53 = 159
Answer i... |
The product of two numbers is 2028 and their H.C.F. is 13. The number of such pairs is: | [
"A.9",
"B.2",
"C.7",
"D.8"
] | 1 | B.2 | aqua_rat | Let the numbers 13a and 13b.
Then, 13a x 13b = 2028
=>ab = 12.
Now, the co-primes with product 12 are (1, 12) and (3, 4).
[Note: Two integers a and b are said to be coprime or relatively prime if they have no common positive factor other than 1 or, equivalently, if their greatest common divisor is 1 ]
So, the required ... |
Renu can do a piece of work in 8 days, but with the help of her friend Suma , she can do it in 4 days. In what time Suma can do it alone? | [
"A.8",
"B.12",
"C.14",
"D.15"
] | 0 | A.8 | aqua_rat | Renu’s one day’s work = 1/8
Suma’s one day’s work = 1/4 - 1/8 = 1/8
Suma can do it alone in 8 days.
ANSWER:A |
There are 4 people who has to cross a stretch of 300 km. They normally run at a speed of 10 kmph. One
of them has a bike that travels at 50 kmph. The bike first takes one person alone and crosses the
stretch while the other two keep running. Then he comes back without wasting time and picks up
another person from the w... | [
"A.24 hrs",
"B.16 hrs",
"C.56/3 hrs",
"D.58/3 hrs"
] | 3 | D.58/3 hrs | aqua_rat | Expl : Time taken to carry 2nd person = 300/50 = 6 hrs.
Time taken to meet 3rd person =(300-6*10)/(50+10) = 4 hrs
Time taken to carry 3rd person = 4 hours
Time taken to meet 4th person = (300 –140)/60 = 8/3
Total time = 6+4+4+8/3+8/3 = 58/3 hours
Answer :D |
If by selling an article for Rs.60, a person loses 1/7 of money, what would he have gained or lost % by selling it for Rs.77? | [
"A.5%",
"B.10%",
"C.20%",
"D.30%"
] | 1 | B.10% | aqua_rat | Sol. CP - = EC7 = 70 1-7 6 77-70 % Profit = 100 = 10%
B |
If a light flashes every 6 seconds, how many times will it flash in ¾ of an hour? | [
"A.451 times",
"B.638 times",
"C.838 times",
"D.436 times"
] | 0 | A.451 times | aqua_rat | There are 60 minutes in an hour.
In ¾ of an hour there are (60 * ¾) minutes = 45 minutes.
In ¾ of an hour there are (60 * 45) seconds = 2700 seconds.
Light flashed for every 6 seconds.
In 2700 seconds 2700/6 = 450 times.
The count start after the first flash, the light will flashes 451 times in ¾ of an hour.
Answer:A |
Revenues were recorded for Store A and Store B over a period of three months. In the first month, Store A's revenues were $40,000 higher than Store B's revenues. In the second month, Store A's revenues were $6,000 higher than Store B's revenues. If Store A's average (arithmetic mean) monthly revenue for the three month... | [
"A. $14,000",
"B. $40,000",
"C. $42,000",
"D. $46,000"
] | 1 | B. $40,000 | aqua_rat | Answer: CIt may be tempting to come up with a lot of variables, one each for each month's revenue for each company. However, focus on the differences. In the first month, the difference was +40 in favor of A. (Note that we can drop the thousands since every number in the question is in terms of thousands.) In the secon... |
some digits were given like 0 2 2 3 3 4 4 then how many no will be there which is greater than 1 lac ,all numbers are distinct | [
"A.530",
"B.540",
"C.550",
"D.560"
] | 1 | B.540 | aqua_rat | ( 6*6*5*4*3*2)/(2! *2!*2!)= 540 ways
ANSWER:B |
A sum of money at simple interest amounts to Rs. 815 in 3 years and to Rs. 854 in 4 years. The sum is: | [
"A.600",
"B.698",
"C.675",
"D.688"
] | 1 | B.698 | aqua_rat | 1 year = Rs. (854 - 815) = Rs. 39.
3 years = Rs.(39 x 3) = Rs. 117.
Principal = Rs. (815 - 117) = Rs. 698
ANSWER B |
Each of the following equations has at least one solution EXCEPT D. Is it true? | [
"A.-2*-a = 2a",
"B.2*a = (–2)*-a",
"C.-4*a = -3-a",
"D.-3*a = -3-a"
] | 3 | D.-3*a = -3-a | aqua_rat | If we put a= 1 then
A. 2
B. 2
C. -4
E. -3
D. -3=-4 Not true |
10 people went to a hotel for combine dinner party 5 of them spent Rs. 20 each on their dinner and rest spent 4 more than the average expenditure of all the 10. What was the total money spent by them. | [
"A.1628.4",
"B.1534",
"C.1492",
"D.240"
] | 3 | D.240 | aqua_rat | Solution: Let average expenditure of 10 people be x.
then,
10x = 20*5+5*(x+4);
Or, 10x = 20*5+5x+20;
Or, x = 24;
So, total money spent = 24*10 = Rs. 240.
Answer: Option D |
If x is the product of the integers from 1 to 150, inclusive, and 5^y is a factor of x, what is the greatest possible value of y ? | [
"A.30",
"B.34",
"C.36",
"D.37"
] | 3 | D.37 | aqua_rat | It basically asks for the number of 5s in 150!
150/5 + 150/25 + 150/125 = 30 + 6 + 1. Hence 37
Answer: D. |
Product M is produced by mixing chemical X and chemical Y in the ratio of 5 : 4. Chemical X is prepared by mixing two raw materials, A and B, in the ratio of 1 : 3. Chemical Y is prepared by mixing raw materials, B and C, in the ratio of 2 : 1. Then the final mixture is prepared by mixing 864 units of product M with wa... | [
"A.328 units",
"B.368 units",
"C.392 units",
"D.616 units"
] | 1 | B.368 units | aqua_rat | The final product is obtained by mixing 864 units of product M with water.
