source string | id string | question string | options list | answer string | reasoning string |
|---|---|---|---|---|---|
AQUA-RAT | AQUA-RAT-38897 | Evaluate: 50 - 12÷4×2 = | [
"44",
"54",
"16",
"27"
] | A | According to order of operations, 12÷4×2 (division and multiplication) is done first from left to right
12÷4×2 = 3 × 2 = 6
Hence
50 - 12÷4×2 = 50 - 6 = 44
correct answer A)44 |
AQUA-RAT | AQUA-RAT-38898 | I sold a book at a profit of 10%. Had I sold it for $120 more, 15% would have been gained. Find the cost price? | [
"$2000",
"$2500",
"$2400",
"$3120"
] | C | 115% of cost - 110% of cost = $120
5% of cost = $120
cost = 120*100/5 = $2400
Answer is C |
AQUA-RAT | AQUA-RAT-38899 | In how many ways can the letters of the word ABROAD be rearranged such that the vowels always appear together? | [
"6!/2!",
"3!*3!",
"4!/2!",
"4! *(3!/2!)"
] | D | In the word ABROAD , there are 3 vowels - 2 A's and O
Number of ways the letters of word ABACUS be rearranged such that the vowels always appear together
= (4! * 3! )/2!
We can consider the the 3 vowels as a single unit and there are 3 ways to arrange them . But since 2 elements of vowel group are identical we divide b... |
AQUA-RAT | AQUA-RAT-38900 | Mohit sold an article for Rs. 18000. Had he offered a discount of 10% on the selling price, he would have earned a profit of 8%. What is the cost price of the article? | [
"15000",
"15002",
"15029",
"15329"
] | A | Let the CP be Rs. x.
Had he offered 10% discount, profit = 8%
Profit = 8/100 x and hence his SP = x + 8/100 x = Rs. 1.08x = 18000 - 10/100(18000) = 18000 - 1800 = Rs. 16200
=> 1.08x = 16200
=> x = 15000
Answer: A |
AQUA-RAT | AQUA-RAT-38901 | A cistern is filled by pipe A in 10 hours and the full cistern can be leaked out by an exhaust pipe B in 15 hours. If both the pipes are opened, in what time the cistern is full? | [
"50hrs",
"30hrs",
"70hrs",
"80hrs"
] | B | time taken to full the cistern=(1/10-1/15)hrs
=1/30
=30hrs
ANSWER:B |
AQUA-RAT | AQUA-RAT-38902 | A and B together can do a piece of work in 8 days. If A alone can do the same work in 12 days, then B alone can do the same work in? | [
"25 days",
"24 days",
"22 days",
"27 days"
] | B | B
24 days
B = 1/8 – 1/2 = 1/24 => 24 days |
AQUA-RAT | AQUA-RAT-38903 | A man invests Rs. 8,000 at the rate of 5% per annum. How much more should he invest at the rate of 8%, so that he can earn a total of 6% per annum? | [
"Rs. 1200",
"Rs. 1300",
"Rs. 1500",
"Rs. 4000"
] | D | Explanation :
Interest on Rs.8000 at 5% per annum = ( 8000 × 5 × 1) / 100 = Rs. 400
Let his additional investment at 8% = x
Interest on Rs.x at 8% per annum = ( x × 8 × 1 ) / 100 = 2x/25.
To earn 6% per annum for the total, interest = (8000 + x) × 6 × 1/100.
=> 400 + 2x/25 = (8000 + x) × 6 × 1/100.
=> 40000 + 8x = (800... |
AQUA-RAT | AQUA-RAT-38904 | For a group of n people, k of whom are of the same sex, the (n-k)/n expression yields an index for a certain phenomenon in group dynamics for members of that sex. For a group that consists of 20 people, 8 of whom are females, by how much does the index for the females exceed the index for the males in the group? | [
" 0.05",
" 0.0625",
" 0.2",
" 0.25"
] | C | Index for females = (20-8)/20 = 3/5 = 0.6
Index for males = (20-12/20 = 2/5 = 0.4
Index for females exceeds males by 0.6 - 0.4 = 0.2
Answer: C |
AQUA-RAT | AQUA-RAT-38905 | There is a 30% increase in the price of an article in the first year, a 20% decrease in the second year and a 10% increase in the next year. If the final price of the article is Rs. 2288, then what was the price of the article initially? | [
"Rs.2038",
"Rs.2073",
"Rs.2000",
"Rs.2027"
] | C | Let the price of the article, four years age be Rs. 100 in the 1st year, price of the article = 100 + 30 = Rs. 130. In the 2nd year, price = 130 - 20% of 130 = 130 - 26 = Rs. 104.
In the 3rd year, price = 104 + 10% of 104 = 104 + 10.4 = Rs. 114.40.
But present price of the article is Rs. 2288
for 114.4 ---> 100 ; 2288 ... |
AQUA-RAT | AQUA-RAT-38906 | There are three foam generators in the factory, each of the first two can generate 10 liters of foam in one hour and the third can generate 18 liters in an hour. The three generators start working together at the same time and after one hour and a half one of the first generators stops working and two hours after that ... | [
"128",
"132.",
"146.",
"154."
] | A | Let the foam generators capacity be -
A = 10 lit/hr
B = 10 lit/hr
C = 18 lit/hr
Total foam generation in 1 hour will be 38 lit ( 10 + 10 + 18 ) ; since in 1 and 1/2 hr they will generate 38 + 19 => 57 litres...
