source stringclasses 6 values | subject stringclasses 26 values | question stringlengths 1 1.14k | options listlengths 3 5 | rationale stringlengths 0 22.5k ⌀ | correct stringclasses 9 values |
|---|---|---|---|---|---|
deepmind/aqua_rat | Maths-Algebra | A man has some hens and cows. If the number of heads be 48 and the number of feet equals 140, then the number of hens will be | [
"A)26",
"B)27",
"C)28",
"D)29",
"E)30"
] | Let number of hens = h and number of cows = c
number of heads = 48
=> h + c = 48 ---(Equation 1)
number of feet = 140
=> 2h + 4c = 140
=> h + 2c = 70 ---(Equation 2)
(Equation 2) - (Equation 1) gives
2c - c = 70 - 48
=> c = 22
Substituting the value of c in Equation 1, we get
h + 22 = 48
=> h = 48 - 22 = 26
i.e., number of hens = 26
Answer is A. | A |
deepmind/aqua_rat | Maths-Algebra | If the true discount on s sum due 2 years hence at 14% per annum be Rs. 182, the sum due is: | [
"A)s. 832",
"B)s. 968",
"C)s. 1960",
"D)s. 2400",
"E)s. 2800"
] | td=pw*r*t/100 so 182=pw*14*2/100 so pw=650
sum=pw+td..
sum=650+182=832
ANSWER:A | A |
deepmind/aqua_rat | Maths-Algebra | Cuboid volume and Base area are 144 m^3 and 18m^3 respectively.Find the height of a cuboid? | [
"A)5m",
"B)12m",
"C)6m",
"D)8m",
"E)10m"
] | Height of the cuboid=Volume* Base area
=144/18
=8 metre
Answer is option D | D |
deepmind/aqua_rat | Maths-Algebra | A train covers a distance of 12 km in 10 min. If it takes 6 sec to pass a telegraph post, then the length of the train is? | [
"A)288",
"B)277",
"C)120",
"D)285",
"E)121"
] | Speed = (12/10 * 60) km/hr = (72 * 5/18) m/sec = 20 m/sec.
Length of the train = 20 * 6 = 120 m.
Answer: C | C |
deepmind/aqua_rat | Maths-Algebra | The average mark of 20 students in a class is 70 years. The average age of 10 students is 65. What is the total mark of remaining 10 students? | [
"A)850",
"B)800",
"C)750",
"D)700",
"E)680"
] | Sum of the ages of 10 students
= (20 * 70) - (10 * 65) = 1400 - 650 = 750
Required Total marks = 750
Answer: C | C |
deepmind/aqua_rat | Maths-Algebra | A coin has two sides. One side has the number 1 on it and the other side has the number 2 on it. If the coin is flipped three times what is the probability that the sum of the numbers on the landing side of the coin will be greater than 6? | [
"A)3/8",
"B)1/16",
"C)1/8",
"D)1/2",
"E)0"
] | One approach to solve the problem is to list the different possibilities for a toss of coin three times. Because there are two outcomes and the coin is tossed three times, the table will have 2*2*2 or 8 rows.
Next add the resulting rows together to find the sum (the fourth column in the table below).
Toss 1 | Toss 2 | Toss 3 | Sum
1 ---------- 1 -------- 1 ------ 3
1 ---------- 1 -------- 2 ------ 4
1 ---------- 2 -------- 1 ------ 4
1 ---------- 2 -------- 2 ------ 5
2 ---------- 1 -------- 1 ------ 4
2 ---------- 1 -------- 2 ------ 5
2 ---------- 2 -------- 1 ------ 5
2 ---------- 2 -------- 2 ------ 6
From the table we see that there are 0 situations where the sum of the tosses will be greater than 6. And there are 8 possible combinations resulting in a probability of
0/8 or a probability of 0.
SO the correct answer is E. | E |
deepmind/aqua_rat | Maths-Algebra | Rs. 6000 is lent out in two parts. One part is lent at 7% p.a simple interest and the other is lent at 10% p.a simple interest. The total interest at the end of one year was Rs. 480. Find the ratio of the amounts lent at the lower rate and higher rate of interest? | [
"A)2:1",
"B)5:6",
"C)5:2",
"D)5:8",
"E)5:2"
] | Let the amount lent at 7% be Rs. x
Amount lent at 10% is Rs. (6000 - x)
Total interest for one year on the two sums lent
= 7/100 x + 10/100 (6000 - x) = 600 - 3x/100
=> 600 - 3/100 x = 480 => x = 5000
Amount lent at 10% = 2000
Required ratio = 2000 : 1000 = 2:1
Answer:A | A |
deepmind/aqua_rat | Maths-Algebra | If 4 and 8 are factors of 60n, what is the minimum value of n? | [
"A) 2",
"B) 3",
"C) 8",
"D) 14",
"E) 56"
] | 60n/4*8 should be integer => 2*2*3*5*n/2*2*2*2*2 = 3*5*n/8must be an integer
for this to be true n must multiple of 8, thus min of n = 8
hence C | C |
deepmind/aqua_rat | Maths-Algebra | In how many ways can be 3 boys and 3 girls sit around circular table so that no two boys sit next to each other? | [
"A)(5!)^2",
"B)(6!)^2",
"C)3!2!",
"D)11!",
"E)(5!)^2*6!"