In 864 units of Product M, amount of B = 864×77/108 = 616
In the final mixture, concentration of B is 50%.
Therefore, the total quantity of final mixture = 616 × 2 = 1232
Water added = 1232 – 864 = 368
The correct answer is Choice B. |
In a 4 person race, medals are awarded to the fastest 3 runners. The first-place runner receives a gold medal, the second-place runner receives a silver medal, and the third-place runner receives a bronze medal. In the event of a tie, the tied runners receive the same color medal. (For example, if there is a two-way ti... | [
"A.24",
"B.52",
"C.96",
"D.144"
] | 1 | B.52 | aqua_rat | Possible scenarios are:
1. Gold/Silver/Bronze/No medal (no ties) - 4!=24;
2. Gold/Gold/Silver/No medal - 4!/2!=12;
3. Gold/Silver/Silver/No medal - 4!/2!=12;
4. Gold/Gold/Gold/No medal - 4!/3!=4.
Total Z: 24+12+12+4=52
Answer: B. |
X completes a work in 20 days and Y complete the same work in 30 days. If both of them work together, then the number of days required to complete the work will be? | [
"A.10 days.",
"B.12 days.",
"C.14 days.",
"D.8 days."
] | 1 | B.12 days. | aqua_rat | If X can complete a work in x days and Y can complete the same work in y days, then, both
of them together can complete the work in x y/ x+ y days
Therefore, here, the required number of days = 20× 30/ 50 = 12 days.
B) |
A chair is bought for Rs.300/- and sold at Rs.420/- find gain or loss percentage | [
"A.15% loss",
"B.40% gain",
"C.25% gain",
"D.30% gain"
] | 1 | B.40% gain | aqua_rat | Formula = (Selling price ~ Cost price)/Cost price * 100
= (450- 300)/300= 40% gain
B |
What is the least number to be subtracted from 696 to make it a perfect square? | [
"A.1",
"B.16",
"C.20",
"D.71"
] | 2 | C.20 | aqua_rat | The numbers less than 696 and are squares of certain numbers are 676, 625.
The least number that should be subtracted from 696 to make it perfect square = 696 - 676 = 20.
ANSWER:C |
There are 8 books on a shelf, of which 2 are paperbacks and 6 are hardbacks. How many possible selections of 3 books from this shelf include at least one paperback? | [
"A.a) 40",
"B.b) 45",
"C.c) 36",
"D.d) 55"
] | 2 | C.c) 36 | aqua_rat | approach 1
at-least 1 paper back = total - no paper back
8c3-6c3 = 36
approach 2
at-least 1 paper back = 1 paper back , 3 hard back or 2 paper back 2 hard back
= 2c1*6c2+2c2*6c1 = 36
Answer is C |
If a sum of money doubles itself in 20 years at simple interest, the ratepercent per annum is | [
"A.12",
"B.12.5",
"C.13",
"D.5"
] | 3 | D.5 | aqua_rat | Explanation:
Let sum = x then Simple Interest = x
Rate = (100 * x) / (x * 20) = 5
Option D |
In a fuel station the service costs $1.15 per car, every liter of fuel costs 0.4$. Assuming that you own 2 sports cars and 2 executive cars and all fuel tanks are empty. How much will it cost to fuel all cars together if a sports car tank is 32 liters and an executive car tank is 75% bigger? | [
"A.37.5$",
"B.75$",
"C.87.5$",
"D.94.5$"
] | 1 | B.75$ | aqua_rat | Total cars=4
1.15*4=4.6->Service Cost
Fuel Cost in Sports Car = 2*32*0.4=25.6
Fuel Cost in Executive Car=25.6*7/4=44.8
Total Fuel Cost = 25.6+44.8=70.4
Cost to fuel car = 70.4+4.6=75
Answer: B |
Choose the missing terms out of the given alternatives.
AZ, BY, CX, DW ? | [
"A.EF",
"B.GH",
"C.EV",
"D.DW"
] | 2 | C.EV | aqua_rat | C
EV
The first letter moves one step forward. The second letter moves one step backward.
Answer is C |
Company Z spent 1/4 of its revenues last year on marketing and 1/7 of the remainder on maintenance of its facilities. What fraction of last year’s original revenues did company Z have left after its marketing and maintenance expenditures? | [
"A.5/14",
"B.1/2",
"C.17/28",
"D.9/14"
] | 3 | D.9/14 | aqua_rat | Total revenues = x
Spent on marketing = x/4
Remaining amount = x-x/4 = 3x/4
1/7 of the remainder on maintenance of its facilities = 3x/4*1/7 = 3x/28
Amount left = 3x/4-3x/28 = 9x/14
Answer D |
A train 360 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 140 m long? | [
"A.40 sec",
"B.42 sec",
"C.45 sec",
"D.48 sec"
] | 0 | A.40 sec | aqua_rat | Speed = 45 * 5/18 = 25/2 m/sec
Total distance covered = 360 + 140 = 500 m
Required time = 500 * 2/25 = 40 sec
ANSWER:A |
What is the scope including 1/21+1/22+1/23+......+1/30? | [
"A.1/6~1/5",
"B.1/5~1/4",
"C.1/4~1/3",
"D.1/3~1/2"
] | 3 | D.1/3~1/2 | aqua_rat | For Maximum value : It should be less than 1/21 + 1/21 +1/21... 10 times = 10/21 ~ 1/2
For Minimum Value : It should be greater than 1/30+ 1/30+ 1/30 .. 10 times = 10/30 = 1/3
Thus, the answer should lie between 1/3 and 1/2. Correct ans : D. |
A bag contains 5 red, 2 green balls. 3 balls are drawn randomly. What is the probability that balls drawn contain exactly two green balls? | [
"A.1/7",
"B.2/9",
"C.3/11",
"D.4/17"
] | 0 | A.1/7 | aqua_rat | Total number of balls = 5+2 = 7
n(S) = 7C3 = 7*6*5 / 3*2 = 35
n(E) = 2C2* 5C1 = 5
Probability = 5/35 = 1/7
Answer is A |
A woman complete a journey in 20 hours. She travels first half of the journey at the rate of 21 km/hr and second half at the rate of 24 km/hr. Find the total journey in km. | [
"A.334 km.",
"B.216 km.",
"C.314 km.",
"D.448 km."