Now one of the first generators stops working ( Say A stops working ) , so we have -
B = 10 lit/hr
C = 18 lit... |
AQUA-RAT | AQUA-RAT-38907 | In 1998 the profits of company N were 10 percent of revenues. In 1999, the revenues of company N fell by 30 percent, but profits were 16 percent of revenues. The profits in 1999 were what percent of the profits in 1998? | [
"80%",
"105%",
"120%",
"112%"
] | D | 0,112R = x/100*0.1R
Answer D |
AQUA-RAT | AQUA-RAT-38908 | 30 percent of Andrea's living room floor is covered by a carpet that is 4 feet by 9 feet. What is the area of her living room floor? | [
"14.4",
"120",
"50.4",
"60"
] | B | 30% of Area of the floor = 4*9 square feet = 36 square feet
i.e. 100% Area of Floor = (36/30)*100 = 120 square feet
Answer: Option B |
AQUA-RAT | AQUA-RAT-38909 | There are 5 chess amateurs playing in Villa's chess club tournament. If each chess amateur plays with exactly 4 other amateurs, what is the total number of chess games possible to be played in the tournament? | [
"10",
"20",
"40",
"60"
] | A | Method 1:
Take the first amateur. He plays a game with each of the other four i.e. 4 games.
Now take the second one. He has already played a game with the first one. He plays 3 games with the rest of the 3 amateurs i.e. 3 more games are played.
Now take the third amateur. He has already played a game each with the firs... |
AQUA-RAT | AQUA-RAT-38910 | If 28a+30b+31c=425.
then a+b+c=?.a,b,c are natural numbers | [
"14",
"8",
"6",
"9"
] | A | have a look on your calender
since,we all knw a year consist of 365 days
february is d only month which has 28 days
4 months in a year has 30 days
and,rest 7 months has 31 days..
so,following d given eq. we can write 28*1 + 30*6 + 31*7..
hence values of a,b and c are 1, 6 and 7 respectively..
a+b+c=14
ANSWER:A |
AQUA-RAT | AQUA-RAT-38911 | A cistern is filled by a tap in 3 1/2 hours. Due to leak in the bottom of the cistern, it takes half an hour longer to fill the cistern. If the cistern is full how long will it take the leak to empty it? | [
"88hours",
"38hours",
"78hours",
"28hours"
] | D | 2/7 - 1/x
= 1/4
x = 28
Answer:D |
AQUA-RAT | AQUA-RAT-38912 | What is the place value of 3 in the numeral 53468? | [
"3000",
"30",
"3",
"330"
] | A | place value of 3 = 3 * 1000 = 3000
Answer is A |
AQUA-RAT | AQUA-RAT-38913 | A child is playing with letter blocks (a playing cube in which an english letter is written). Before leaving the child to play on her own, her mon arranged 5 blocks into the word APPLE. How many different 6 letter words can the child make with these 5 blocks (Words need not have a meaning.She is just a child!) ? | [
"2!",
"3!",
"4!",
"5!"
] | C | There are 6 letter blocks to be arranged. Note that the letter P occurs twice. 2 'P' blocks can be arranged only in one way, since the two blocks are exactly the same(PP is same as PP). So we can consider PP as one letter and proceed to find the arrangement of 4 letters, A, PP, L, E. These four blocks can be arranged i... |
AQUA-RAT | AQUA-RAT-38914 | A certain company charges $6 per package to ship packages weighing less than 2 pounds each. For a package weighing 2 pounds or more, the company charges an initial fee of $6 plus $2 per pound. If the company charged $30 to ship a certain package, which of the following was the weight of the package, in pounds? | [
"6",
"8",
"10",
"12"
] | D | Let the weight of the package be X.
2X + 6= 30
X = 12
The answer is D. |
AQUA-RAT | AQUA-RAT-38915 | If four coins are tossed, the probability of getting two heads and two tails is | [
"3/8",
"6/11",
"2/5",
"4/5"
] | A | Since four coins are tossed, sample space = 24
Getting two heads and two tails can happen in six ways.
n(E) = six ways
p(E) = 6/24 = 3/8
Answer : A |
AQUA-RAT | AQUA-RAT-38916 | If 0.75: x :: 5:9, then x is equal to: | [
"1.12",
"1.16",
"1.2",
"1.35"
] | D | Explanation:
(x * 5) = (0.75 *9)
X=6.75/5 = 1.35
Answer: D |
AQUA-RAT | AQUA-RAT-38917 | By investing in 16 2/3% stock at 64, one earns Rs. 1500. The investment made is: | [
"Rs. 5640",
"Rs. 5760",
"Rs. 7500",
"Rs. 8600"
] | B | To earn Rs. 50/3 , investment = Rs. 64.
To earn Rs. 1500, investment = Rs.64 x 3/50x 1500 = Rs. 5760.
ANSWER :B |
AQUA-RAT | AQUA-RAT-38918 | A dishonest dealer professes to sell goods at the cost price but uses a weight of 720 grams per kg, what is his percent? | [
"15%",
"25%",
"38.9%",
"45%"
] | C | Explanation:
720 --- 280
100 --- ? => 38.9%
Answer: C |
AQUA-RAT | AQUA-RAT-38919 | A 600 meter long train crosses a signal post in 40 seconds. How long will it take to cross a 3 kilometer long bridge, at the same speed? | [
"240",
"288",
"665",
"199"
] | A | S = 600/40 = 15 mps
S = 3600/15 = 240 sec
= 4 min
Answer: A |
AQUA-RAT | AQUA-RAT-38920 | By selling an article at Rs.800, a shopkeeper makes a profit of 25%. At what price should he sell the article so as to make a loss of 25%? | [
"123",
"480",
"266",
"1251"
] | B | SP = 800
Profit = 25%
CP = (SP)*[100/(100+P)]
= 800 * [100/125]
= 640
Loss = 25% = 25% of 640 = Rs.160
SP = CP - Loss = 640 - 160 = Rs.480Answer: B |
AQUA-RAT | AQUA-RAT-38921 | A bag contains 2 white balls, 3 black balls and 4 red balls. In how many ways can 3 balls be drawn from the bag, if at least one black ball is to be included in the draw | [
"64",
"128",
"132",
"222"
] | A | Explanation:
From 2 white balls, 3 black balls and 4 red balls, 3 balls are to be selected such that
at least one black ball should be there.
