source string | id string | question string | options list | answer string | reasoning string |
|---|---|---|---|---|---|
AQUA-RAT | AQUA-RAT-37097 | A license plate in the country Kerrania consists of four digits followed by two letters. The letters A, B, and C are used only by government vehicles while the letters D through Z are used by non-government vehicles. Kerrania's intelligence agency has recently captured a message from the country Gonzalia indicating tha... | [
" 18/79",
" 16/900",
" 1/25",
" 1/50"
] | B | Everything is correct except that you assumed the letters can't be repeated. It can be repeated.
AA
BB
CC
AB, AC, BC, BA, CA, CB.
Thus; total government vehicles = (10)^2*(3)^2 = 100*9 = 900
Vehicles inspected within 3 hours = 60*3/12 = 16
P = 16/900
Ans:B |
AQUA-RAT | AQUA-RAT-37098 | Dan’s car gets 32 miles per gallon. If gas costs $4/gallon, then how many miles can Dan’s car go on $54 of gas? | [
"236",
"354",
"432",
"512"
] | C | 54/4 = 13.5 gallons
13.5*32 = 432 miles
The answer is C. |
AQUA-RAT | AQUA-RAT-37099 | Two assembly line inspectors, Lauren and Steven, inspect widgets as they come off the assembly line. If Lauren inspects every fifth widget, starting with the fifth, and Steven inspects every third, starting with the third, how many of the 95 widgets produced in the first hour of operation are not inspected by either in... | [
"50",
"43",
"45",
"55"
] | A | Widgets inspected by Lauren: ((95-5)/5)+1=18+1=19
Widgets inspected by Steven: ((93-3)/3)+1 =31+1 =32
Widgets inspected by both: ((90/15)+1 =6
Total : 19+32 -6=45
hence, widgets not inspected: 95-45=50
Option A |
AQUA-RAT | AQUA-RAT-37100 | Bob bikes to school every day at a steady rate of a miles per hour. On a particular day, Bob had a flat tire exactly halfway to school. He immediately started walking to school at a steady pace of y miles per hour. He arrived at school exactly t hours after leaving his home. How many miles is it from the school to Bob'... | [
"(a + y) / t",
"2(a + t) / ay",
"2ayt / (a + y)",
"2(a + y + t) / ay"
] | C | If we choose for d (distance): 10 miles, for a 10 and for y 5.
t would be 90 minutes or 1,5 hours.
If I try this for answer choice C it fits. |
AQUA-RAT | AQUA-RAT-37101 | A company has a job to prepare certain number of cans and there are three machines A, B and C for this job. A can complete the job in 2 days, B can complete the job in 5 days and C can complete the job in 7 days. How many days the company will it take to complete the job if all the machines are used simultaneously? | [
"71/59 days",
"70/59 days",
"3 days",
"12days"
] | B | Let the total number of cans to be prepared be 70.
The number of cans prepared by A in 1 day = 35.
The number of cans prepared by B in 1 day = 14.
The number of cans prepared by C in 1 day = 10.
Thus, the total number of cans that can be prepared by all the machines working simultaneously in a single day = 59.
Therefor... |
AQUA-RAT | AQUA-RAT-37102 | An error 4% in excess is made while measuring the side of a square. What is the percentage of error in the calculated area of the square? | [
"4.05%",
"4.02%",
"8.16%",
"3%"
] | C | Percentage error in calculated area
=(4+4+(4×4)/100)%
=8.16%
ANSWER:C |
AQUA-RAT | AQUA-RAT-37103 | The average of five numbers is 60. If one number is excluded, the average becomes 65. The excluded number is? | [
"40",
"6",
"58",
"35"
] | A | Excluded number
= (60 * 5) - (65 * 4)
= 300 - 260 = 40
Answer:A |
AQUA-RAT | AQUA-RAT-37104 | Anil invested a sum of money at a certain rate of simple interest for a period of five years. Had he invested the sum for a period of eight years for the same rate, the total intrest earned by him would have been sixty percent more than the earlier interest amount. Find the rate of interest p.a. | [
"5352",
"5355",
"2789",
"2689"
] | B | Let the sum lent by Manoj to Ramu be Rs.P.
Amount gained by Manoj = P. 3.9 /100 = 3450.3.6/100
= Rs.824.85
27P = 62100
= 82485
P = (82485 + 62100)/27 = 3055 + 2300
= Rs.5355
Answer: B |
AQUA-RAT | AQUA-RAT-37105 | What is the 100th digit of (3!*5! + 4!*3!)/2? | [
"4",
"3",
"2",
"7"
] | A | (3!*5! + 4!*3!)/2
=3!(5! + 4!)/2
=6 (120+24)/2
=432
100th digit of the above product will be equal to 4
Answer A |
AQUA-RAT | AQUA-RAT-37106 | From a nine-member dance group, five will be chosen at random to volunteer at a youth dance event. If Kori and Jason are two of the nine members, what is the probability that both will be chosen to volunteer? | [
"a) 1/21",
"b) 35/2",
"c) 4/21",
"d) 2/7"
] | B | Total number of ways to choose 5 out of 9 = 9C5 = 144.
Number of ways to choose 2 (any but Kori and Jason) out of 7 (excluding Kori and Jason) = 7C2 = 2520.
P = favorable/total = 2520/144 = 35/2.
Answer: B. |
AQUA-RAT | AQUA-RAT-37107 | A began business with Rs.45000 and was joined afterwards by B with Rs.5400. When did B join if the profits at the end of the year were divided in the ratio of 2:1? | [
"6",
"9",
"7",
"5"
] | C | 45*12 : 54*x = 2: 1
x = 5
12 -5 = 7
Answer: C |
AQUA-RAT | AQUA-RAT-37108 | W is an even integer greater than 300,000 and smaller than 1,000,000. How many numbers can W be? | [
"300,000",
"349,999",
"350,000",
"399,999"
] | B | W 1,000,000-300,000=700,000 integers
700,000/2= 350,000 even integers.