] | 3 | D.448 km. | aqua_rat | 0.5x/21 + 0.5x/24 = 20
--> x/21 + x/24 = 40
--> x =448 km.
D |
The average height in a group of 4 people is 175 cm. If the average height increased when 2 more people were added to the group, which of the following cannot be the heights of the two new people? | [
"A.179 cm and 172 cm",
"B.181 cm and 169 cm",
"C.173 cm and 178 cm",
"D.176 cm and 176 cm"
] | 1 | B.181 cm and 169 cm | aqua_rat | Denote X as the sum of the heights of the two new people. From the stem it follows that (700+X)6>175. This reduces to X>350. Only the heights from B add up to 350 cm. All other pairs add up to more than 350 cm.
Answer: B |
The sum of the present ages of two persons A and B is 60. If the age of A is twice that of B, find the sum of their ages 5 years hence? | [
"A.70",
"B.55",
"C.60",
"D.65"
] | 0 | A.70 | aqua_rat | A+B=60 A=2B
2B+B=60===>B=20
A=40
5 yrs ages 45 and 25
Sum of their ages = 70
ANSWER A |
Find the number which when multiplied by 15 is increased by 196. | [
"A.14",
"B.20",
"C.26",
"D.28"
] | 0 | A.14 | aqua_rat | Let the number be x. Then, 15x - x = 196
<=> 14x = 196 <=> x = 14.
Answer :A |
A number X equals 80% of the average of 5, 7, 14 and a number Y. If the average of X and Y is 26, the value of Y is? | [
"A.13",
"B.26",
"C.39",
"D.36"
] | 2 | C.39 | aqua_rat | Average of 5, 7, 14 and Y = ( 5 + 7 + 14 + Y )/ 4
Therefore, X = 80% of ( 5 + 7 + 14 + y )/ 4
= (80/100) x (26 + Y)/4
=> X = (26 + Y)/5
5X - Y = 26----- (i)
Also, (X + Y)/2 = 26 ----- (ii)
From (i)and (ii)
X = 13
Y = 39.
ANSWER:C |
A man covers a distance on scooter. Had he moved 3kmph faster he would have taken 40 min less. If he had moved 2kmph slower, he would have taken 40min more. The distance is. | [
"A.30 km",
"B.40 km",
"C.45 km",
"D.50 km"
] | 1 | B.40 km | aqua_rat | Let distance = x m
Usual rate = y kmph
x/y – x/y+3 = 40/60 hr
2y(y+3) = 9x ---------------------------------(1)
x/y-2 – x/y = 40/60 hr y(y-2) = 3x -----------(2)
divide 1 & 2 equations
by solving we get x = 40 km
Answer : B |
The number of livestock in a farm at the beginning of year 2000 was 130,000. During the year, the number increased by p%. During the next year 2001, there was a famine and the number decreased by q%. A census at the end of year 2001 revealed that the number of livestock in the farm was 130,000. Which of the following e... | [
"A.With the exception of 1 instance, p will be equal to q",
"B.q > p",
"C.p = q",
"D.p > q"
] | 3 | D.p > q | aqua_rat | Number plugging in will be best strategy for this question.
Let p = 5%,
Per the question 100000(1.05)(1-q/100) = 100000 ---> q = 4.7%. Thus p > q and hence D is the correct answer. |
If 3 men or 4 women can reap a field in 10 days how long will 5 men and 6 women take to reap it? | [
"A.19/60",
"B.9/60",
"C.2/3",
"D.5/18"
] | 0 | A.19/60 | aqua_rat | Explanation:
3 men reap 1/10 field in 1 day
1 man reap 1/(3 x 10)
4 women reap 1/10 field in 1 day
1 woman reap 1/(10 x 4)
5 men and 6 women reap (5/(3 x 10)+ 6/(4 x 10)) =19/60 in 1 day
5 men and 6 women will reap the field in 19/60 days
Answer: Option A |
On Monday, a certain animal shelter housed 45 cats and dogs. By Friday, 1/5 of the cats and 1/4 of the dogs had been adopted; no new cats or dogs were brought to the shelter during this period. What is the greatest possible number of pets that could have been adopted from the animal shelter between Monday and Friday? | [
"A.10",
"B.11",
"C.12",
"D.13"
] | 1 | B.11 | aqua_rat | To maximize the number of pets adopted, we should maximize the number of dogs adopted since 1/4 > 1/5.
The greatest multiple of 4 less than 45 is 40 (such that the remaining number is divisible by 5), so let's assume there were 40 dogs and 5 cats.