Hence we have 3 choices
All three are black
Two are black and one is non black
One is black and two are non black
Total number of ways
= 3C3 + (3C2 x 6C1) + (3C1 x 6C2) [because ... |
AQUA-RAT | AQUA-RAT-38922 | A drought decreased the amount of water in city X’s reservoirs from 118 million gallons to 96 million gallons. If the reservoirs were at 79 percent of total capacity before the drought began, approximately how many million gallons were the reservoirs below total capacity after the drought? | [
"67",
"58",
"54",
"46"
] | C | let T be the total capacity of the reservoir.
Now we can equate before cases i.e 79/100(T) = 118.
Lets take approximate values for easy calculation 80/100(T) = 120 => T = 150 MG.
We need to subtract total - after drought case = 150 - 96 = 54 MG..
Option C is correct answer... |
AQUA-RAT | AQUA-RAT-38923 | Evaluate : 986 x 237 + 986 x 863 | [
"986000",
"968000",
"978000",
"987000"
] | A | 986 x 137 + 986 x 863 = 986 x (137 + 863) = 986 x 1000 = 986000.
Answer is A. |
AQUA-RAT | AQUA-RAT-38924 | The class mean score on a test was 50, and the standard deviation was 15. If Jack's score was within 2 standard deviations of the mean, what is the lowest score he could have received? | [
"20",
"31",
"45",
"90"
] | A | 1SD from the mean ranges from 35 to 65, where 65 is within SD above the mean and 35 within 1SD below the mean
2SD=15 TWICE=30 from the the mean, which is 80 to 20, where 80 is within 2 SD above the mean AND 20 is within 2 SD below the mean.
Answer = A |
AQUA-RAT | AQUA-RAT-38925 | 256, 225, 196, 169, 144, ? | [
"49",
"64",
"81",
"121"
] | D | Explanation :
The pattern is 16^2, 15^2, 14^2, 13^2, 12^2, ...
So next number is 11^2 = 121
Answer : Option D |
AQUA-RAT | AQUA-RAT-38926 | In a shop, 40% socks are white and rest are black. 60% socks are made of cotton and rest are made of wool. 25% white socks are made of cotton and 20 of the black socks are made of wool. How many black socks Z are made of cotton? | [
"100",
"80",
"60",
"50"
] | A | I'll prefer to solve this with plug n play method.
As we know, White Cotton socks are only 25% and Total Cotton socks is 60% - Hence Black Cotton socks Z has to be [highlight]HIGH[/highlight]number. Thats why we've to pick high number... say 100 or 80.
100 fits perfectly after relevant calculations. Hence answer A. |
AQUA-RAT | AQUA-RAT-38927 | A certain junior class has 3000 students and a certain senior class has 800 students. Among these students, there are 60 siblings pairs each consisting of 1 junior and 1 senior. If 1 student is to be selected at random from each class, what is the probability that the 2 students selected will be a sibling pair? | [
"1/40000",
"1/3600",
"9/2000",
"1/60"
] | A | Let's see
Pick 60/3000 first
Then we can only pick 1 other pair from the 800
So total will be 60 / 800 *3000
Simplify and you get 1/40000
Answer is A |
AQUA-RAT | AQUA-RAT-38928 | A sum amounts to Rs.4410 in 2 years at the rate of 5% p.a. If interest was compounded yearly then what was the principal? | [
"Rs.4000",
"Rs.5000",
"Rs.4500",
"Rs.4800"
] | A | CI=4410,R=5,N=2
CI=P[1+R/100]^2
=P[1+5/100]^2
4410=P[21/20]^2
4410[20/21]^2
4000
ANSWER:A |
AQUA-RAT | AQUA-RAT-38929 | A jar full of whisky contains 40% alcohol. A part of this whisky is replaced by another containg 19% alcohol and now the percentage of alcohol was found to be 26%. What quantity of whisky is replaced ? | [
"1/3",
"2/3",
"2/5",
"3/5"
] | B | Let us assume the total original amount of whiskey = 10 ml ---> 4 ml alcohol and 6 ml non-alcohol.
Let x ml be the amount removed ---> total alcohol left = 4-0.4x
New quantity of whiskey added = x ml out of which 0.19 is the alcohol.
Thus, the final quantity of alcohol = 4-0.4x+0.19x ----> (4-0.21x)/ 10 = 0.26 ---> x =... |
AQUA-RAT | AQUA-RAT-38930 | In store A there are 50 pairs of pants for every 40 store B has. The price ratio between the pants in store B and the pants in store A is 3:4. If all the pants were sold in both places until the stock ran out, what is the ratio between the total amount stores A earned to the total amount store B earned? | [
"3:16.",
"2:3.",
"5:3.",
"3:4."
] | C | 1st statement : ratio of pants
Store A : Store B
50x : 40x
5X:4X
Price :
4y:3y
Total revenue
20xy : 12xy
5:3
Answer is C |
AQUA-RAT | AQUA-RAT-38931 | The side of a cube is 15 m, find it's surface area? | [
"1350",
"1750",
"1150",
"1450"
] | A | Surface area = 6 a(power)2 sq. units
6 a(power)2 = 6 × 225 = 1350 m(power)2
Answer is A. |
AQUA-RAT | AQUA-RAT-38932 | A train 220 m long is running with a speed of 59 kmph.. In what will it pass a man who is running at 7 kmph in the direction opposite to that in which the train is going | [
"8 sec",
"10 sec",
"12 sec",
"14 sec"
] | C | Explanation:
Speed of the train relative to man = (59 + 7) kmph
= 66 ×5/18 m/sec = 55/3 m/sec.