350,000+1 inclusive. But since 1,000,000 and 300,000 are not included.
350,001-2=349,999
B |
AQUA-RAT | AQUA-RAT-37109 | If the letters of the word PLACE are arranged taken all at a time, find how many do not start with AE | [
"110",
"114",
"118",
"120"
] | B | Total no'of arrangements 5P5 = 5! = 120
no'of arrangements start with AE = 1 × 6 = 6
no'of arrangements which do not start with AE = 120 - 6 = 114.
B) |
AQUA-RAT | AQUA-RAT-37110 | At a recent small town election for mayor a total of 967 votes were cast for the four candidates, the winner exceeding his opponents by 53, 79 and 105 votes, respectively. How many votes were cast for the candidate in fourth place? | [
"134",
"178",
"196",
"166"
] | C | The number of votes the winning candidate received was
967 + 53 + 79 + 105 /4= 301.
The fourth place received 301 – 105 = 196.
C |
AQUA-RAT | AQUA-RAT-37111 | Find the value of x from the below equation? : x^2+5x+4 = 0 | [
"1",
"-3",
"3",
"2"
] | B | a = 1, b = 5, c = 4
x1,2 = (-5 ± √(5^2 - 4×1×4)) / (2×1) = (-5 ± √(25-16)) / 2 = (-5 ± 3) / 2
x1 = (-5 + 3)/2 = -2/2 = -1
x2 = (-5 - 1)/2 = -6/2 = -3
B |
AQUA-RAT | AQUA-RAT-37112 | In a sequence of 39 numbers, each term, except for the first one, is 7 less than the previous term. If the greatest term in the sequence is 281, what is the smallest term in the sequence? | [
"2",
"-2",
"0",
"18"
] | D | Which term is the greatest? The first or the last? It is given to you that every term is 7 less than the previous term. Hence as you go on, your terms keep becoming smaller and smaller. The first term is the greatest term.
An = 281 + (39- 1)*(-7)
An = 281 - 266 = 15
D |
AQUA-RAT | AQUA-RAT-37113 | Arun borrowed a certain sum from Manish at a certain rate of simple interest for 2 years. He lent this sum to Sunil at the same rate of interest compounded annually for the same period. At the end of two years, he received Rs. 2400 as compound interest but paid Rs. 2000 only as simple interest. Find the rate of interes... | [
"20%",
"10%",
"40%",
"50%"
] | C | Explanation:
Let the sum be x
Simple interest on x for 2 years = Rs.2000
Simple interest = PRT/100
2000 = x × R × 2100
⇒ xR = 100000 --- (1)
Compound Interest on x for 2 years = 2400
P(1+R/100)T−P=2400
x(1+R/100)2 − x = 2400
x(1+2R/100 + R2/10000) − x = 2400
x(2R/100 + R2/10000) = 2400
2xR/100 + xR2/10000 = 2400 --- (2... |
AQUA-RAT | AQUA-RAT-37114 | A man sells a horse for Rs.600 and loses something, if he had sold it for Rs.720 , his gain would have been double the former loss. Find the cost price of the horse? | [
"27",
"98",
"27",
"40"
] | D | CP = SP + 1CP = SP - g
600 + x = 720 - 2x
3x = 120 => x = 40
Answer:D |
AQUA-RAT | AQUA-RAT-37115 | In what ratio must a grocer mix rice worth Rs.60 a kg and Rs.65 a kg.So that by selling the mixture at Rs. 68.20 a kg, He may gain 10%? | [
"1:2",
"3:2",
"4:5",
"1:3"
] | B | S.P of 1kg mix = RS.68.20,
Gain = 10% C.P of 1kg mix =Rs.(100/110 x 68.20) =Rs.62 = 3 : 2
ANSWER B |
AQUA-RAT | AQUA-RAT-37116 | A and B enter into partnership with capitals in the ratio 3 : 4. At the end of 10 months A withdraws,and the profits now are divided in the ratio of 5 : 4. Find how long B remained in the business? | [
"9 months",
"8 months",
"7 months",
"6 months"
] | D | Initially A’s investment = 3x and B’s investment = 4x
Let B remain in the business for ‘n’ months.
⇒ 3x × 10 : 4x × n = 5 : 4
∴ 3x × 10 × 4 = 4x × n × 5
⇒ n = 6
Answer D |
AQUA-RAT | AQUA-RAT-37117 | A group of hikers is planning a trip that will take them up a mountain using one route and back down using another route. They plan to travel down the mountain at a rate of one and a half times the rate they will use on the way up, but the time each route will take is the same. If they will go up the mountain at a rate... | [
"16",
"17",
"18",
"19"
] | C | On the way down, the rate is 1.5*6 = 9 miles per day.
The distance of the route down the mountain is 2*9 = 18 miles.
The answer is C. |
AQUA-RAT | AQUA-RAT-37118 | Peter is a trail runner who decides to take a day off work to run up and down a local mountain. He runs uphill at an average speed of 4 miles per hour and returns along the same route at an average speed of 6 miles per hour. Of the following, which is the closest to his average speed, in miles per hour, for the trip up... | [
" 4.8",
" 5.8",
" 6.0",
" 6.3"
] | A | to calculate average of 2 speeds a and b when distance is constant
Formula - 2ab/(a+b)
Here Peter's uphill speed = 4 mph
Peter's downhill speed = 6 mph
2*4*6/(4+6) = 48/10 = 4.8
Correct answer - A |
AQUA-RAT | AQUA-RAT-37119 | Calculate the different number of ways 7 boys and 2 girls can sit on a bench? | [
"362881",
"362880",
"311880",
"362280"
] | B | npn = n!