Then the maximum number of adopted pets is 1/4*(40) + 1/5*(5) = 10 + 1 =... |
A shopkeeper gave an additional 20 per cent concession on the reduced price after giving 30 per cent standard concession on an article. If Arun bought that article for 1,120, what was the original price? | [
"A.3,000",
"B.4,000",
"C.2,400",
"D.2,000"
] | 3 | D.2,000 | aqua_rat | Original price = 1120 × 100⁄70 × 100⁄80 = 2000
Answer D |
The total age of A and B is 10 years more than the total age of B and C. C is how many years younger than A.? | [
"A.16",
"B.12",
"C.10",
"D.20"
] | 2 | C.10 | aqua_rat | (A+B)-(B-C)=10
A-C=10
Answer is C |
In an election between two candidates, 10% of votes are were declares invalid. First candidate got 3600 votes which were 60% of the total valid votes . The total number of votes enrolled in that election was: | [
"A.9000",
"B.98000",
"C.20000",
"D.11000"
] | 2 | C.20000 | aqua_rat | 100 % - 10 % = 90 %
54%-36%=18%
18% ------> 3600 ( 18 × 200 = 3600)
100% -------> 20000 votes (100 × 200 = 20000)
C |
Find a 8 digit number that if multiplied by the number 9 or any of its multiplications products (18, 27, 36, 45,..) will result in the multiplication factor repeated (n) number of times. | [
"A.12345679",
"B.42345675",
"C.22347379",
"D.52345673"
] | 0 | A.12345679 | aqua_rat | A
The number is: 12345679
12345679 * 9 = 111111111
12345679 * 18 = 222222222
12345679 * 27 = 333333333
And so on... |
A and B invests Rs.3000 and Rs.7000 respectively in a business. If A doubles his capital after 6 months. In what ratio should A and B divide that year's profit? | [
"A.9:6",
"B.9:8",
"C.9:14",
"D.9:9"
] | 2 | C.9:14 | aqua_rat | (3*6 + 6*6): (7*12)
54:84 => 9:14.Answer:C |
A man saves 20% of his monthly salary. If an account of dearness of things he is to increase his monthly expenses by 20%, he is only able to save Rs. 200 per month. What is his monthly salary? | [
"A.5000",
"B.2889",
"C.2779",
"D.6257"
] | 0 | A.5000 | aqua_rat | Income = Rs. 100
Expenditure = Rs. 80
Savings = Rs. 20
Present Expenditure 80*(20/100) = Rs. 96
Present Savings = 100 – 96 =Rs. 4
100 ------ 4
? --------- 200 => 5000
Answer: A |
A boat covers a certain distance downstream in 1 hour, while it comes back in 11â„2 hours. If the speed of the stream be 3 kmph, what is the speed of the boat in still water? | [
"A.31 kmph",
"B.16 kmph",
"C.19 kmph",
"D.15 kmph"
] | 3 | D.15 kmph | aqua_rat | Let the speed of the water in still water =x
Given that speed of the stream = 3 kmph
Speed downstream =(x+3) kmph
Speed upstream =(x−3) kmph
He travels a certain distance downstream in 1 hour and come back in 11â„2 hour.
i.e., distance travelled downstream in 1 hour = distance travelled upstream in 11â„2 hour
Since... |
A and B invests Rs.4000 and Rs.6000 in a business. After 4 months, A withdraws three-fourth of his capital and 4 months later, B withdraws half of his capital. In what ratio should they share the profits at the end of the year? | [
"A.2:5",
"B.3:5",
"C.4:5",
"D.3:7"
] | 0 | A.2:5 | aqua_rat | A : B
(4000*4)+(1000*8) : (6000*8)+(3000*4)
24000 : 60000
2 : 5
Answer: A |
0.5, 0.55, 0.65, 0.8, ? | [
"A.0.7",
"B.0.9",
"C.0.95",
"D.1"
] | 3 | D.1 | aqua_rat | The pattern is + 0.05, + 0.10, + 0.15, .....
Answer : D. |
If 15 women or 10 men can complete a project in 55 days, in how many days will 5 women and 4 men working together complete the same project ? | [
"A.75",
"B.8",
"C.9",
"D.85"
] | 0 | A.75 | aqua_rat | 15 W = 10 M
Now, 5W + 4M = 5W + 4×15/10W = 5W + 6W = = 11 W
If 15 women can complete the project in 55 days,
11 women can complete the same project in
55×15/11=75days
Answer A |
If n is a positive integer and n^2 is divisible by 450, then what is the largest positive integer that must divide n? | [
"A.10",
"B.20",
"C.30",
"D.40"
] | 2 | C.30 | aqua_rat | 450 = 2 * 3^2 * 5^2
If 450 divides n^2, then n must be divisible by 2 * 3 * 5 = 30
The answer is C. |
Two pipes A and B can separately fill a cistern in 10 and 15 minutes respectively. A person opens both the pipes together when the cistern should have been was full he finds the waste pipe open. He then closes the waste pipe and in another 4 minutes the cistern was full. In what time can the waste pipe empty the cister... | [
"A.6",
"B.8",
"C.7",
"D.4"
] | 1 | B.8 | aqua_rat | 1/10 + 1/15 = 1/6 * 4 = 2/3
1 - 2/3 = 1/3
1/10 + 1/15 - 1/x = 1/3
x = 8
Answer:B |
A certain club has 14 members, including Harry. One of the 14 members is to be chosen at random to be the president, one of the remaining 13 members is to be chosen at random to be the secretary, and one of the remaining 12 members is to be chosen at random to be the treasurer. What is the probability that Harry will e... | [
"A.5/7",
"B.4/7",
"C.3/7",
"D.1/7"
] | 3 | D.1/7 | aqua_rat | Each member out of 14, including Harry, has equal chances to be selected for any of the positions (the sequence of the selection is given just to confuse us). The probability that Harry will be selected to be the secretary is 1/14 and the probability that Harry will be selected to be the treasurer is also 1/14. So, the... |
Afreena walks 8 km towards East and then walks 13 km back, then she turns left and walks 4 km; then walks 5 km after turning left; she turns left again and walks 3 km. How far is she from the starting point ? | [
"A.3 km",
"B.2 km",
"C.1 km",
"D.6 km"
] | 2 | C.1 km | aqua_rat | Explanation:
From given details we know that she walks in square shaped path and will be in 1 km away from starting point.