Time taken by the train to cross the man = Time taken by it to cover 220 m
at (55/3) m / sec = (220 ×3/55) sec = 12 sec
Answer: Option C |
AQUA-RAT | AQUA-RAT-38933 | A train 500m long takes 10 sec to cross a man walking at 5kmph in a direction opposite to that of the train. Find the speed of the train? | [
"175kmph",
"150kmph",
"162kmph",
"145kmph"
] | A | Let the speed of the train be x kmph
Speed of the train relative to man = x+5 = (x+5)*5/18 m/sec
500/[(x+5)*5/18] = 10
10(x+5) = 1800
x = 175kmph
Answer is A |
AQUA-RAT | AQUA-RAT-38934 | The average age of applicants for a new job is 20, with a standard deviation of 8. The hiring manager is only willing to accept applicants whose age is within one standard deviation of the average age. Assuming that all applicants' ages are integers and that the endpoints of the range are included, what is the maximum ... | [
"8",
"16",
"17",
"18"
] | C | Minimum age = Average - 1 Standard deviation = 20 - 8 = 12
Maximum age = average + 1 Standard deviation = 20+ 8 = 28
Maximum number of different ages of the applicants = 28 - 12 + 1 = 17
Answer C |
AQUA-RAT | AQUA-RAT-38935 | A batsman makes a score of 87 runs in the 17th inning and thus increases his averages by 3. What is his average after 17th inning? | [
"39",
"35",
"42",
"40.5"
] | A | let the average after 16th inning =x
then total run after 16th inning=16x
then total run after 17th inning=16x+87
then average run after 17th inning=(16x+87)/17
(16x+87)/17=x+3;
x=36;
average after 17th inning =36+3=39
ANSWER:A |
AQUA-RAT | AQUA-RAT-38936 | Set S consists of integers {8, 11, 12, 14, 15}. If integer n is included in the set, the average (arithmetic mean) of set S will increase by 25%. What is the value of integer n? | [
"28",
"32",
"36",
"40"
] | D | The average of the numbers in set S is 12.
If we increase the mean by 25%, the new mean is 15.
Thus, on average, 5 numbers increase by 5.
Therefore n = 15+25 = 40
The answer is D. |
AQUA-RAT | AQUA-RAT-38937 | There are 6 people and 6 chairs. In how many different ways people can occupy the chairs? | [
"360",
"500",
"420",
"720"
] | D | number of ways =6! = 720
Answer is D |
AQUA-RAT | AQUA-RAT-38938 | The edges of cuboid are 4 cm; 5 cm and 6 cm. Find its surface area? | [
"228",
"148",
"992",
"772"
] | B | 2(4*5 + 5*6 + 4*6) = 148
Answer: B |
AQUA-RAT | AQUA-RAT-38939 | The average score in an examination of 10 students of a class is 60. If the scores of the top five students are not considered, the average score of the remaining students falls by 5. The pass mark was 30 and the maximum mark was 100. It is also known that none of the students failed. If each of the top five scorers ha... | [
"89",
"90",
"92",
"99"
] | D | The average score in an examination of 10 students of a class is 60 --> the total score = 10*60 = 600;
The 5 smallest scores have an average of 55 --> the total score of the 5 smallest scores = 275.
From above, the total score of the 5 largest scores = 600 - 275 = 325.
Say the 5 largest scores are a, b, c, d, and e (wh... |
AQUA-RAT | AQUA-RAT-38940 | Let us say that a table tennis tournament was going on with knock out terms which means the one who loses the match is out of the tournament. 86 players took part in that tournament. How many matches were played? | [
"90 matches",
"95 matches",
"99 matches",
"85 matches"
] | D | D 85 matches. The number of matches will always sum up to one less than the number of players in a knock out tournament. You may calculate it in any manner. Thus 85 matches were played. |
AQUA-RAT | AQUA-RAT-38941 | The speed at which a man can row a boat in still water is 15 km/hr. If he rows downstream, where the speed of current is 3 km/hr, how many seconds will he take to cover 100 meters? | [
"14",
"16",
"18",
"20"
] | D | The speed of the boat downstream = 15 + 3 = 18 km/hr
18 km/hr * 5/18 = 5 m/s
The time taken to cover 100 meters = 100/5 = 20 seconds.
The answer is D. |
AQUA-RAT | AQUA-RAT-38942 | In a sports club with 30 members, 17 play badminton and 18 play tennis and 2 do not play either. How many members play both badminton and tennis? | [
"7",
"8",
"9",
"10"
] | A | Let x play both badminton and tennis so 17-x play only badminton and 19-x play only tennis. 2 play none and there are total 30 students. hence,
(17-x)+(18-x)+x+2=30
37-2x+x=30
37-x=30
x=7
So 7 members play both badminton and tennis.
A |
AQUA-RAT | AQUA-RAT-38943 | The positive value of x that satisfies the equation (1 + 2x)^3 = (1 + 3x)^4 is between
Bunuel, can you please explain this one? | [
"0 and 0.5",
"0.5 and 1",
"1 and 1.5",
"1.5 and 2"
] | B | Trial and error would probably be the easiest way to solve this problem. When x is large enough positive number, then because of the exponents (5>4), LHS will be more than RHS (as you increase the positive value of x the distance between the values of LHS and RHS will increase).
Try x=1 --> LHS=3^5=81*3=243 and RHS=4^4... |
AQUA-RAT | AQUA-RAT-38944 | The average of first five multiples of 2 is? | [
"6",
"8",
"9",
"5"
] | A | Average = 2(1 + 2 + 3 + 4 + 5)/5
= 30/5
= 6.
Answer:A |
AQUA-RAT | AQUA-RAT-38945 | When positive integer A is divided by positive integer B, the result is 9.44. Which of the following could be the integer B is ? | [
"11",
"44",
"24",
"25"
] | D | the remainder will be obtained from the decimal part when A is divided by B i.e. 0.44
0.44 = 44/100 = 11/25 so possible remainders are 11,22,33,44.