9p9 = 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 = 362880
B |
AQUA-RAT | AQUA-RAT-37120 | The population of a town increased from 1,75,000 to 2,10,000 in a decade. The average percent increase of population per year is | [
"2%",
"5%",
"6%",
"8.75%"
] | A | Solution
Increase in 10 years = (210000 - 175000)
= 35000.
Increase% = (35000/175000×100)%
= 20%.
Required average = (20/10)%
= 2%.
Answer A |
AQUA-RAT | AQUA-RAT-37121 | Mysoon collects glass ornaments. Ten more than 1/6 of the ornaments in her collection are handmade, and 1/2 of the handmade ornaments are antiques. If 1/6 of the ornaments in her collection are handmade antiques, how many ornaments are in her collection? | [
"36",
"60",
"108",
"60"
] | D | The number of ornaments = a
Ten more than 1/6 of the ornaments in her collection are handmade => Handmade = 10+a/6
1/2 of the handmade ornaments are antiques => Handmade ornaments = 1/2*(10+a/6) = 5 + a/12
1/6 of the ornaments in her collection are handmade antiques => Handmade ornaments = a/6
=> 5 + a/12 = a/6 => a = ... |
AQUA-RAT | AQUA-RAT-37122 | The smallest 4 digit prime number is? | [
"A)101",
"B)1003",
"C)109",
"D)113"
] | B | The smallest 3-digit number is 1000, which is divisible by 2.
1000 is not a prime number.
1003< 11 and 101 is not divisible by any of the prime numbers 2, 3, 5, 7, 11.
1003 is a prime number.
Hence 1003 is the smallest 4-digit prime number.
B) |
AQUA-RAT | AQUA-RAT-37123 | The smallest number which when divided by 20, 25, 35 and 40 leaves a remainder of 14, 19, 29 and 34 respectively is? | [
"1994",
"1494",
"1349",
"1496"
] | C | LCM = 1400
1400 - 6 = 1394
ANSWER:C |
AQUA-RAT | AQUA-RAT-37124 | a bank was to give a loan out to a newly married couple for 800,000 with no interest for 2 years and raise the price to 900,000 after 2 years. what is the interest rate? | [
"17%",
"13%",
"12%",
"7%"
] | D | for 0 years = (900,000- 800,000) = 100,000.
for 2 years = (100,000 x 2)/2= 100,000
Principal = (800,000 - 100,000) = 700,000.
Hence, rate = (100 x 100,000)/(700,000x2) = 7% ANSWER: D |
AQUA-RAT | AQUA-RAT-37125 | A horse chases a pony 8 hours after the pony runs. Horse takes 12 hours to reach the pony. If the average speed of the horse is 320 kmph, what s the average speed of the pony? | [
"182kmph",
"192kmph",
"193kmph",
"196kmph"
] | B | pony take 20 hours and horse take 12 hours...then Distance chased by them is 320*12.so speed of pony is (320*12)/20=192kmph.
ANSWER IS B |
AQUA-RAT | AQUA-RAT-37126 | How much time will take for an amount of Rs. 480 to yield Rs. 81 as interest at 4.5% per annum of simple interest? | [
"8 years",
"4 years",
"3 years 9 months",
"9 years"
] | C | Time = (100 * 81) / (480 * 4.5)
= 3 years 9 months
Answer: C |
AQUA-RAT | AQUA-RAT-37127 | A, B and C invests Rs.2000, Rs.3000 and Rs.4000 in a business. After one year A removed his money; B and C continued the business for one more year. If the net profit after 2 years be Rs.3200, then A's share in the profit is? | [
"388",
"299",
"266",
"400"
] | D | 2*12 : 3*12 : 4*24
1: 3: 4
1/8 * 3200 = 400.Answer: D |
AQUA-RAT | AQUA-RAT-37128 | 195,383,575,763,955,___ | [
"1153",
"1143",
"1243",
"1343"
] | B | 19*1 = 19 5
19*2 = 38 3
19*3 = 57 5
19*4 = 76 3
19*5 = 95 5
19*6 = 114 3
so ans=1143
ANSWER:B |
AQUA-RAT | AQUA-RAT-37129 | Find the number of ways of arranging the letters of the word "MATERIAL" such that all the vowels in the word are to come together? | [
"1446",
"1440",
"1444",
"1441"
] | B | In the word, "MATERIAL" there are three vowels A, I, E.
If all the vowels are together, the arrangement is MTRL'AAEI'.
Consider AAEI as one unit. The arrangement is as follows.
M T R L A A E I
The above 5 items can be arranged in 5! ways and AAEI can be arranged among themselves in 4!/2! ways.
Number of required ways o... |
AQUA-RAT | AQUA-RAT-37130 | In a manufacturing plant, it takes 36 machines 8 hours of continuous work to fill 8 standard orders. At this rate, how many hours of continuous work by 72 machines are required to fill 12 standard orders? | [
"3",
"6",
"8",
"9"
] | B | the choices give away the answer..
36 machines take 4 hours to fill 8 standard orders..
in next eq we aredoubling the machines from 36 to 72, but thework is not doubling(only 1 1/2 times), = 8*36/72*12/8 = 6
Ans B |
AQUA-RAT | AQUA-RAT-37131 | A sum of money deposited at C.I. amounts to Rs.6000 in 6 years and to Rs.7500 in 7 years. Find the rate percent? | [
"25%",
"20%",
"15%",
"10%"
] | A | 6000 --- 1500
100 --- ? => 25%
Answer: A |
AQUA-RAT | AQUA-RAT-37132 | In what time will a train 120 m long cross an electric pole, it its speed be 144 km/hr? | [
"3 sec",
"2.9 sec",
"3.5 sec",
"7.5 sec"
] | A | Speed = 144 * 5/18 = 40 m/sec
Time taken = 120/40
= 3 sec.