ANSWER IS C |
A coed soccer team has W women and M men on the team. If 4 women and 2 men are added to the team roster, and if one person on the team is selected at random to serve as team captain, then the probability that the team captain will be a woman can be represented as | [
"A.(W + 4)/(W + M + 6)",
"B.(W + 4)/(W + M + 2)",
"C.(W + 4)/(M + 2)",
"D.(W + 4)/(W + M)"
] | 0 | A.(W + 4)/(W + M + 6) | aqua_rat | W women and M men..now 4 women and 2 men are added then total women = W+4 and total men = M+2.. if we club both as total one team (W + M + 6)
We need to find the probability that the team captain will be a woman => W+4 / (W + M + 6)..
IMO option A is correct answer... |
A man is 30 years older than his son. In two years, his age will be twice the age of his son. The present age of the son is | [
"A.14 years",
"B.28 years",
"C.20 years",
"D.22 years"
] | 1 | B.28 years | aqua_rat | Solution
Let the son's present age be x years .Then, man's present age = (x+30)years.
Then ‹=›(x+30)+2= 2(x+2)
‹=›x+32=2x+4
x= 28.
Answer B |
Chris mixed 3 pounds of raisins with 3 pounds of nuts. If a pound of nuts costs 3 times as much as a pound of raisins, then the total cost of the raisins was what fraction of the total cost of the mixture? | [
"A. 1/7",
"B. 1/5",
"C. 1/4",
"D. 1/3"
] | 2 | C. 1/4 | aqua_rat | 1 lbs of raisin = $1
3 lbs of raisin = $3
1 lbs of nuts = $3
3 lbs of nuts = $9
Total value of mixture = 9+3 = 12
Fraction of the value of raisin = 3/12 = 1/4
Ans:C |
If 2^(2w) = 8^(w−2), what is the value of w? | [
"A.3",
"B.6",
"C.9",
"D.12"
] | 1 | B.6 | aqua_rat | 2^(2w) = 8^(w−2)
2^(2w) = 2^(3*(w−2))
2^(2w) = 2^(3w-6)
Let's equate the exponents as the bases are equal.
2w = 3w-6
w = 6
The answer is B. |
A watch which gains uniformly is 2 minutes low at noon on Monday and is 4 min. 48 sec fast at 2 p.m. on the following Monday. When was it correct? | [
"A.2 p.m. on Tuesday",
"B.2 p.m. on Wednesday",
"C.3 p.m. on Thursday",
"D.1 p.m. on Friday"
] | 1 | B.2 p.m. on Wednesday | aqua_rat | Solution
Time from 12 p.m. on Monday to 2 p.m. on the following Monday = 7 days 2 hours.
=170 hours.
The watch gains = (2 + 4 x4/5)min
= 34 / 5 min.in 170 hrs.
Now,34/5 min are gained in 170 hrs.
2 min are gained in(170x 5/34 x2)hrs.
Watch is correct 2 days 2 hrs. after 12 p.m. on Monday i.e., it will be correct at 2 p... |
Otto and Han are driving at constant speeds in opposite directions on a straight highway. At a certain time they are driving toward each other and are 40 miles apart. One and a half hours later, they are again 40 miles apart, driving away from each other. If Otto drives at a speed of x miles per hour, then, in terms of... | [
"A.a) 80-x",
"B.b) 53.33-x",
"C.c) 80-2x",
"D.d) 120-x"
] | 1 | B.b) 53.33-x | aqua_rat | Let's say the two cars have speeds V1 and V2. The fact that they are moving in opposite direction means that their relative speed is (V1 + V2). In other words, any gap between them will be changing in size at a rate of (V1 + V2). It doesn't matter whether they are moving toward each other or away from each other. If th... |
A jeep takes 4 hours to cover a distance of 620 Km. how much should the speed in Kmph be maintained to cover the same direction in 3/2th of the previous time? | [
"A.148 Kmph",
"B.152 Kmph",
"C.106 Kmph",
"D.103 Kmph"
] | 3 | D.103 Kmph | aqua_rat | Time = 4
Distance = 620
3/2 of 4 hours = 4 * 3/2 = 6 Hours
Required speed = 620/6 = 103 Kmph
D) |
Find at what time between 8 and 9 o'clock will the hands of a clock be in the same straight line but not together. | [
"A.10x11/10",
"B.10x10/11",
"C.11x10/11",
"D.12x10/11"
] | 1 | B.10x10/11 | aqua_rat | Solution
At 8 o'clock, the hour is at 8 and the minute hand is at 12,i.e. the two hands are 20 min. Spaces apart.
So, the minute hand gain = (30 - 20)minute
55 minutes will be gained in 60 min.
10 minutes spaces will be gained in (60/55 x10) min. = 10x10/11 min.