Only option A-11 satisfies this
for remainder 11,
A=236 and B=25
Ans - D |
AQUA-RAT | AQUA-RAT-38946 | Three persons invested Rs.9000 in a joint business. The second person invested Rs.1000 more than the first and the third Rs.1000 more than second. After two years, they gained Rs.3600. How much third person will get? | [
"2400",
"1600",
"2980",
"2707"
] | B | First persons investment = x
Second persons investment = x + 1000
Third persons investments = x + 2000
x + x + 1000 + x + 2000 = 9000
3x = 6000
x = 2000
Ratio = 2000 : 3000 : 4000
2:3:4
4/9 * 3600 = 1600
Answer:B |
AQUA-RAT | AQUA-RAT-38947 | If 10 crates have 98 apples each and how many apples more is required in order to make 100 apples in each crate? | [
"5",
"10",
"15",
"20"
] | D | Each crate requires 2 apples and totally there are 10 crates so required apples = 10 * 2 = 20
Answer: D |
AQUA-RAT | AQUA-RAT-38948 | A company that ships boxes to a total of 15 distribution centers uses color coding to identify each center. If either a single color or a pair of two different colors is chosen to represent each center and if each center is uniquely represented by that choice of one or two colors, what is the minimum number of colors n... | [
"8",
"7",
"6",
"5"
] | D | Back-solving is the best way to solve this problem.
You basically need 12 combinations (including single colors)
If we start from option 1->
1=> 4C2 + 4 = 10 (Not enough)
2=> 5C2 + 5 = 15 (Enough)
Since the minimum number is asked. It should be 5.
Answer - D |
AQUA-RAT | AQUA-RAT-38949 | What is the difference between the compound interest on Rs.12000 at 20% p.a. for one year when compounded yearly and half yearly? | [
"Rs.140",
"Rs.120",
"Rs.130",
"Rs.110"
] | B | When compounded annually, interest
= 12000[1 + 20/100]1 - 12000 = Rs.2400
When compounded semi-annually, interest
= 12000[1 + 10/100]2 - 12000 = Rs.2520
Required difference = 2520 - 2400 = Rs.120
ANSWER:B |
AQUA-RAT | AQUA-RAT-38950 | If the probability E of rain on any given day in city x is 50% what is the probability it with rain on exactly 3 days in a five day period? | [
"8/125",
"2/25",
"5/16",
"8/25"
] | C | 5C3 (1/2)^3(1/2)^2
= (5 * 4 * 3!)/2!3! * 1/32
E= 5/16
Answer - C |
AQUA-RAT | AQUA-RAT-38951 | The sector of a circle has radius of 28 cm and central angle 90o. Find its perimeter? | [
"100 cm",
"85 cm",
"75 cm",
"95 cm"
] | A | Perimeter of the sector = length of the arc + 2(radius)
= (90/360 * 2 * 22/7 * 21) + 2(28)
= 44 + 56 = 100 cm
Answer: A |
AQUA-RAT | AQUA-RAT-38952 | how many internal diagonals does a nonagon (nine sided polygon) have? | [
"25",
"27",
"40",
"56"
] | B | Number of diagonals in any polygon can be found using this formula: n(n-3)/2
Here n = 9
No. of diagonals = 9(9 - 3)/2
= 27
Ans B |
AQUA-RAT | AQUA-RAT-38953 | Students in Class I, II and III of a school are in the ratio of 3 : 5 : 8. Had 15 more students admitted to each class, the ratio would have become 6 : 8 : 11. How many total students were there in the beginning? | [
"112",
"64",
"96",
"80"
] | D | Explanation:
Increase in ratio for 3 classes is 6 - 3 = 8 - 5 = 11 - 8 = 3.
Given, 15 more students are admitted to each class.
Therefore, 3 :: 15 ⇒ 1 :: 5
Therefore, 3 + 5 + 8 = 16 :: 16 x 5 = 80.
Hence, total students in the beginning were 80.
Correct Option: D |
AQUA-RAT | AQUA-RAT-38954 | A voltmeter is used: | [
"22",
"266",
"27",
"26"
] | C | Explanation:
Answer: Option C |
AQUA-RAT | AQUA-RAT-38955 | Of the three-digit integers greater than 900, how many have two digits that are equal to each other and the remaining digit different from the other two? | [
" 90",
" 82",
" 80",
" 45"
] | A | Let the three digit number be represented as X Y Z.
There are 3 cases:
Case I.[ X=Y ]Z is not equal to XY :XXZorYYZ
X can be either 7, 8 or 9, so digit at X can be chosen in 3 ways
After X is chosen, Y can be chosen in 1 way
After XY are chosen, Z can be chosen in 9 ways
Thus, possible No of digits = (3 ways) * (1 way)... |
AQUA-RAT | AQUA-RAT-38956 | 0, 6, 18, 36, 60, 90, ?
What number should replace the question mark? | [
"126",
"120",
"119",
"126"
] | A | A 126
add 6, 12,18,24,..... |
AQUA-RAT | AQUA-RAT-38957 | In how many ways can 7 boys be seated in a circular order? | [
"120",
"360",
"420",
"720"
] | D | Number of arrangements possible = (7-1)!
= 6!
= 6*5*4*3*2*1
=720
Ans -D |
AQUA-RAT | AQUA-RAT-38958 | A grocer has a sale of Rs 6435, Rs. 6927, Rs. 6855, Rs. 7230 and Rs. 6562 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Rs, 6500 ? | [
"4991",
"4992",
"2777",
"2977"
] | A | Total sale for 5 months = Rs. (6435 + 6927 + 6855 + 7230 + 6562) = Rs. 34009.
Required sale = Rs.[(6500 x 6) - 34009]
= Rs. (39000 - 34009)
= Rs. 4991.
Answer: A |
AQUA-RAT | AQUA-RAT-38959 | A and B started a business investing Rs. 10,000 and Rs 20,000 respectively. In what ratio the profit earned after 2 years be divided between A and B respectively? | [
"3:2",
"9:2",
"18:20",
"1:2"
] | D | A: B = 10000 : 20000 = 1 : 2
ANSWER:D |
AQUA-RAT | AQUA-RAT-38960 | There is a circular table. It has 60 chairs. Drakula came and sit on a chair beside another person. What is the minimum no. of person will be so, that wherever he sits he always gets to sit beside a person | [
"30",
"20",
"15",
"10"
] | B | if total seats N = 5 in a circular arrangement ( _ _ M _ _ M ) where first ( _ ) is connected with last Man(M), then min no of persons required= 2.
similarly If N = 9, Man required = 3 i.e,( _ _ M _ _ M _ _ M )
If N= 12, Man required = 4 i.e, ( _ _ M _ _ M _ _ M _ _ M)
have u got any relation??