Answer: A |
AQUA-RAT | AQUA-RAT-37133 | The speeds of three motor bikes are in the ratio 6 : 5 : 4. The ratio between the time taken by them to
travel the same distance is : | [
"10 : 12 : 15",
"12 : 10 : 8",
"15 : 12: 10",
"10 : 15 : 12"
] | A | Expl : Ratio of time taken : 1/6 :1/5 : 1/4 = 10 : 12 : 15
Answer: A |
AQUA-RAT | AQUA-RAT-37134 | A sum of money at simple interest amounts to $ 780 in 3 years and to $930 in 4 years. The sum is: | [
"$153",
"$698",
"$330",
"$549"
] | C | C
$330
S.I. for 1 year = $(930 - 780) = $150.
S.I. for 3 years = $(150 x 3) = $450.
Principal = $(780 - 450) = $330. |
AQUA-RAT | AQUA-RAT-37135 | A student chose a number, multiplied it by 2, then subtracted 138 from the result and got 102. What was the number he chose? | [
"240",
"120",
"150",
"200"
] | B | Let x be the number he chose, then
2⋅x−138=102
2x=240
x=120
So answer is B |
AQUA-RAT | AQUA-RAT-37136 | In how many ways can the letters {U, R, R, R, R} be arranged? | [
"5",
"20",
"120",
"720"
] | A | My answer : A
There is 5! ways to arrange those letters in total, however letter U repeats 1! times and letter R repeats 4! times
=> the way to arrange without repeating = 5!/ [1!x4!] = 5 |
AQUA-RAT | AQUA-RAT-37137 | A local elementary school has 1049 students and nine teachers, How many students would have to be added to the school to make sure each teacher has the same amount of students in their classroom? | [
"4",
"6",
"5",
"1"
] | A | Using the rule on the divisibility of nine, we add the digits of 1049 together to get 14. Since we are doing addition, the next number that is divisible by nine would be 18. Therefore, our answer 4(option A) |
AQUA-RAT | AQUA-RAT-37138 | A and B entered into a partnership investing Rs.25000 and Rs.30000 respectively. After 4 months C also joined the business with an investment of Rs.35000. What is the share of C in an annual profit of Rs.47000? | [
"14028",
"14038",
"14079",
"14000"
] | D | 25*12: 30*12: 35*8
15:18:14
14/47 * 47000 = 14000
Answer:D |
AQUA-RAT | AQUA-RAT-37139 | If the roots of a quadratic equation are 20 and -7, then find the equation? | [
"x2 + 13x - 140 = 0",
"x2 - 13x + 140 = 0",
"x2 - 13x - 140 = 0",
"x2 + 13x + 140 = 0"
] | C | Explanation:
Any quadratic equation is of the form
x2 - (sum of the roots)x + (product of the roots) = 0 ---- (1)
where x is a real variable. As sum of the roots is 13 and product of the roots is -140, the quadratic equation with roots as 20 and -7 is: x2 - 13x - 140 = 0.
ANSWER IS C |
AQUA-RAT | AQUA-RAT-37140 | 38, 87, 22,76, 31,47, 13, 82
Which of the following numbers is greater than three-fourth of the numbers but less than one-fourth of the numbers in the list above? | [
"a- 55",
"b- 68",
"c- 79",
"d- 81"
] | C | Important:- Arrange the numbers in ascending order first.
13, 22, 31, 38, 47, 76, 82, 87
3/4th of the number list represents- 76 (6th number)
remaining 1/4th list represents 82 (7 th number)
79 fits in between above 2
Answer:- C |
AQUA-RAT | AQUA-RAT-37141 | Find the least number which when divided by 5,6,7, and 8 leaves a remainder 3, but when divided by 9 leaves no remainder . | [
"1638",
"1863",
"1683",
"1836"
] | C | L.C.M. of 5,6,7,8 = 840.
Required number is of the form 840k + 3
Least value of k for which (840k + 3) is divisible by 9 is k = 2.
Required number = (840 X 2 + 3)=1683
Answer is C. |
AQUA-RAT | AQUA-RAT-37142 | Tom and John traveled in the same direction along the equal route at their constant speed rates of 15 km per hour and 10 km per hour, respectively. After 15 minutes Tom passed John, Tom reaches a certain Gas station, how many T minutes it takes John to reach the station? | [
"5 min",
"6 min",
"7 and 1/2 min",
"8 min"
] | C | Since the question states “after 15 minutes”, we can say Tom traveled 15/4km for 15 minutes as he can travel 15km per hour. Hence, using the same logic, we can say John traveled 10/4km as he travels 10km per hour. So, John has to travel (15/4)-(10/4)km=5/4km more. Since John’s speed is 10km/hour, which means 1km/6minut... |
AQUA-RAT | AQUA-RAT-37143 | How many 1/4s are there in 37 1/2? | [
"150",
"450",
"500",
"650"
] | A | Required number = (75/2)/(1/4)
= (75/2 x 4/1)
= 150.
ANSWER:A |
AQUA-RAT | AQUA-RAT-37144 | When a certain number X is divided by 52, the remainder is 19. What is the remainder when X is divided by 7? | [
"2",
"3",
"4",
"5"
] | D | When a certain number X is divided by 52, the remainder is 19. What is the remainder when X is divided by 7?
Putting a value say x = 19 we get remainder as 19 when divided by 52.
When 19 divided by 7 we get 5 as remainder.