] | first fix one boy and place other 2 in alt seats so total ways is 3!
now place each girl between a pair of boys... total ways of seating arrangement of girls 3!
total is 2!*3!
ANS C | C |
deepmind/aqua_rat | Maths-Algebra | A driving school claims an average test pass rate of 76.8 percent. What is the least number of pupils required to achieve this result? | [
"A)125",
"B)113",
"C)189",
"D)153",
"E)142"
] | A
125
96 passes out of 125 give an average of 76.8% . | A |
deepmind/aqua_rat | Maths-Algebra | If (x + yi) / i = ( 7 + 9i ) , where x and y are real, what is the value of (x + yi)(x - yi)? | [
"A)120",
"B)130",
"C)150",
"D)170",
"E)200"
] | (x + yi) / i = ( 7 + 9i )
(x + yi) = i(7 + 9i) = -9 + 7i
(x + yi)(x - yi) = (-9 + 7i)(-9 - 7i) = 81 + 49 = 130
CORRECT ANSWER IS B) 130 | B |
deepmind/aqua_rat | Maths-Algebra | 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? | [
"A)4 min",
"B)6 min",
"C)8 min",
"D)2 min",
"E)9 min"
] | S = 600/40 = 15 mps
S = 3600/15 = 240 sec = 4 min
Answer: A | A |
deepmind/aqua_rat | Maths-Algebra | The difference of the cubes of two consecutive even integers is divisible by which of the following integers? | [
"A)3",
"B)6",
"C)4",
"D)5",
"E)2"
] | Solution: let take 2 consecutive even numbers 2 and 4.
=> (4*4*4)-(2*2*2)=64-8=56 which is divisible by 4.
Answer C | C |
deepmind/aqua_rat | Maths-Algebra | From a total of 5 boys and 5 girls, how many 4-person committees can be selected if the committee must have exactly 2 boys and 2 girls? | [
"A)16",
"B)24",
"C)60",
"D)100",
"E)240"
] | Answer=D=100
No of 4 person committees that can be formed=5C2*5C2=100
Answer D | D |
deepmind/aqua_rat | Maths-Algebra | If a two-digit positive integer has its digits reversed, the resulting integer differs from the original by 54. By how much do the two digits differ? | [
"A) 3",
"B) 4",
"C) 5",
"D) 6",
"E) 7"
] | Given that (10a + b) - (10b + a) = 54 --> 9a - 9b =54 --> a - b = 6.
Answer: D. | D |
deepmind/aqua_rat | Maths-Algebra | If x+y=280, x-y=200, for integers of x and y, y=? | [
"A)200",
"B)240",
"C)50",
"D)115",
"E)150"
] | x+y = 280
x-y = 200
2x = 80
x = 40
y = 240
Answer is B | B |
deepmind/aqua_rat | Maths-Algebra | How many multiples of 7 are there between 14 and 343, exclusive ? | [
"A)48",
"B)47",
"C)46",
"D)45",
"E)44"
] | 7 * 2 = 14
7 * 49 = 343
Total multiples = (49-2) + 1 = 48
Exclude 7 343 = 48-2 = 46
Answer is (C) | C |
deepmind/aqua_rat | Maths-Algebra | The probability of a team winning a match given Matt is playing the match is 0.75. The probability of the team winning a match given Matt is not playing the match is 0.7. The probability of Matt playing any match is 0.8.
If it is known that the team has won the last match, what is the probability that Matt played the match? | [
"A)0.8321",
"B)0.7",
"C)0.8108",
"D)0.7531",
"E)0.8213"
] | Out of 100 matches:
Matt is plays in 80 and not plays in 20.
Out of 80 matches Matt plays in, team wins 0.75*80 = 60.
Out of 20 matches Matt does not play in, team wins 0.7*20 = 14.
So, out of 100 matches 60 + 14 = 74 are won.
It is known that the team has won the last match. Out of 74 matches won, Matt is in 60: 60/74 = 0.8108...
Answer: C. | C |
deepmind/aqua_rat | Maths-Algebra | A luxury liner, Queen Marry II, is transporting several cats as well as the crew (sailors, a cook, and captain) to a nearby port. Altogether, these passengers have 15 heads and 42 legs. How many cats does the ship host? | [
"A)5",
"B)6",
"C)7",
"D)8",
"E)9"
] | sa's +co +ca +cats = 15. sa's + 1 +1 +cats =15 or sa's +cats =13.
sa's(2) +2 +2 +cats*4 =42 sa's*2 +cats*4 = 38 or sa's +cats*2 =19 or 13-cats +cat*2 =19
then cats =6
B | B |
deepmind/aqua_rat | Maths-Algebra | What will come in place of the x in the following Number series? 6, 12, 21, x , 48 | [
"A)33",
"B)35",
"C)39",
"D)41",
"E)42"
] | (A)
The pattern is + 6, + 9, + 12, +15 ………..