the no of man required i... |
AQUA-RAT | AQUA-RAT-38961 | An employer pays Rs.20 for each day a worker works and for felts Rs.3 for each day is ideal at the end of sixty days a worker gets Rs.280 . for how many days did the worker remain ideal? | [
"10",
"40",
"30",
"20"
] | B | Suppose a worker remained ideal for x days then he worked for 60-x days
20*(60-x)-3x=280
1200-23x=280
23x=920
x=40
Answer is B. |
AQUA-RAT | AQUA-RAT-38962 | If a and b are the two values of t that satisfy
the equation t2 – 6t + 8 = 0, with a > b, what is the value of a – b? | [
"2",
"4",
"6",
"8"
] | A | Factor the left side of the equation:
t2 – 6t + 8 = 0
(t – 2)(t – 4) = 0
Split this equation into two equations and solve:
t – 2 = 0 t – 4 = 0
t = 2 t = 4
Thus, a = 4 and b = 2. So a – b = 4 – 2 = 2.
correct answer A)2 |
AQUA-RAT | AQUA-RAT-38963 | A and B can do a piece of work in 11 days. With the help of C they finish the work in 5 days. C alone can do that piece of work in? | [
"15.5 days",
"19.5 days",
"17.5 days",
"9.2 days"
] | D | C = 1/5 – 1/11 = 6/55 => 9.2 days
ANSWER:D |
AQUA-RAT | AQUA-RAT-38964 | Rahul went to a shop and bought things worth Rs. 25, out of which 30 Paise went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items? | [
"Rs. 15",
"Rs. 12.10",
"Rs. 19.70",
"Rs. 16.80"
] | C | Explanation :
Total cost of the items he purchased = Rs.25
Given that out of this Rs.25, 30 Paise is given as tax
=> Total tax incurred = 30 Paise = Rs.30/100
Let the cost of the tax free items = x
Given that tax rate = 6%
∴ (25 − (30/100) − x)(6/100) = 30/100
⇒ 6(25 − 0.3 − x) = 30
⇒ (25 − 0.3 − x) = 5
⇒ x = 25 − 0.3 ... |
AQUA-RAT | AQUA-RAT-38965 | In an exam, Amar scored 64 percent, Bhavan scored 36 percent and Chetan 44 percent. The maximum score awarded in the exam is 500. Find the average mark scored by all the three boys? | [
"384",
"826",
"240",
"269"
] | C | Average mark scored by all the three boys =
[64/100 (500) + 36/100 (500) + 44/100 (500)] / 3
= 240
Answer: C |
AQUA-RAT | AQUA-RAT-38966 | Mike took a taxi to the airport and paid $2.50 to start plus $0.25 per mile. Annie took a different route to the airport and paid $2.50 plus $5.00 in bridge toll fees plus $0.25 per mile. If each was charged exactly the same amount, and Annie's ride was 22 miles, how many miles was Mike's ride? | [
"30",
"36",
"42",
"48"
] | C | The cost of Annie's ride was 2.5+5+(0.25*22) = $13
Let x be the distance of Mike's ride.
The cost of Mike's ride is 2.5+(0.25*x) = 13
0.25*x = 10.5
x = 42 miles
The answer is C. |
AQUA-RAT | AQUA-RAT-38967 | A dinner has to be hosted with 5 managers.Find the number of ways in which the managers may be selected from among 9 managers,if 2 managers will not attend the meeting together. | [
"1.35",
"2.None of these",
"3.12",
"4.126"
] | B | 9 managers, but two of them cannot attend the meeting together.
We can split it into two cases.
1. Meeting without these two managers in it. That would mean selecting 5, from the remaining 7 which is 7C5 = 21
2. Meeting with one of the two managers. select 1 manager from two, and then select 4 from the remaining 7, whi... |
AQUA-RAT | AQUA-RAT-38968 | Braun invested a certain sum of money at 8% p.a. simple interest for 'n' years. At the end of 'n' years, Braun got back 6 times his original investment. What is the value of n? | [
"50 years",
"25 years",
"62 years 6 months",
"37 years 6 months"
] | C | Explanatory Answer
Let us say Braun invested $100.
Then, at the end of 'n' years he would have got back $600.
Therefore, the Simple Interest earned = 600 - 100 = $500.
We know that Simple Interest = (Principal * number of years * rate of interest) / 100
Substituting the values in the above equation we get 500 = (100 * ... |
AQUA-RAT | AQUA-RAT-38969 | The cost price of a cow and a horse is 3 lakhs. The cow is sold at 20% profit and horse at 10% loss.Overall gain is Rs.4200. What is the cost price of the cow? | [
"113000",
"114000",
"115000",
"116000"
] | B | let costs of cow and horse are x,y so x+y=300000------(1)
(x*120/100)+(y*90/100)=304200
120x+90y=30420000------(2).
solve equations (1) and (2)
x=114000
ANSWER:B |
AQUA-RAT | AQUA-RAT-38970 | A committee of 3 has to be formed randomly from a group of 6 people. If Tom and Mary are in this group of 6, what is the probability that Tom will be selected into the committee but Mary will not? | [
"1/10",
"1/5",
"3/10",
"2/5"
] | C | We have three units - Tom (T), Mary (M) & the Rest (R).
Total ways of making a community of 3 from 6 people = 6 x 5 x 4 = 120
Now ways the community can be formed with Tom in it and Mary NOT in it:
TRR
RTR
RRT
TRR posb = 1 (way of picking Tom) x 4 (4 people left excluding Tom and Mary) x 3 (3 people left after excludin... |
AQUA-RAT | AQUA-RAT-38971 | 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? | [
"40",
"28",
"26",
"27"
] | A | Speed = 45 * 5/18 = 25/2 m/sec
Total distance covered = 360 + 140 = 500 m
Required time = 500 * 2/25 = 40 sec
Answer: A |
AQUA-RAT | AQUA-RAT-38972 | If 5% more is gained by selling an article for Rs. 360 than by selling it for Rs. 340, the cost of the article is? | [
"127",
"688",
"400",
"121"
] | C | Let C.P. be Rs. x.