D is the answer. |
AQUA-RAT | AQUA-RAT-37145 | A cycle is bought for Rs.800 and sold for Rs.1080, find the gain percent? | [
"22",
"20",
"35",
"88"
] | C | 800 ---- 180
100 ---- ? => 35%
Answer:C |
AQUA-RAT | AQUA-RAT-37146 | The cost of producing x tools by a company is given by
C(x) = 2500 x + 5500 (in $)
a) What is the cost of 100 tools? | [
"222500 $",
"125800 $",
"225900 $",
"255500 $"
] | D | Solution
C(100) = 2500*100 + 5500 = 255500 $
Answer D |
AQUA-RAT | AQUA-RAT-37147 | If n is an integer, then the least possible value of |31 - 4n| is? | [
"0",
"1",
"2",
"3"
] | B | |31 - 4n| represents the distance between 31 and 4n on the number line. Now, the distance will be minimized when 4n, which is multiple of 4, is closest to 31. Multiple of 4 which is closest to 31 is 32 (for n = 8),
so the least distance is 1: |31 - 32| = 1.
Answer: B. |
AQUA-RAT | AQUA-RAT-37148 | A can do a job in 10days and B in 20days. If they work on it together for 4 days, then the fraction of the work that is left is? | [
"2/5",
"8/15",
"3/11",
"1/12"
] | A | A's 1 day work = 1/10
B's 1day work = 1/20
A+B 1day work = 1/10 + 1/20 = 3/20
A+B 4days work = 3/20*4 = 3/5
Remaining work = 1 - 3/5 = 2/5
Answer is A |
AQUA-RAT | AQUA-RAT-37149 | Which of the following inequalities is equivalent to −4 < x < 8? | [
"|x - 1| < 7",
"|x + 2| < 6",
"|x + 3| < 5",
"|x - 2| < 6"
] | D | We know that |x| < a means -a < x < a, where Sum of lower limit of x (i.e -a) and the upper limit of x (i.e a), is 0
Given is, -4 < x < 8, let's say by adding y to this inequality we will get into the above format
-4+y < x+y < 8+y
Now, to move this into the mod format, we need to have (-4+y) + (8+y) = 0 => y = -2
Thus,... |
AQUA-RAT | AQUA-RAT-37150 | If (x - 1)^2 = 324, which of the following could be the value of x - 3? | [
"17",
"15",
"13",
"-20"
] | D | (x - 1)^2 = 324
(x - 1) = 18 or -18
x = 19 or -17
x - 3 = 16 or -20
The answer is D. |
AQUA-RAT | AQUA-RAT-37151 | The average of five numbers is 27. If one number is excluded, the average becomes 20. The excluded number is? | [
"52",
"53",
"54",
"55"
] | D | Excluded number = (27 * 5) - (20 * 4)
= 135 - 80
= 55.
Answer: D |
AQUA-RAT | AQUA-RAT-37152 | If the average (arithmetic mean) of the four numbers K, 2K + 3, 3K – 5 and 5K + 1 is 118, what is the value of K? | [
" 11",
" 15 3/4",
" 22",
" 118"
] | D | K + 2K +3 + 3K - 5 + 5K +1 = 11K -1
(11K -1)/4 = 118
11K = 118 * 4 +1 = 472 +1 = 473
K = 473 / 11 = 43.
Answer D. |
AQUA-RAT | AQUA-RAT-37153 | A boy was asked to multiply a number by 22. He instead multiplied the number by 44 and got the answer 308 more than the correct answer. What was the number to be multiplied? | [
"10",
"12",
"08",
"14"
] | D | Let the number be x
22x + 308 = 44x
=> 44x - 22x = 308
=> 22x = 308
=> x = 308/22 = 154/11 = 14
Answer is D. |
AQUA-RAT | AQUA-RAT-37154 | The average weight of 2 person's increases by 4.5 kg when a new person comes in place of one of them weighing 65 kg. What might be the weight of the new person? | [
"74 kg",
"76.5 kg",
"85 kg",
"78"
] | A | Explanation:
Total weight increased = (2 x 4.5) kg = 9 kg.
Weight of new person = (65 + 9) kg = 74 kg.
Answer: A |
AQUA-RAT | AQUA-RAT-37155 | A pair of articles was bought for $720 at a discount of 10%. What must be the marked price of each of the article? | [
"$300",
"$500",
"$350",
"$400"
] | D | S.P. of each of the article = 720/2 = $360
Let M.P = $x
90% of x = 360
x = 360*100/90 =$400
Answer is D |
AQUA-RAT | AQUA-RAT-37156 | A pipe can filled a tank in 40 minutes and another pipe can empty it in 1hour. If the tank is already half full and both the taps are opened together, then the tank is filled in how many minutes? | [
"25min",
"20min",
"15min",
"10min"
] | A | T = 1/2 (25*50 / 50-25) = 25 minutes
Tank is filled in 25 minutes
Answer is A |
AQUA-RAT | AQUA-RAT-37157 | Two people P Q start a race in a circular track in opposite way different but constant speed. First they meet 900m cw from the starting pt. Then they meet 800m ccw from the starting pt. What's the circumference of the circle. | [
"2600",
"2700",
"2800",
"2900"
] | A | when they first met 900m cw from the starting pt.
second time, they will meet at 1800 m cw from starting point which is 800 m CCW from starting point.