The hands will be in the same straight line but not toget... |
On Sunday morning, Pugsley and Wednesday are trading pet spiders. If Pugsley were to give Wednesday four of his spiders, Wednesday would then have four times as many spiders as Pugsley does. But, if Wednesday were to give Pugsley five of her spiders, Pugsley would now have five fewer spiders than Wednesday had before t... | [
"A.6",
"B.7",
"C.8",
"D.10"
] | 3 | D.10 | aqua_rat | If Pugsley were to give Wednesday four of his spiders, Wednesday would then have five times as many spiders as Pugsley does:
(w + 4) = 4(p - 4)
If Wednesday were to give Pugsley five of her spiders, Pugsley would now have five fewer spiders than Wednesday had before they traded:
p + 5 = w - 5
Solving gives p = 10 and w... |
To apply for the position of photographer at a local magazine, a photographer needs to include two or three photos in an envelope accompanying the application. If the photographer has pre-selected six photos representative of her work, how many choices does she have to provide the photos for the magazine? | [
"A.32",
"B.35",
"C.36",
"D.40"
] | 1 | B.35 | aqua_rat | 6C2 + 6C3 = 15 + 20 = 35
The answer is B. |
If x is an integer and y = 3x + 2, which of the following CANNOT be a divisor of y? | [
"A.4",
"B.5",
"C.6",
"D.7"
] | 2 | C.6 | aqua_rat | Just to add some more to Bunuel's explanation, if a number is a multiple of 3, it will be in a form:
n = 3*k, where k is an integer
And if a number is a multiple of 6, it will be in a form :
m = 6*l, where l is an integer
so m = 2 * 3 * l = (2*l) * 3 = 3 * p, where p is an integer.
In other words, the prime factorizati... |
A book store bought copies of a new book by a popular author, in anticipation of robust sales. The store bought 400 copies from their supplier, each copy at wholesale price W. The store sold the first 150 copies in the first week at 80% more than W, and then over the next month, sold a 100 more at 20% more than W. Fina... | [
"A.30% loss",
"B.10% loss",
"C.10% profit",
"D.20% profit"
] | 3 | D.20% profit | aqua_rat | C.P. = 400W
S.P. = 1.8W*150 + 1.2W*100 + 0.6W*150 = 480W
Since, S.P. > C.P., there is net profit.
Profit = S.P. - C.P. = 480W - 400W = 80W
Profit % = (Profit/C.P.)*100 = (80W/400W)*100 = 20%
So, the correct answer is D. |
A committee of 2 people is to be selected out of 3 teachers and 4 preachers. If the committee is selected at random, what is the probability that the committee will be composed of at least 1 preacher? | [
"A.1/4",
"B.1/3",
"C.2/3",
"D.6/7"
] | 3 | D.6/7 | aqua_rat | Total no of ways in which you can select a committee of 2 people out of 7 people is 7C2 ways= 21 ways
Requirement is at-least 1 preacher= 4C1*3C1+4C2 or 7C2-3C2=18 ways
Probability= 18/21 = 6/7
ANSWER:D |
If 73! has 16 zeroes at the end, how many zeroes will 80! have at the end? | [
"A.16",
"B.17",
"C.18",
"D.19"
] | 3 | D.19 | aqua_rat | Prime Factoring: you need a 2 and a 5 to make a 10 (a "zero"), and there are TONS of 2's so let's skip these and focus on the (rarer) 5s:
80! = 1*2*3*4*5*6...*78*79*80
Since there are 80 consecutive numbers, there are 16 multiples of 5 in there, but if we're prime factoring, we need to remember that SOME multiples of 5... |
Mary's income is 60 percent more than Tim's income, and Tim's income is 40 percent less than Juan's income. What percent of Juan's income is Mary's income? | [
"A.124%",
"B.120%",
"C.96%",
"D.80%"
] | 2 | C.96% | aqua_rat | Juan's income = 100 (assume);
Tim's income = 60 (40 percent less than Juan's income);
Mary's income = 96 (60 percent more than Tim's income).
Thus, Mary's income (96) is 96% of Juan's income (100).
Answer: C |
P is two years older than Q who is twice as old as R. The total of the ages of P, Q and R is 25. How old is Q? | [
"A.7.2 years",
"B.8.2 years",
"C.9.8 years",
"D.9.2 years"
] | 3 | D.9.2 years | aqua_rat | Let age of R =x. Then,
Age of Q =2x
Age of P =2+2x
Total age of P,Q and R =25
⇒(2+2x)+2x+x=25
⇒5x=23
⇒x=23/5=4.6 years
B's age =2x=2×4.6=9.2 years
ANSWER:D |
A man can row with a speed of 20 kmph in still water. If the stream flows at 7 kmph, then the speed in downstream is? | [
"A.27",
"B.23",
"C.20",
"D.27"
] | 3 | D.27 | aqua_rat | M = 20
S = 7
DS = 20 + 7 = 27
Answer: D |
A theater box office sold an average (arithmetic mean) of 65 tickets per staff member to a particular movie. Among the daytime staff, the average number sold per member was 75, and among the evening staff, the average number sold was 60. If there are no other employees, what was the ratio of the number of daytime staff... | [
"A.1:2",
"B.1:4",
"C.5:11",
"D.1:3"
] | 0 | A.1:2 | aqua_rat | Deviation from the mean for the daytime staff = 75 - 65 = 10.
Deviation from the mean for the evening staff = 65 - 60 = 5.
Thus, the ratio of the number of daytime staff members to the number of evening staff members is 5:10 = 1:2.
The answer is A. |
Present ages of Sameer and Anand are in the ratio of 5 : 4 respectively. Four years hence, the ratio of their ages will become 11 : 9 respectively. What is Anand's present age in years? | [
"A.A)24",
"B.B)89",
"C.C)67",
"D.D)32"
] | 3 | D.D)32 | aqua_rat | Let the present ages of Sameer and Anand be 5x years and 4x years respectively.
Then, (5x + 4/4x + 4)=11/9
9(5x + 4) = 11(4x + 4)
45x + 36 = 44x + 44
45x - 44x = 44 - 36
x = 8.
Anand's present age = 4x = 32 years.
Answer:D |
How many meaningful English words can be formed with the letters ESRO using each letter only once in each word? | [
"A.1",
"B.3",
"C.4",
"D.8"
] | 1 | B.3 | aqua_rat | Explanation:
Meaningful words are ROSE, SORE and EROS.
Note the meaning of the words SORE and EROS with the help of dictionary.