So the missing term is = 21 + 12 = 33 | A |
deepmind/aqua_rat | Maths-Algebra | Sunil invested $ 1800 fir 2 years and $ 1400 for 3 years at the same rate of Simple Interest. If the total interest from these investments is $ 810, what is the rate of interest? | [
"A)12 3/4%",
"B)25 1/3%",
"C)10 1/4%",
"D)8%",
"E)13 2/4%"
] | (1800x2xR)/100+(1400x3xR)/100=810
78R=810
R= 10 1/4%
Answer is C | C |
deepmind/aqua_rat | Maths-Algebra | A shepherd has 1million sheep at the beginning of Year 2010. The no's grow by xx during the yr. A famine hits his village in the next year & many of his sheep die. The sheep population decreases by yy during 2001 and at the beginning of 2011 the shepherd finds that he is left with 1million sheep. Which of the following is correct? | [
"A)x<y",
"B)x>y",
"C)x=y",
"D)x<=y",
"E)x>=y"
] | Let us assume the value of xx to be 10%10%.
Therefore, the number of sheep in the herd at the beginning of year 2001 (end of 2000) will be 1 million + 10%10% of 1 million = 1.1 million
In 2001, the numbers decrease by y%y% and at the end of the year the number sheep in the herd = 1 million.
i.e., 0.1 million sheep have died in 2001.
In terms of the percentage of the number of sheep alive at the beginning of 2001,
it will be (0.1/1.1)×100%=9.09%(0.1/1.1)×100%=9.09%.
From the above illustration it is clear that x>y
B | B |
deepmind/aqua_rat | Maths-Algebra | To furnish a room in a model home an interior decorator is to select 2 chairs and 2 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 150 different combinations are possible, how many tables are there in the warehouse? | [
"A)6",
"B)8",
"C)10",
"D)15",
"E)30"
] | Total number of ways to choose 2 chairs from 5= 5C2=10
Total number of combination=150
That means we need get 15 combinations from the selection of tables....
Screening through the answers.... 6C2=15..... 15*10=150
Answer is 6... A | A |
deepmind/aqua_rat | Maths-Algebra | Two kinds of Vodka are mixed in the ratio 1:2 and 2:1 and they are sold fetching the profit 10% and 10% respectively. If the vodkas are mixed in equal ratio and the individual profit percent on them are increased by 4/3 and 5/3 times respectively, then the mixture will fetch the profit of | [
"A)10%",
"B)20%",
"C)21%",
"D)23%",
"E)Cannot be determined"
] | Answer: A. | A |
deepmind/aqua_rat | Maths-Algebra | Money invested at x%, compounded annually, triples in value in approximately every 112/x years. If $3500 is invested at a rate of 8%, compounded annually, what will be its approximate worth in 28 years? | [
"A)$3,750",
"B)$5,600",
"C)$8,100",
"D)$15,000",
"E)$31,500"
] | x=8%
112/x years=112/8=14 years
Now, money triples every 14 years
Therefore, in 14 yrs , if $3500 triples to $10500, in 28 years, it will again triple to $10500*3=$31,500
Answer E | E |
deepmind/aqua_rat | Maths-Algebra | If a man lost 5% by selling apples at the rate of 15 a rupee at how many a rupee must he sell them to gain 25%? | [
"A)9.4",
"B)10.4",
"C)11.4",
"D)12.4",
"E)13.4"
] | 95% ---- 15
125% ---- ?
95/125 * 15 = 11.4
Answer: C | C |
deepmind/aqua_rat | Maths-Algebra | A cistern is two-third full of water. Pipe A can fill the remaining part in 12 minutes and pipe B in 8 minutes. Once the cistern is emptied, how much time will they take to fill it together completely? | [
"A)12 minutes",
"B)12.5 min",
"C)14.4 min",
"D)10.2 min",
"E)14.66 min"
] | As pipe A takes 12min. to fill remaining one-third it takes 36min. to fill completely. similarly pipe B takes 24min. to fill completely
so, total time taken by both together is reciprocal of:
(1/36)+(1/24)=5/72
ans:14.4 min.
ANSWER:C | C |
deepmind/aqua_rat | Maths-Algebra | An investment compounds annually at an interest rate of 34.1% What is the smallest investment period by which time the investment will more than triple in value? | [
"A)4",
"B)5",
"C)6",
"D)7",
"E)8"
] | 1 year: 100/3 = 33.33 approx $34: Total: 134
2nd year: 134/3 = 45: Total: 134+45 = 179
3rd year: 179/3 = 60: Total: 179+60 = 239
4th year: 239/3 = 80: Total: 239+80 = 319 > 3(100)
;4 years;
ANSWER:A | A |
deepmind/aqua_rat | Maths-Algebra | In a bag containing 3balls, a white ball was placed and then 1ball was taken out at random. What is the probability that the extracted ball would turn on to be white, if all possible hypothesis concerning the color of theballs that initiallyin the bag were equally possible ? | [
"A)2/3",
"B)5/8",
"C)3/5",
"D)4/7",
"E)4/9"
] | Since, all possible hypothesis regarding the colour of the balls are equally likely, therefore these could be 3 white balls, initially in the bag.