so circumference of circle = 1800+800 = 2600 m
ANSWER:A |
AQUA-RAT | AQUA-RAT-37158 | In a triangle, the ratio of two angles is 7:2, and the third angle is the difference between the first two angles. What is the smallest angle, in degrees? | [
"90/11",
"120/7",
"150/11",
"180/7"
] | D | the three angles are 7x, 2x, and (7x-2x)=5x for some value x (to create the ratio)
the three angles of a triangle add up to 180, so 7x+2x+5x = 180
14x = 180
x=180/14
x = 90/7
the smallest angle is 2x = 2*(90/7) = 180/7
D |
AQUA-RAT | AQUA-RAT-37159 | Ravi and sunil are partners in a business. Ravi invests Rs.12,000 for 4 months and Sunil invested Rs.10000 for 5 months then after one year ratio of their profits will be | [
"1:3",
"2:3",
"24:25",
"20:22"
] | C | =(12000*4):(10000*5)
=48000:50000
=24:25
ANSWER:C |
AQUA-RAT | AQUA-RAT-37160 | A train covers a distance in 50 min, if it runs at a speed of 48kmph on an average. The speed at which the train must run to reduce the time of journey to 50min will be. | [
"60 km/h",
"55 km/h",
"48 km/h",
"70 km/h"
] | C | Time=50/60 hr=5/6hr
Speed=48mph
distance=S*T=48*5/6=40km
time=50/60hr=5/6hr
New speed = 40* 6/5 kmph= 48kmph
Answer : C |
AQUA-RAT | AQUA-RAT-37161 | 135 kg of an alloy A is mixed with 145 kg of alloy B. If alloy A has lead and tin in the ratio 3:5 and alloy B has tin and copper in the ratio 2:3, then the amount of tin in the new alloy is? | [
"100.6kg",
"142kg",
"135kg",
"110.8kg"
] | B | Quantity of tin in 135kg of A = 135*5/8 = 84kg
Quantity of tin in 145kg of B = 145*2/5 = 58kg
Quantity of tin in the new alloy = 84+58 = 142kg
Answer is B |
AQUA-RAT | AQUA-RAT-37162 | Carrie likes to buy t-shirts at the local clothing store. They cost $9.65 each. One day, she bought 12 t-shirts. How much money did she spend? | [
"$115.8",
"$248.75",
"$200",
"$171.6"
] | A | $9.65*12=$115.8. Answer is A. |
AQUA-RAT | AQUA-RAT-37163 | On Thursday Mabel handled 90 transactions. Anthony handled 10% more transactions than Mabel, Cal handled 2/3rds of the transactions that Anthony handled, and Jade handled 14 more transactions than Cal. How much transactions did Jade handled? | [
"80",
"81",
"82",
"83"
] | A | Solution:
Mabel handled 90 transactions
Anthony handled 10% more transactions than Mabel
Anthony = 90 + 90 × 10%
= 90 + 90 × 0.10
= 90 + 9
= 99
Cal handled 2/3rds of the transactions than Anthony handled
Cal = 2/3 × 99
= 66
Jade handled 14 more transactions than Cal.
Jade = 66 + 14
= 80
Jade handled = 80 transactions.
... |
AQUA-RAT | AQUA-RAT-37164 | The length of a rectangle is twice its breadth. If its length is decreased by 5 cm and breadth is increased by 5 cm, the area of the rectangle is increased by 70 sq. cm. Find the length of the rectangle. | [
"12cm",
"14cm",
"16cm",
"18cm"
] | D | Explanation:
Let breadth = x. Then, length = 2x. Then,
(2x - 5) (x + 5) - 2x * x = 70 => 5x - 25 = 70 => x = 18.
Length of the rectangle = 18 cm.
Answer: Option D |
AQUA-RAT | AQUA-RAT-37165 | A batsman in his 11th inning makes a score of 69 and their by increasing his average by 1. What is his average after the 11th inning? | [
"58",
"59",
"68",
"69"
] | B | 10x + 69 = 11(x + 1)
x = 58 + 1 = 59
Answer:B |
AQUA-RAT | AQUA-RAT-37166 | A man sells a horse for Rs.800 and loses something, if he had sold it for Rs.980, his gain would have been double the former loss. Find the cost price of the horse? | [
"27",
"98",
"27",
"60"
] | D | CP = SP + 1CP = SP - g
800 + x = 980 - 2x
3x = 180 => x = 60
Answer:D |
AQUA-RAT | AQUA-RAT-37167 | In how many different number of ways 7 boys and 4 girls can sit on a shopa which can accommodate 3 persons? | [
"800",
"900",
"200",
"990"
] | D | Option 'D'
11p3 = 11x10x9 = 990 |
AQUA-RAT | AQUA-RAT-37168 | Sun Life Insurance company issues standard, preferred and ultra-preferred policies. Among the company's policy holders of a certain age, 50 are standard with the probability of 0.01 dying in the next year, 30 are preferred with a probability of 0.008 of dying in the next year and 20 are ultra-preferred with a probabili... | [
"0.1591",
"0.2727",
"0.375",
"0.2767"
] | B | Explanation :
The percentage of three different types of policy holders and the corresponding probability of dying in the next 1 year are as follow :
Type, Standard, Preferred, Ultra-Preferred
Percentage , 50 , 30, 20
Probability, 0.01 , 0.008, 0.007
The expected number of deaths among all the policy holders of the giv... |
AQUA-RAT | AQUA-RAT-37169 | A train 100 meters long completely crosses a 300 meters long bridge in 45 seconds. What is the speed of the train is? | [
"25 kmph",
"32 kmph",
"40 kmph",
"38 kmph"
] | B | S = (100 + 300)/45 = 400/45 * 18/5 = 32 kmph
answer :B |
AQUA-RAT | AQUA-RAT-37170 | Nine friends are planning to attend a concert. If another friend also goes with them, they will get a group discount on their tickets. If the new total price of the tickets with the group discount is the same as the original total price of the tickets without the group discount, how much is the discount? | [
"5%",
"10%",
"20%",
"25%"
] | B | Let x be the original price of one ticket.
The total original cost is 9x.
The new cost is 10y, where y is the discounted price of one ticket.
9x = 10y
y = 9x/10 = 0.9x which is a discount of 10%.