Answer: B) Three |
If S is the product of all positive integers less than 31, than what is the greatest integer k for which S/18^k is an integer? | [
"A.3",
"B.6",
"C.7",
"D.14"
] | 2 | C.7 | aqua_rat | 30! S must be divisible by (3*3*2)^k.
As I will find a lot of 2's among 30!'s factors I will focus on the 3's (that also occurs twice instead of only once as a factor in 18).
Every multiple of 3 will provide me with atleast one factor of 3. There aren't that many so I list them quickly.
3 6 9*
12 15 18*
21 24 27**
30
T... |
What is the ratio between perimeters of two squares one having 3 times the diagonal then the other? | [
"A.3: 8",
"B.3: 6",
"C.3: 7",
"D.3: 1"
] | 3 | D.3: 1 | aqua_rat | d = 3d d = d
a√2 = 3d a√2 = d
a = 3d/√2 a = d/√2 => 3: 1
Answer:D |
Six bells commence tolling together and toll at intervals of 2, 4, 6, 8 10 and 12 seconds respectively. In 30 minutes, how many times do they toll together ? | [
"A.22",
"B.72",
"C.37",
"D.16"
] | 3 | D.16 | aqua_rat | Explanation:
L.C.M. of 2, 4, 6, 8, 10, 12 is 120.
So, the bells will toll together after every 120 seconds(2 minutes).
In 30 minutes,they will together (30/2)+1=16 times
Answer: D) 16 |
A train of length 150 metres takes 40.5 seconds to cross a tunnel of length 300 metres. What is the speed of the train in km/hr ? | [
"A.13.33",
"B.26.67",
"C.40",
"D.66.67"
] | 2 | C.40 | aqua_rat | Explanation:
Speed = 150+300/40.5m/sec
=450/40.5=18/5km/hr = 40 km/hr.
ANSWER IS C |
Three numbers are in the ratio 1 : 2 : 3 and their H.C.F is 3. The numbers are | [
"A.12, 24, 30",
"B.12, 24, 38",
"C.12, 24, 362",
"D.3, 6, 9"
] | 3 | D.3, 6, 9 | aqua_rat | Explanation:
Let the required numbers be x, 2x, 3x. Then, their H.C.F =x. so, x= 3
\inline \fn_jvn \therefore The numbers are 3, 6, 9
Answer: D) 3, 6, 9 |
A miniature roulette wheel is divided into 10 equal sectors, each bearing a distinct integer from 1 to 10, inclusive. Each time the wheel is spun, a ball randomly determines the winning sector by settling in that sector. If the wheel is spun two times, approximately what is the probability that the product of the two w... | [
"A.88%",
"B.75%",
"C.67%",
"D.63%"
] | 1 | B.75% | aqua_rat | The only way to have an odd product is if both integers are odd.
P(odd product) = 1/2*1/2 = 1/4
P(even product) = 1 - 1/4 = 3/4 = 75%
The answer is B. |
What is the lowest positive integer that is divisible by each of the integers 1 through 8, inclusive? | [
"A.420",
"B.560",
"C.840",
"D.960"
] | 2 | C.840 | aqua_rat | The integers are 1 , 2 , 3 , 4 , 5 , 6 , 7 and 8
Lowest positive integer that is is divisible by each of the integers 1 through 8
= 2^3 * 3 * 5 * 7
=8*3 *5 *7
=24 * 35
= 840
Answer C |
There are two water tanks A and B, A is much smaller than B. While water fills at the rate of one liter every hour in A, it gets filled up like 10, 20, 40, 80, 160 in tank B. (At the end of first hour, B has 10 liters, second hour it has 20, third hour it has 40 and so on). If tank B is 1/32 filled after 21 hours, what... | [
"A.22",
"B.28",
"C.269",
"D.26"
] | 3 | D.26 | aqua_rat | The data related to the first tank A is not necessary. As you can see, the capacity that gets filled in the tank B after each hour is doubled. So If the tank is 1/32nd part is full after 21 hours, it is 1/16th part full after 22 hours, 1/8th part full after 23 hours, 1/4th part full after 24 hours, 1/2 full after 25 ho... |
Find the sum of first 30 natural numbers | [
"A.470",
"B.468",
"C.465",
"D.463"
] | 2 | C.465 | aqua_rat | Explanation:
Sum of n natural numbers
=n(n+1) / 2
=30(30+1) / 2=30(31) / 2=465
Option C |
A and B rent a pasture for 10 months. A put in 80 cows for 7 months. How many can B put in for the remaining 3 months, if he pays half as much again as A? | [
"A.298",
"B.608",
"C.279",
"D.280"
] | 3 | D.280 | aqua_rat | 80* 7: x* 3 = 1:1 1/2
560: 3x = 2: 3
x = 280
Answer:D |
John takes a trip and drives 9 hours from Town X to Town Z at a rate of 60 miles per hour. On his way back, John drives 85 miles per hour and stops in Town Y which is midway between Town X and Town Z. How many hours does it take Scott to drive from Town Z to Town Y? | [
"A.1.75",
"B.1.25",
"C.1.45",
"D.4.15"
] | 3 | D.4.15 | aqua_rat | distance from X to Z =9 hr* 60 mph= 540 miles
hence distance from Y to Z= 1/2*540=270
time=270/85=4.15 hrs
IMO: D |
A company has 100 employees, 40% of whom are employed part time. If it hires 25 new employees, 40% of whom are employed part time, what will be the percent increase in part time employees? | [
"A.1 2/3 %",
"B.2 2/3 %",
"C.4 %",
"D.25 %"
] | 3 | D.25 % | aqua_rat | Total employee = 100
Part time Empl = 40
New part time empl = 25 * (40/100)
= 10
Total new part time Emp = 10+40= 50
Old part time Emp = 40
% increase = (new - old)*100/old
=10*100/40
= 25%
Ans-D |
In a class of 60 students, the number of boys and girls participating in the annual sports is in the ratio 3 : 2 respectively. The number of girls not participating in the sports is 5 more than the number of boys not participating in the sports. If the number of boys participating in the sports is 15, then how many gir... | [
"A.22",
"B.32",
"C.30",
"D.28"
] | 2 | C.30 | aqua_rat | Let the number of boys and girls participating in sports be 3x and 2x respectively.