∴ Required probability = 1/4 [1 + 3/4 + 1/2 + 1/4]
= 1/4 [(4 + 3 + 2 + 1)/4] = 5/8
B | B |
deepmind/aqua_rat | Maths-Algebra | The function f is defined by subtracting 25 from the square of a number and the function a is defined as the square root of one-half of a number. If a(f(x))=10, then which of the following is a possible value of x? | [
"A)-15",
"B)-5",
"C)0",
"D)5",
"E)25"
] | f(x) = x^2-25
a(x) = sqrt(x/2) not sqrt(x)/2, because the question clearly says its square root of (half of the number).
a(f(x)) = 10
a(x^2-25) =10
sqrt((x^2-25)/2) = 10
=> (x^2-25)/2 = 100
=>x^2 = 225
=> x = 15 or -15
Answer is A. | A |
deepmind/aqua_rat | Maths-Algebra | The triplicate ratio of 1:2 is? | [
"A)1:64",
"B)1:8",
"C)1:10",
"D)3:8",
"E)5:64"
] | 1^3: 2^3 = 1:8
ANSWER:B | B |
deepmind/aqua_rat | Maths-Algebra | John weighs twice as much as Susan. Susan's weight is 60% of Sam's weight. Mark weighs 50% of Lynn's weight. Lynn weighs 170% of John's weight. Which of these 5 people weighs the least? | [
"A)John",
"B)Susan",
"C)Sam",
"D)Mark",
"E)Lynn"
] | John weighs twice as much as Susan --> J=2S --> John cannot weigh the least;
Susan's weight is 60% of Sam's weight --> S=0.6*Sam --> Sam cannot weigh the least;
Mark weighs 50% of Lynn's weight --> M=0.5*L --> Lynn cannot weigh the least;
Lynn weighs 170% of John's weight --> L=1.9*J --> John cannot weigh the least (we already know that);
As you can see the answer is either Susan (S) or Mark (M). To compare their weights we should express their weights in regards of the same person: M=0.5*L=0.5*(1.7*J)=0.85*J and from J=2S, S=0.5*J --> Susan weights the least: Susan's weight is 50% of that of John and Mark's weight ismore than 50%of that of John.
Answer: B. | B |
deepmind/aqua_rat | Maths-Algebra | Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2 vowels can be formed? | [
"A)210",
"B)7200",
"C)1890",
"D)31970",
"E)10984"
] | Number of ways of selecting (3 consonants out of 7) and (2 vowels out of 4)
= (7C3 x 4C2)
= 210.
ANSWER A 210 | A |
deepmind/aqua_rat | Maths-Algebra | In a 1000 m race, A beats B by 200 meters or 25 seconds. Find the speed of B? | [
"A)8",
"B)9",
"C)7",
"D)6",
"E)5"
] | Since A beats B by 200 m or 25 seconds, i
t implies that B covers 200 m in 25 seconds.
Hence speed of B = 200/25 = 8 m/s.
Answer:A | A |
deepmind/aqua_rat | Maths-Algebra | If each digit in the set of A = {0,1,2,3,4,5,6,7,8,9} is exactly used once, in how many ways can the digits be arranged such that the 2 and 5 are not adjacent? | [
"A)10! / 2!",
"B)10! - 9!",
"C)9!",
"D)10!",
"E)8*9!"
] | The answer should be the (total arrangements) - (arrangements when 2 and 5 are adjacent).
The number of ways to arrange 10 units is 10!
If we think of 2 and 5 as one single unit, the number of arrangements is 9!
Note that 2 and 5 can have two arrangements, so we multiply by 2 to get 2*9!
The total number of valid arrangements is 10! - 2*9! = 10*9! - 2*9! = 8*9!
The answer is E. | E |
deepmind/aqua_rat | Maths-Algebra | Three taps A, B and C can fill a tank in 12, 15 and 20 hours respectively. If A is open all the time and B and C are open for one hour each alternately, the tank will be full is? | [
"A)7",
"B)8",
"C)10",
"D)5",
"E)2"
] | (A + B)'s 1 hour work = (1/12 + 1/15) = 3/20
(A + C)'s 1 hour work = (1/12 + 1/20) = 2/15
Part filled in 2 hrs = (3/20 + 2/15) = 17/60
Part filled in 6 hrs = 3 * 17/60 = 17/20
Remaining part = 1 - 17/20 = 3/20
Now, it is the turn of A and B and 3/20 part is filled by A and B in 1 hour.