The answer is B. |
AQUA-RAT | AQUA-RAT-37171 | A certain sum of money is divided among A, B and C so that for each Rs. A has, B has 65 paisa and C 40 paisa. If C's share is Rs.40, find the sum of money? | [
"228",
"267",
"911",
"205"
] | D | A:B:C = 100:65:40
= 20:13:8
8 ---- 40
41 ---- ? => Rs.205
Answer: D |
AQUA-RAT | AQUA-RAT-37172 | A rectangular park 60 m long and 40 m wide has two concrete crossroads running in the middle of the park and rest of the park has been used as a lawn. If the area of the lawn is 2109 sq. m, then what is the width of the road? | [
"2.91 m",
"3 m",
"5.82 m",
"None of these"
] | B | Explanation:
Area of the park = (60 x 40) m2 = 2400 m2
Area of the lawn = 2109 m2
Area of the crossroads = (2400 - 2109) = 291
Let the width of the road be x metres. Then,
60x + 40x - x2 = 291
=> x2 - 100x + 291 = 0
=> (x - 97)(x - 3) = 0
=> x = 3
Answer: B |
AQUA-RAT | AQUA-RAT-37173 | 15.06 * 0.000001 = ? | [
"15060000",
"0.001506",
"0.01506",
"1.506e-05"
] | D | Explanation:
Clearly after decimal 8 digits should be there.
Option D |
AQUA-RAT | AQUA-RAT-37174 | How many 3-letter words with or without meaning, can be formed out of the letters of the word, 'LOGARITHMS', if repetition of letters is not allowed? | [
"720",
"420",
"450",
"350"
] | A | Explanation:
The word 'LOGARITHMS' has 10 different letters.
Hence, the number of 3-letter words(with or without meaning) formed by using these letters =10X9X8
=720
ANSWER IS A |
AQUA-RAT | AQUA-RAT-37175 | A fish tank is half full of water. If 10 gallons of water were added, the tank would be 7/8 full. What is the capacity of the tank (in gallons)? | [
"11 3/7",
"22 3/7",
"26 2/3",
"30 3/8"
] | C | Solution -
Let capacity of tank be X gallons.
Water level increased to 7/8 from 1/2 when 10 gallons of water added ---> (7/8 - 1/2)*X = 10
X = 80/3 = 26 2/3.
ANS C. |
AQUA-RAT | AQUA-RAT-37176 | The banker's discount on a bill due 4 months hence at 15% is Rs. 420. The true discount is: | [
"400",
"360",
"480",
"320"
] | A | T.D. = B.D. x 100 / 100 + (R x T)
= Rs.(420 x 100 / 100 + (15 x 1/3))
= Rs. (420 x 100 / 105)
= Rs. 400.
Correct Answer is A. |
AQUA-RAT | AQUA-RAT-37177 | A worker is paid a regular rate of Rs.20 for completing a survey. The worker completes 50 surveys per week. For any survey involving the use of her cellphone, she is paid at a rate of that is 10% higher than her regular rate. If she completed 35 surveys involving the use of her cellphone, how much did she get that week... | [
"570",
"670",
"1070",
"470"
] | C | amount earned by using her cell phone = 35 * 22 = 770
amount earned as usual = 15 * 20 = 300
Total = 770+300 = 1070
Answer : C |
AQUA-RAT | AQUA-RAT-37178 | Six students are equally divided into 3 groups, then, the three groups were assigned to three different topics. How many different arrangements Q are possible? | [
" 30",
" 60",
" 90",
" 180"
] | C | 90 is the number of ways you can assign 3 teams formed out of 12 people to 3 different tasks.
But now you can order the 3 tasks in 3! ways. T1 T2 T3 or T2 T1 T3.... etc etc.
I was confused between 90 and 540 but since question used the wordarrangementsdecided to go with complete arrangements Q including the order of ta... |
AQUA-RAT | AQUA-RAT-37179 | A batsman in his 19th inning makes a score of 100 and their by increasing his average by 2. What is his average after the 19th inning? | [
"58",
"60",
"62",
"64"
] | D | 18x + 100 = 19(x + 2)
x = 62 + 2 = 64
Answer:D |
AQUA-RAT | AQUA-RAT-37180 | A certain lab experiments with white and brown mice only. In one experiment, 2/3 of the mice are white. If there are 13 brown mice in the experiment, how many mice in total are in the experiment? | [
"39",
"33",
"26",
"21"
] | A | Let total number of mice = M
Number of white mice = 2/3 M
Number of brown mice = 1/3 M = 13
=> M = 39
Answer A |
AQUA-RAT | AQUA-RAT-37181 | If u r genius solve it:-
40 * 14 = 11
30 * 13 = 12
20 * 12 = 6
10 * 11 = ? | [
"1",
"2",
"3",
"4"
] | B | B
2
Logic :
40*14=560=5+6+0=11
30*13=390=3+9+0=12
20*12=240=2+4+0=6
So 10*11=110=1+1+0=2 |
AQUA-RAT | AQUA-RAT-37182 | A team of eight entered for a shooting competition. The best marks man scored 85 points. If he had scored 92 points, the average scores for. The team would have been 84. How many points altogether did the team score? | [
"288",
"665",
"168",
"127"
] | B | Explanation:
8 * 84 = 672 – 7 = 665
Answer:B |
AQUA-RAT | AQUA-RAT-37183 | How many integers are there between 55 and 108, inclusive? | [
"51",
"54",
"56",
"57"
] | B | I guess the easiest way to answer this is -
Say you have two positive integers, x and y where y > x
Then the number of integers between x and y is given by - (y - x) + 1
In this case, it's (108 - 55) + 1 =54. Option B |
AQUA-RAT | AQUA-RAT-37184 | 3 of the 4 expressions (1), (2), (3) & (4) given below are exactly equal . Which of the expression is not equal to the other four expressions? | [
"(A + B)2 - 4AB",
"(A – B)2 + 4AB",
"A2 + B2 - 4AB + 2AB",
"A2 – B2 + 2B(B – A)"
] | B | 1) (A + B)2 – 4AB = A2 + 2AB + B2 - 4AB = A2 + B2 - 2AB
2) (A – B)2 + 4AB = A2 – 2AB + B2 + 4AB = A2+ B2 + 2AB
3) A2 +B2 – 4AB + 2AB = A2 + B2 - 2AB
4) A2 – B2 + 2B(B – A) = A2 – B2 + 2B2 – 2AB = A2 + B2 – 2AB
Therefore, (1) = (3) = (4) ≠ (2)
Therefore, expression (2) is wrong
ANSWER IS B |
AQUA-RAT | AQUA-RAT-37185 | P is three times as fast as Q and working together, they can complete a work in 36 days. In how many days can Q alone complete the work? | [
"16",
"48",
"88",
"55"
] | B | P = 3Q
P + Q = 3Q + Q = 4Q
These 4Q people can do the work in 36 days, which means Q can do the work in 144 days.