Then, 3x = 15 or x = 5.
So, number of girls participating in sports = 2x = 10.
Number of students not participating in sports = 60 - (15 + 10) = 35.
Let number of boys not participating in sports be y.
Then, number of girls not particip... |
To furnish a room in a model home an interior decorator is to select 4 chairs and 4 tables from the collection of chairs and tables in a warehouse that are all different from each other. If there are 5 chairs in the warehouse and if 75 different combinations are possible, how many tables are there in the warehouse? | [
"A.A)6",
"B.B)8",
"C.C)10",
"D.D)15"
] | 0 | A.A)6 | aqua_rat | Total number of ways to choose 4 chairs from 5= 5C4=5
Total number of combination=75
That means we need get 15 combinations from the selection of tables....
Screening through the answers.... 6C4=15..... 15*5=75
Answer is 6... A |
A train overtakes two persons walking along a railway track. The first one walks at 4.5 km/hr. The other one walks at 5.4 km/hr. The train needs 8.4 and 8.5 seconds respectively to overtake them. What is the speed of the train if both the persons are walking in the same direction as the train? | [
"A.66 km/hr",
"B.72 km/hr",
"C.78 km/hr",
"D.81 km/hr"
] | 3 | D.81 km/hr | aqua_rat | Explanation:
4.5 km/hr =(4.5 x 5/18)m/sec = 5/4m/sec = 1.25 m/sec, and
5.4 km/hr =(5.4 x5/18)m/sec =3/2m/sec = 1.5 m/sec.
Let the speed of the train be x m/sec.
Then, (x - 1.25) x 8.4 = (x - 1.5) x 8.5
=> 8.4x - 10.5 = 8.5x - 12.75
=> 0.1x = 2.25
=> x = 22.5
Speed of the train =(22.5 x 18/5)km/hr = 81 km/hr.
ANSWER IS ... |
160 is what percent of 50 ? | [
"A. 5%",
"B. 20%",
"C. 320%",
"D. 200%"
] | 2 | C. 320% | aqua_rat | 50*x=160 --> x=3.2 --> 3.2 expressed as percent is 320%.
Answer: C. |
What will come in place of the x in the following Number series? 46080, 3840, ?, 48, 8, 2, 1 | [
"A.1",
"B.384",
"C.5",
"D.7"
] | 1 | B.384 | aqua_rat | 46080 /12 = 3840
3840 /10 = 384
384 /8 = 48
48 /6 = 8
8/4 = 2
2 /2 = 1
B |
The length of a rectangle is reduced by 20%. By what % would the width have to be increased to maintainthe original area? | [
"A.10%",
"B.20%",
"C.25%",
"D.30%"
] | 2 | C.25% | aqua_rat | Sol. Required change = (20*100)/(100-20)=25%
C |
Find the average of first 20 natural numbers? | [
"A.5.5",
"B.7.2",
"C.10.5",
"D.12.3"
] | 2 | C.10.5 | aqua_rat | Sum of first n natural numbers = n(n+1)/2
sum of first 20 natural numbers = 20*21/2 =210
average = 210/20 = 10.5
Answer is C |
The inverse ratio of 4: 2: 1 is? | [
"A.2:4:8",
"B.2:3:9",
"C.2:3:2",
"D.2:3:6"
] | 0 | A.2:4:8 | aqua_rat | 1/4: 1/2: 1/1 = 2:4:8
Answer:A |
If a man lost 4% by selling oranges at the rate of 12 a rupee at how many a rupee must he sell them to gain 44%? | [
"A.3",
"B.8",
"C.9",
"D.6"
] | 1 | B.8 | aqua_rat | 96% ---- 12
144% ---- ?
96/144 * 12 = 8
Answer: B |
NHAI employs 100 men to build a highway of 2km in 50 days working 8 hours a day. If in 25 days they completed 1/3 part of work .than how many more employees should NHAI hire to finish it in time working 10 hours a day? | [
"A.22",
"B.60",
"C.28",
"D.11"
] | 1 | B.60 | aqua_rat | Here 2km is immaterial. The given problem can be written in a tabular form like below.
We can apply chain rule now.
Total men required to complete the remaining work = 100×2525×810×2313100×2525×810×2313 = 160
So additional men required = 160 - 100 = 60
Answer:B |
A train 500 m long is running at a speed of 78 km/hr. If it crosses a tunnel in 1 min, then the length of the tunnel is? | [
"A.277 m",
"B.700 m",
"C.800 m",
"D.187 m"
] | 2 | C.800 m | aqua_rat | Speed = 78 * 5/18 = 65/3 m/sec.
Time = 1 min = 60 sec.
Let the length of the train be x meters.
Then, (500 + x)/60 = 65/3
x = 800 m.
Answer:C |
The price of a radio was increased by 25 percent. The new price was then increased by 40 percent. A single increase of what percent is equivalent to these two successive increases? | [
"A.80%",
"B.75%",
"C.65%",
"D.50%"
] | 1 | B.75% | aqua_rat | consider base price - $100
25% increase = 1.25*100 = $125
another 40% increase on new price = 1.4* 125 = $175
so final price of radio - $175
therefore a 75% increase
correct option - B |
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