Total time taken to fill the tank = (6 + 1) = 7 hrs
ANSWER A | A |
deepmind/aqua_rat | Maths-Algebra | If Re.1 amounts to Rs.9 over a period of 10 years. What is the rate of simple interest? | [
"A)90%",
"B)30%",
"C)50%",
"D)80%",
"E)70%"
] | 8 = (1*10*R)/100
R = 80%
ANSWER:D | D |
deepmind/aqua_rat | Maths-Algebra | If a and b are the roots of the equation x2 - 7x + 7 = 0, then the value of a2 + b2 is: | [
"A)35",
"B)24",
"C)17",
"D)6",
"E)5"
] | Sol.(b) The sum of roots = a+ b = 7
Product of roots = ab = 8
Now, a2 + b2 = (a + b)2 - 2ab = 49 - 14 = 35
Answer A | A |
deepmind/aqua_rat | Maths-Algebra | If the simple interest on a certain sum of money for 4 years is one–fifth of the sum, then the rate of interest per annum is | [
"A)4%",
"B)7%",
"C)6%",
"D)5%",
"E)3%"
] | Explanation:
Let the Principal(P) be x
Then, Simple Interest(SI) = x/5
Time(T) = 4 years
Rate of interest per annum(R) = (100×SI)/PT
= (100 × (x/5)/(x × 4) = 20/4 = 5%
Answer: Option D | D |
deepmind/aqua_rat | Maths-Algebra | A train 180 m long passed a pole in 10 sec. How long will it take to pass a platform 800 m long? | [
"A)80",
"B)89",
"C)54",
"D)67",
"E)56"
] | Speed = 180/10= 18 m/sec.
Required time = (180+ 800)/18 = 54 sec.
Answer: Option C | C |
deepmind/aqua_rat | Maths-Algebra | A basketball coach will select the members of a five-player team from among 10 players, including John and Peter. If the five players are chosen at random, what is the probability that the coach chooses a team that includes both John and Peter? | [
"A)1/9",
"B)1/6",
"C)2/9",
"D)5/18",
"E)1/3"
] | straight forward way is to group J and P as always present on the team and as order does not matter so we just need to find the total number of ways to select rest three players = 8c3
total number of ways of selecting 5 players out of 10 = 10c5
probability = 8c3/10c5 =2/9
C | C |
deepmind/aqua_rat | Maths-Algebra | If two numbers are in the ratio 2:3. If 17 is added to both of the numbers then the ratio becomes 3:4 then find the smallest number? | [
"A)A)10",
"B)B)20",
"C)C)34",
"D)D)30",
"E)E)35"
] | 2:3
2x + 17 : 3x + 17 = 3 : 4
4[2x + 17] = 3[3x + 17]
8x + 68 = 9x + 51
9x - 8x = 68 - 51
x = 17
Then smallest number is = 2
2x = 34
Correct Option C | C |
deepmind/aqua_rat | Maths-Algebra | The area of a square field is 900 km2. How long will it take for a horse to run around at the speed of 12 km/h ? | [
"A)12 h",
"B)10 h",
"C)8 h",
"D)6 h",
"E)None of these"
] | Explanation Area of field = 900 km2. Then, each side of field = √900=30km Distance covered by the horse = Perimeter of square field = 30 × 4 = 120 km ∴ Time taken by horse = distances/peed=120/12=10h Answer B | B |
deepmind/aqua_rat | Maths-Algebra | If a and b are two different prime numbers, which of the following cannot be true? | [
"A)ab is odd.",
"B)a/b is an integer",
"C)a +b is odd.",
"D)ab is even.",
"E)a + b is even"
] | A prime number is a positive integer with exactly two distinct positive divisors: 1 and itself. So, a prime number cannot be a multiple of another prime number. Which makes option C not possible (a/b=integer means that a is a multiple ofb).
Answer: C.
All other options are possible:
A. ab is odd --> a=3 and b=5;
B. a + b is even --> a=3 and b=5;
C. a + b is odd --> a=2 and b=3;
D. ab is even --> a=2 and b=3;
C | C |
deepmind/aqua_rat | Maths-Algebra | The sum of the ages of 5 children born at the intervals of 3 years each is 80 years. What is the age of the youngest child? | [
"A)2 years",
"B)4 years",
"C)6 years",
"D)8 years",
"E)10 years"
] | Let the ages of the children be x, (x + 3), (x + 6), (x + 9) and (x +12) years.
Then, x + (x + 3) + (x + 6) + (x + 9) + (x + 12) = 80
5x = 50 => x = 10.
Age of youngest child = x = 10 years.
ANSWER:E | E |
deepmind/aqua_rat | Maths-Algebra | The ratio between the number of sheep and the number of horses at the Stewart farm is 4 to 7, If each horse is fed 230 ounces of horse food per day and the farm needs a total 12,880 ounces of horse food per day, what is the number of sheep in the farm? | [
"A)18",
"B)28",
"C)32",
"D)56",
"E)60"
] | Actual number of horses = 12,880/230 (hold it since it is a harder calculation)
Ratio multiplier = 1288/(23*7)
Actual number of sheep = 1288/(23*7) * 4.