Then, 5% of x = 360 - 340 = 20
x/20 = 20 => x = 400
Answer: C |
AQUA-RAT | AQUA-RAT-38973 | Difference between the length &breadth of a rectangle is 15m. If its perimeter is 206 m, then its area is? | [
"1400 m^2",
"2500 m^2",
"2520 m^2",
"1800 m^2"
] | D | Solving the two equations, we get: l = 45 and b = 40.
Area = (l x b) = (45 x 40) m2 = 1800 m^2
D |
AQUA-RAT | AQUA-RAT-38974 | By selling 8 pens for a rupee a woman loses 25%. How many for a rupee should he sell in order to gain 25%? | [
"2",
"14",
"3",
"5"
] | D | D
75% --- 8
125% --- ?
75/125 * 8 = 5 |
AQUA-RAT | AQUA-RAT-38975 | If the wheel is 10 cm then the number of revolutions to cover a distance of 1056 cm is? | [
"16.8",
"26",
"14",
"12"
] | A | 2 * 22/7 * 10 * x = 1056 => x
= 16.8
Answer: A |
AQUA-RAT | AQUA-RAT-38976 | If the price of rice rises from Rs. 6 per kg to Rs. 8 per kg, to have no increase in his expenditure on rice, a person will have to reduce his consumption of sugar by | [
"25",
"62",
"27",
"19"
] | A | Explanation:
Let original consumption = 100 kg and consumption = y kg.
So, 100 x 6 = y x 8
y = 75 kg
Reduction in consumption = 25 %.
ANSWER: A |
AQUA-RAT | AQUA-RAT-38977 | If the area of circle is 616 sq cm then its circumference? | [
"22",
"88",
"99",
"66"
] | B | 22/7 r2 = 616 => r = 14
2 * 22/7 * 14 = 88.Answer:B |
AQUA-RAT | AQUA-RAT-38978 | If x+y=25 and x^2y^3 + y^2x^3=25, what is the value of xy? | [
"0",
"1",
"2",
"3"
] | B | x^2*y^3 + y^2*x^3=25
=> x^2*y^2*(y+x)=25
=> x^2*y^2*25=25 [given, x+y=25]
=> (xy)^2 = 1
=> xy = 1
ANSWER:B |
AQUA-RAT | AQUA-RAT-38979 | The last time Rahul bought Diwali cards, he found that the four types of cards that he liked were priced Rs.4.50, Rs.5.50, Rs.8.00 and Rs.10.00 each. As Rahul wanted 40 cards, he took five each of two kinds and fifteen each of the other two, putting down the exact number of 10 rupees notes on the counter payment. How m... | [
"25",
"20",
"24",
"32"
] | D | Explanation :
Let the four cards be a, b ,c and d. 'x' be the number of notes.
Then, according to the question,
=> 5a + 5b + 15c + 15d = 10*x.
=> a + b + 3(c+d) = 2 * x . -----------------------------(i)
Since, a + b = 4.5+5.5 =10.
And,
=> c + d = 8+10=18
Putting these values in (i), we get :-
=> 10+ 3 * 18 = 2 * x.
=>... |
AQUA-RAT | AQUA-RAT-38980 | A family consists of grandparents, parents and three grandchildren. The average age of the grandparents is 67 years, that of the parents is 35 years and that of the grandchildren is 6 years. What is the average age of the family? | [
"38 5/7 years",
"31 5/7 years",
"81 5/7 years",
"31 9/7 years"
] | B | Required Average
= [(67 * 2) + (35 * 2 ) + (6 * 3)]/(2 + 2 + 3)
= (134 + 70 + 18)/7 = 31 5/7 years.
Answer:B |
AQUA-RAT | AQUA-RAT-38981 | A magician has five animals in his magic hat: 3 doves and 2 rabbits. If he pulls two animals out of the hat at random, what is the chance V that he will have a matched pair? | [
"V=2/5",
"V=3/5",
"1/5",
"1/2"
] | A | P(both doves) + P(both rabbits) = p(matched pair)
(3/5)*(2/4) + (2/5)*(1/4) = 2/5
Hi How did you get the probability 2/4 and 1/4???
You have 3 doves and 2 rabbits i.e. a total of 5 animals.
The probability that you pick a dove on your first pick is 3/5 (since there are 3 doves)
The probability that you pick a dove on y... |
AQUA-RAT | AQUA-RAT-38982 | Charlene's annual bonus is calculated in the following manner: Charlene receives 20 percent of her first $11,000 in sales and 32 percent of her sales in excess of $11,000. If Charlene received a bonus of $7,300, what were her annual sales? | [
"$ 18,687",
"$ 22,000",
"$ 24,000",
"$ 26,000"
] | A | Let x be the total sales in $.
For the 1st 11,000 you get 20% ---> 0.2*11000 = 2200$
For the remaining (x-11000) $, you get 32% ---> 0.32*(x-11000)
Thus, 0.32*(x-11000) + 2200 = 7300 ----> x= 18,687 $
A is thus the correct answer. |
AQUA-RAT | AQUA-RAT-38983 | If the perimeter of a rectangular garden is 600 m, its length when its breadth is 200 m is? | [
"299 m",
"777 m",
"200 m",
"100 m"
] | D | 2(l + 200) = 600 => l
= 100 m
Answer:D |
AQUA-RAT | AQUA-RAT-38984 | A 140 m long train is running at a speed of 55 Km/hr. It crossed a platform of length 520 m in ? | [
"41.1 sec",
"20.2 sec",
"31.8 sec",
"43.2 sec"
] | D | Speed = 55 Km/hr
(to convert km/hr in to M/s)
= 55 x 5/18 M/s
Distance = 140 m + 520 m ( If questions is about train crossing a post you need to consider only the length of Train, )
= 660 m
Time = Distance / Speed
= 660 x 18 / (5 x 55)
= 43.2 sec
Ans is :D |
AQUA-RAT | AQUA-RAT-38985 | If S is the sum of the reciprocals of the consecutive integers from 71 to 80, inclusive, which of the following is less than S?