Hence, P can do the work in 48 days.
Answer:B |
AQUA-RAT | AQUA-RAT-37186 | Difference between two numbers is 5, six times of the smaller lacks by 8 from the four times of the greater. Find the numbers? | [
"5,1",
"7,3",
"9,8",
"11,6"
] | D | Explanation:
x – y = 5
4x – 6y = 8
x = 11 y = 6
D) |
AQUA-RAT | AQUA-RAT-37187 | A, B and C can do a piece of work in 20, 30 and 60 days respectively. In how many days can A do the work if he is assisted by B and C on every third day? | [
"12",
"13",
"15",
"16"
] | C | 2 day work = 1/20*2=1/10
A+B+C 1 day work = 1/10
work done in 3 days = 1/5
1/5 work is done in 3 days
whole work will done in (3*5)=15 days |
AQUA-RAT | AQUA-RAT-37188 | Some of 10%-intensity red paint is replaced with 20% solution of red paint such that the new paint intensity is 15%. What fraction of the original paint was replaced? | [
"2/5",
"2/3",
"1/2",
"1/3"
] | C | Let total paint = 1
Let amount replaced = x
10 (1-x) + 20x = 15
x = 1/2
ANSWER:C |
AQUA-RAT | AQUA-RAT-37189 | Solve x2 – 7x = 0 | [
"0,7",
"1.7",
"2.7",
"3,7"
] | A | This quadratic factors easily: Copyright © Elizabeth Stapel 2002-2011 All Rights Reserved
x2 – 7x = 0
x(x – 7) = 0
x = 0 or x – 7 = 0
x = 0 or x = 7
The solution is x = 0, 7
ANSWER A |
AQUA-RAT | AQUA-RAT-37190 | The ratio of the present ages of P and Q is 3:4. 5 years ago, the ratio of their ages was 5:7. Find the their present ages? | [
"30, 40",
"30, 46",
"30, 29",
"31, 40"
] | A | Their present ages be 3X and 4X.
5 years age, the ratio of their ages was 5:7, then (3X - 5):(4X - 5) = 5:7
X = 35 - 25 => X = 10.
Their present ages are: 30, 40.
Answer: A |
AQUA-RAT | AQUA-RAT-37191 | Three business people wish to invest in a new company. Each person is willing to pay one third of the total investment. After careful calculations, they realize that each of them would pay $2,200 less if they could find two more equal investors. How much is the total investment in the new business? | [
"$11,000",
"$50,000",
"$16,500",
"$ 6,600"
] | C | Total Investment between 5: (x/5)
Total investment including 2200 less between 3 people(x-(2200*3))/3
Set both eq. equal to each other.
16,500
Answer C) |
AQUA-RAT | AQUA-RAT-37192 | In a game of billiards, A can give B 20 points in 60 and he can give C 30 points in 60. How many points can B give C in a game of 100? | [
"15",
"77",
"25",
"18"
] | C | A scores 60 while B score 40 and C scores 30.
The number of points that C scores when B scores 100 = (100 * 30)/40 = 25 * 3 = 75.
In a game of 100 points, B gives (100 - 75) = 25 points to C.
Answer:C |
AQUA-RAT | AQUA-RAT-37193 | A car dealer has only blue and white cars in his show room. He has 24 blue cars and 30 white cars. He wants to have 60% more blue cars then white. How many whites cars does he have to sell to achieve his sales goal? | [
"12",
"13",
"14",
"15"
] | C | We can use simple arithmetic to solve this problem by testing our answers.
Lets test B:
If he sold 13 white cars:
24 blue cars and 17 white cars for a total of 41 cars
24/41=58.5% not quite our answer
Lets test C
If he sold 14 white cars
24 blue cars and 16 white cars for a total of 40 cars
24/40=60%
Our answer is C |
AQUA-RAT | AQUA-RAT-37194 | if x:y = 1:5, then find the value of
(7x+3y):(2x+y) | [
"14:5",
"15:5",
"16:5",
"22:7"
] | D | Explanation:
let x = 1k and y = 5k, so
=7(k)+3(5k)/ 2(k)+1(5k)
=22k/7k
=22:7
Option D |
AQUA-RAT | AQUA-RAT-37195 | If the arithmetic mean of seventy five numbers is calculated, it is 35. If each number is increased by 5, then mean of new number is? | [
"43",
"40",
"87",
"77"
] | B | A.M. of 75 numbers = 35
Sum of 75 numbers = 75 * 35 = 2625
Total increase = 75 * 5 = 375
Increased sum = 2625 + 375 = 3000
Increased average = 3000/75 = 40.
Answer:B |
AQUA-RAT | AQUA-RAT-37196 | The denominator of a fraction is 6 greater than the numerator. If the numerator and the denominator are increased by 1, the resulting fraction is equal to 4â„5. What is the value of the original fraction? | [
"17/23",
"23/29",
"29/35",
"31/37"
] | B | Let the numerator be x.
Then the denominator is x+6.
x+1 / x+7 = 4/5.
5x+5=4x+28.
x=23.
The original fraction is 23/29.
The answer is B. |
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