First divide 1288 by 7 to get: 184*4/23
Use the last digit to figure out that 23 will go 8 times into 184. Confirm. 8*4 = 32
Answer (C) | C |
deepmind/aqua_rat | Maths-Algebra | A cistern can be filled by a tap in 4 hours while it can be emptied by another tap in 9 hours. If both the taps are opened simultaneously, then after how much time cistern will get filled ? | [
"A)7 hours",
"B)7.1 hours",
"C)7.2 hours",
"D)7.3 hours",
"E)7.4 hours"
] | Explanation:
When we have question like one is filling the tank and other is empting it, then we subtraction as,
Filled in 1 hour = 1/4
Empties in 1 hour = 1/9
Net filled in 1 hour = 1/4 - 1/9
= 5/36
So cistern will be filled in 36/5 hours i.e. 7.2 hours
ANSWER IS C | C |
deepmind/aqua_rat | Maths-Algebra | At a certain diner, Joe ordered 3 doughnuts and a cup of coffee and was charged $ 2.25. Stella ordered 2 doughnuts and a cup of coffee and was charged $ 1.60. What is the price of 2 doughnuts? | [
"A)$ 0.55",
"B)$ 1.00",
"C)$ 1.10",
"D)$ 1.30",
"E)$ 1.80"
] | 3D + C = 2.25......(1)
2D + C = 1.6........(2)
(1) - (2) --> D = 0.65 --> 2D = 1.3
Answer: D | D |
deepmind/aqua_rat | Maths-Algebra | An aeroplane covers a certain distance of 480 Kmph in 4 hours. to cover the same distance in 4 1/3 hours, it Must travel at a speed of | [
"A)440",
"B)540",
"C)443",
"D)740",
"E)250"
] | Speed of aeroplane = 480 Kmph
Distance travelled in 4 hours
= 480 * 4 = 1920 Km
Speed of aeroplane to acver 1920 Km in 13/3
= 1920*3/13 = 443 Km
Answer C. | C |
deepmind/aqua_rat | Maths-Algebra | The list price of an article is Rs.65. A customer pays Rs.56.16 for it. He was given two successive discounts, one of them being 10%. The other discount is? | [
"A)6%",
"B)3%",
"C)8%",
"D)1%",
"E)4%"
] | 65*(90/100)*((100-x)/100) = 56.16
x = 4%
Answer: E | E |
deepmind/aqua_rat | Maths-Algebra | Three 6 faced dice are thrown together. The probability that exactly two dice show the same number on them is | [
"A)5/18",
"B)5/12",
"C)5/19",
"D)5/15",
"E)5/11"
] | Using question number 11 and 12, we get the probability as
1 - (1/36 + 5/9) = 5/12
Answer: B | B |
deepmind/aqua_rat | Maths-Algebra | Two trains are running at 40 km/hr and 20 km/hr respectively in the same direction. Fast train completely passes a man sitting in the slower train in 5 sec. What is the length of the fast train? | [
"A)27 7/5",
"B)27 7/09",
"C)27 7/2",
"D)27 7/9",
"E)24 7/2"
] | Relative speed = (40 - 20) = 20 km/hr.
= 20 * 5/ 18 = 50/9 m/sec.
Length of faster train = 50/9 * 5 = 250/9 = 27 7/9 m.
Answer: D | D |
deepmind/aqua_rat | Maths-Algebra | Both Robert and Alice leave from the same location at 7:00 a.m. driving in the same direction, but in separate cars. Robert drives 30 miles per hour while Alice drives 50 miles per hour. After 6 hours, Alice’s car stops. At what time will Robert’s car reach Alice’s car? | [
"A)1 p.m.",
"B)3 p.m.",
"C)4 p.m.",
"D)7 p.m.",
"E)9 p.m."
] | 7:00 am so 6 hours later is 1:00 pm
In six hours, Robert will have driven 6*30 = 180 miles
In six hours, Alive will have driven 6*50 = 300 miles
So Robert needs 300-180 = 120 miles do catch Alice up.
So at 30 mph, he will need 2 hours
1:00 pm + 6 hours = 7:00 pm
ANS : D | D |
deepmind/aqua_rat | Maths-Algebra | If the diameter of circle R is 40% of the diameter of circle S, the area of circle R is what percent of the area of circle S? | [
"A)16%",
"B)18%",
"C)20%",
"D)22%",
"E)24%"
] | Let diameter of circle R , dr = 40
and diameter of circle S , ds = 100
Radius of circle R , Rr = 20
Radius of circle S , Rs = 50
Area of circle R/ Area of circle S = (pi * Rr ^2 ) /( pi * Rs^2 )
= (20/50)^2 = (4/10)^2
=16%
Answer :A | A |
deepmind/aqua_rat | Maths-Algebra | What is the area of square field whose side of length 13 m? | [
"A)225",
"B)662",
"C)169",
"D)882",
"E)21"
] | 13 * 13
= 169 sq m
Answer:C | C |
deepmind/aqua_rat | Maths-Algebra | Look at this series: 53, 53, 40, 40, 27, 27, ... What number should come next? | [
"A)14",
"B)15",
"C)17",
"D)19",
"E)11"
] | A
14
In this series, each number is repeated, then 13 is subtracted to arrive at the next number. | A |
deepmind/aqua_rat | Maths-Algebra | Each student is given a five-character identification code. The first two characters are selected from the numbers 0 to 9 inclusive, and the last three characters are selected from the 26 letters of the alphabet. If characters may be repeated and the same characters used in a different order constitute a different code, how many different identification codes can be generated following these rules? | [
"A)1,491,000",
"B)1,527,200",
"C)1,638,400",
"D)1,757,600",
"E)1,841,800"
] | The number of possible codes is 10*10*26*26*26=1,757,600.