I. 1/7
II. 1/8
III. 1/9
IV. 1/7>S >1/8 | [
"I",
"IV",
"II",
"III"
] | B | Since we summarize the reciprocals from 80 to 71, we can say also that we add ten numbers who are all (with one exception 1/80) greater than 1/80, so that the sum must be greater than 1/8.
On the other side we can say that we add the reciprocals from 71 to 80, so that the sum has to be less than the sum of ten times 1/... |
AQUA-RAT | AQUA-RAT-38986 | A ship sails 4 degrees north, then 13 S. then 17 N. then 19 S. and has finally 11 degrees of south latitude. What was her latitude at starting ? | [
"STARTED WITH EQUATOR",
"STARTER WITH NORTH POLE",
"STARTER WITH SOUTH POLE",
"STARTER WITH 80 DEGREE NORTH POLE"
] | A | Let x = the latitude sought.
Then marking the northings +, and the southings -;
By the statement x + 4 - 13 + 17 - 19 = -11
And x = 0. |
AQUA-RAT | AQUA-RAT-38987 | The product of the digits of the four-digit number E is 36. No two digits of are identical. How many different numbers are possible values of E ? | [
"6",
"12",
"24",
"36"
] | C | The main question here is how can you arrange 4 different digits E. We don't even need to find the number. from the question itself we know that there are 4 different digits and none of them is 0 as the product is non-zero.
Therefore no of ways to arrange 4 diff. digits is 4! which is 24
hence C |
AQUA-RAT | AQUA-RAT-38988 | A cricketer has a certain average for 10 innings. In the eleventh inning, he scored 108 runs, there by increasing his average by 6 runs. His new average is: | [
"48 runs",
"50 runs",
"70 runs",
"75 runs"
] | A | Let average for 10 innings be x. Then,
(10x + 108)/11 = x + 6
= 11x + 66 = 10x + 108
= x = 42.
New average = (x + 6) = 48 runs.
ANSWER A |
AQUA-RAT | AQUA-RAT-38989 | In a city where all streets run east-to-west, all avenues run north-to-south, and all intersections are right angles as shown below, Jessica needs to walk from the corner of 6th Street and 3rd Avenue to the corner of 1st Street and 1st Avenue. If Jessica will randomly choose from any route that allows her to walk the f... | [
"1/21",
"1/7",
"4/21",
"10/21"
] | C | She choose a route which allows her to walk fewest number of blocks
there are 2 blocks she will cross towards east moves represented by E,E and there will be 5 blocks she will cross towards south represented by S,S,S,S,S
total number of ways 7!5!2!7!5!2!
there are 4 ways she can cross 2 blocks on av.1 as shown in attac... |
AQUA-RAT | AQUA-RAT-38990 | At lovely gym class can be divided into 8 teams with an equal number of players on each team or into 12 teams with an equal number of players on each team. What is the lowest possible number of students in the class? | [
" 20",
" 24",
" 36",
" 48"
] | B | We are given that at lovely gym class can be divided into 8 teams or 12 teams, with an equal number of players on each team. Translating this into two mathematical expressions we can say, where G is the total number of students in the gym class, that:
G/8 = integer and G/12 = integer
This means that G is a multiple of ... |
AQUA-RAT | AQUA-RAT-38991 | What is the perimeter of a square with area 9p^2/25 ? | [
"3p/4",
"3p^2/4",
"12p/5",
"3p^2"
] | C | Area of square, (side)^2 = (3p/5)^2
Therefore side of the square = 3p/5
Perimeter of square = 4*side = 4* (3p/5) = 12p/5
Answer is C. |
AQUA-RAT | AQUA-RAT-38992 | A certain no. when divided by 35leaves aremainder 25, what is the remainder if the same no.be divided by 15? | [
"1",
"3",
"4",
"6"
] | C | Explanation:
35 + 25 = 60/15 = 4 (Remainder)
C |
AQUA-RAT | AQUA-RAT-38993 | Ritesh and Co. generated revenue of Rs. 2,500 in 2006. This was 12.5% of its gross revenue. In 2007, the gross revenue grew by Rs. 2,500. What is the percentage increase in the revenue in 2007? | [
"12.5%",
"20%",
"25%",
"50%"
] | A | Explanation :
Given, Ritesh and Co. generated revenue of Rs. 2,500 in 2006 and that this was 12.5% of the gross revenue.
Hence, if 2500 is 12.5% of the revenue, then 100% (gross revenue) is:
=>(100/12.5)×2500.
=>20,000.
Hence, the total revenue by end of 2007 is Rs. 10,000. In 2006, revenue grew by Rs. 2500. This is a ... |
AQUA-RAT | AQUA-RAT-38994 | Rose is two years older than Bruce who is twice as old as Chris. If the total of the age of Rose, B and Chris be 37 years, then how old is Chris ? | [
"7 years",
"10 years",
"12 years",
"13 years"
] | A | Let Chris's age be x years. Then, Bruce's age = 2x years.Rose's age = (2x + 2) years.
(2x + 2) + 2x + x = 37
5x = 35
x = 7
Hence, Chris's age =7 years.
Answer : A |
AQUA-RAT | AQUA-RAT-38995 | A clock shows the time as 12 a.m. If the minute hand gains 5 minutes every hour, how many minutes will the clock gain by 6 p.m.? | [
"45 minutes",
"55 minutes",
"35 minutes",
"30 minutes"
] | D | there are 6 hours in between 12 a.m. to 6 p.m.
6*5=30 minutes.
ANSWER:D |
AQUA-RAT | AQUA-RAT-38996 | The length of a rectangle is increased by 25% and its breadth is decreased by 20%. What is the effect on its area? | [
"1288",
"1299",
"1000",
"10000"
] | D | 100 * 100 = 10000
125 * 80 = 10000
Answer: D |
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