The answer is D. | D |
deepmind/aqua_rat | Maths-Algebra | A box contains nine bulbs out of which 4 are defective. If four bulbs are chosen at random, find the probability that all the four bulbs are defective? | [
"A)1/127",
"B)1/129",
"C)1/128",
"D)1/198",
"E)1/126"
] | Out of nine, five are good and four are defective. Required probability
= ⁴C₄/⁹C₄
= 1/126
Answer: E | E |
deepmind/aqua_rat | Maths-Algebra | find S.P when CP=Rs 80.40,loss=5% | [
"A)Rs 66.34",
"B)Rs 69.34",
"C)Rs 58.34",
"D)Rs 68.34",
"E)Rs 60.34"
] | CP=Rs 80.40,loss=5%
sol: sp=85% of Rs 80.40
=Rs {(85/100)*80.40}=Rs 68.34.
Answer is D. | D |
deepmind/aqua_rat | Maths-Algebra | How many words can be formed by using all letters of the word ‘DAUGHTER’ so that the vowels always come together? | [
"A)42",
"B)420",
"C)470",
"D)5400",
"E)4320"
] | Sol. Given word contains 8 different letters. When the vowels AUE are always together, we may suppose them to form an entity, treated as one letter.
Then, the letters to be arranged are DGNTR (AUE).
Then 6 letters to be arranged in 6p6 = 6! = 720 ways.
The vowels in the group (AUE) may be arranged in 3! = 6 ways.
Required number of words = (720x6) = 4320.
ANSWER E | E |
deepmind/aqua_rat | Maths-Algebra | A man gets a simple interest of Rs.500 on a certain principal at the rate of 5% p.a in two years. Find the compound interest the man will get on twice the principal in two years at the same rate. | [
"A)Rs.500",
"B)Rs.250",
"C)Rs.5012.50",
"D)Rs.5062.50",
"E)None of these."
] | Let the principal be Rs.P
S.I at 5% p.a in 8 years on Rs.P = Rs.500
(P)(8)(5)/100 = 500
P = 1250
C.I on Rs.2P i.e., Rs.2500 at 5% p.a in two years
=2500{ [1 + 5/100]2 - 1} = 2500{ 212 - 202 /202}
= 2500/400(441 - 400)
= 25/4(41) = 1025/4 = Rs.256.25
ANSWER:E | E |
deepmind/aqua_rat | Maths-Algebra | Jacob is 18years old. He is 2 times as old as his brother. How old will Jacob be when he is twice as old? | [
"A)36",
"B)38",
"C)33",
"D)32",
"E)38"
] | j=18;
j=2b;
b=18/2=9;
twice as old so b=9(now)+(9)=18;
jacob is 18+18=36
ANSWER:A | A |
deepmind/aqua_rat | Maths-Algebra | The price for a loaf of bread in April was $1.23, in May the price was $1.22, and in June the price was $1.08. If 2/3 as much bread was sold in April as in May, and twice as much was sold in June as in April, what was the average price for a loaf of bread sold during the three-month period? | [
"A)$1.16",
"B)$1.15",
"C)$1.14",
"D)$1.13",
"E)$1.12"
] | Let x be the number of loaves sold in May.
Then 2x/3 loaves were sold in April and 4x/3 loaves were sold in June.
The average price was (2x/3)(123) + 122x + (4x/3)(108) / (2x/3 + x + 4x/3) =
(82 + 122 + 144) / (3) = 348/3 = $1.16
The answer is A. | A |
deepmind/aqua_rat | Maths-Algebra | The total price of a basic computer and printer are $2,500. If the same printer had been purchased with an enhanced computer whose price was $500 more than the price of the basic computer, then the price of the printer would have been 1/4 of that total. What was the price of the basic computer? | [
"A)1500",
"B)1600",
"C)1750",
"D)1900",
"E)2000"
] | Let the price of basic computer be C and the price of the printer be P: C+P=$2,500.
The price of the enhanced computer will be C+500 and total price for that computer and the printer will be 2,500+500=$3,000. Now, we are told that the price of the printer is 1/4 of that new total price: P=1/4*$3,000=$750.
Plug this value in the first equation: C+750=$2,500 --> C=$1,750
Answer: C. | C |
deepmind/aqua_rat | Maths-Algebra | To fill a tank, 25 buckets of water is required. How many buckets of water will be required to fill the same tank if the capacity of the bucket is reduced to 3/10 of its present? | [
"A)61.5",
"B)60.5",
"C)63.5",
"D)83.333",
"E)64.5"
] | Let capacity of 1 bucket = x
Capacity of the tank = 25x
New capacity of the bucket = 3x/10
Hence, number of buckets needed = 25x/(3x/10)=(25×10)/3=83.33333
Answer is D. | D |
deepmind/aqua_rat | Maths-Algebra | 207,200,...,186,179,172
Insert the missing number | [
"A)190",
"B)191",
"C)192",
"D)189",
"E)193"
] | Missing number : 193
Answer : E | E |
deepmind/aqua_rat | Maths-Algebra | 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 14 percent of revenues. The profits in 1999 were what percent of the profits in 1998? | [
"A)80%",
"B)105%",
"C)120%",
"D)124.2%",
"E)98%"
] | 0,098R = x/100*0.1R
Answer E | E |
deepmind/aqua_rat | Maths-Algebra | A certain store sells small, medium, and large toy trucks in each of the colors red, blue, green, and yellow. The store has an equal number of trucks of each possible color-size combination. If Paul wants a medium, red truck and his mother will randomly select one the trucks in the store, what is the probability that the truck she selects will have at least one of the two features Paul wants? | [
"A)1/4",
"B)1/3",
"C)1/2",
"D)7/12",
"E)2/3"
] | No. of colors=4
no. of sizes=3
Total outcomes=12
Remaining outcomes=6
hence probability that truck is neither red nor of medium size is 6/126/12.
hence probability that the truck she selects will have at least one of the two features Paul wants will be 1−6/121−6/12 or 1/2
ANSWER:C | C |
deepmind/aqua_rat | Maths-Algebra | How many days will there be from 26th January,1996 to 15th May,1996(both days included)? | [
"A)102",
"B)103",
"C)111",
"D)120",
"E)None of these"
] | Explanation :
Number of days from 26-Jan-1996 to 15-May-1996 (both days included)
= 6(Jan) + 29(Feb) + 31 (Mar) + 30(Apr)+ 15(May) = 111.. Answer : Option C | C |
deepmind/aqua_rat | Maths-Algebra | The present age of a father is 3 years more than three times the age of his son.Three years hence,father as age will be 8 years more than twice the age of the son.Find the present age of the father. | [
"A)88",
"B)77",
"C)33",
"D)44",
"E)27"
] | Explanation:
Let the present age be 'x' years. Then father's present age is 3x+3 years. Three years hence (3x+3)+3=2(x+3)+8 x=8 Hence father's present age = 3x+3 =[ (3 x 8) + 3] = 27 years.
Answer: E | E |
deepmind/aqua_rat | Maths-Algebra | If both 5^2 and 3^4 are factors of the number a*4^3*6^2*13^11, then what is the smallest possible value of a? | [
"A)80",
"B)120",
"C)150",
"D)225",
"E)300"
] | The number a must include at least 3^2*5^2 = 225
The answer is D. | D |
deepmind/aqua_rat | Maths-Algebra | The ratio, by volume, of bleach to detergent to water in a certain solution is 2 : 40 : 100. The solution will be altered so that the ratio of bleach(B) to detergent is tripled while the ratio of detergent to water is halved. If the altered solution will contain 300 liters of water, how many liters of detergent will it contain? | [
"A)40",
"B)60",
"C)50",
"D)30",
"E)70"
] | B:D:W = 2:40:100
Bnew / Dnew = (1/3)*(2/40) = (1/60)
Dnew / Wnew = (1/2)*(40/100) = (1/5)
Wnew = 300
Dnew = Wnew/5 = 300/5 = 60
So, answer will be B
B | B |
deepmind/aqua_rat | Maths-Algebra | How long will it take a sum of money invested at 5% p.a. S.I. to increase its value by 50%? | [
"A)10 years.",
"B)4 years.",
"C)8 years.",
"D)12 years.",
"E)14 years."
] | Sol.
Let the sum be x. Then, S.I. = 50% of x = x/2; Rate =5%.
∴ Time = [100 * x/2 * 1/x*5] = 10 years.
Answer A | A |
deepmind/aqua_rat | Maths-Algebra | Find the difference between the average of first n even numbers and the average of all the even numbers up to n (n is an even number). | [
"A)n",
"B)(n-1)/2",
"C)n/2",
"D)cannot be determined",
"E)None of these"
] | Explanation :
(n+1)-((n/2)+1)
Answer : C | C |
deepmind/aqua_rat | Maths-Algebra | Which is next
KUZ, MOX, OIV, QET | [
"A)SUR",
"B)SAQ",
"C)RAR",
"D)SPZ",
"E)SAR"
] | First letter in each word increases by 2
K+2=M, M+2=O, O+2=Q, Q+2=S
2nd letter decreases by 6 FOR 1ST 2 WORDS ND DEC BY 4 FOR NEXT 2 WORDS
U-6=O, O-6=I, I-4=E, E-4=A
3rd letter decreases by 2
Z-2=X, X-2=V, V-2=T, T-2=R
So the next word is SAR
ANSWER:E | E |
deepmind/aqua_rat | Maths-Algebra | Which of the following is closest to 10^180 – 10^20 ? | [
"A)10^210",
"B)10^180",
"C)10^150",
"D)10^90",
"E)10^6"
] | 10^180 – 10^20
10^20 * (10^160 – 1)
as we know 10^2 - 1 means 100-1 and we get 99, which is approximately 100. hence (10^160 – 1) would remain as 10^160.
and 10^20 * 10^160 = 10^180. Answer is B. | B |
deepmind/aqua_rat | Maths-Algebra | The maitre 'd at an expensive Manhattan restaurant has noticed that 60% of the couples order dessert and coffee. However, 20% of the couples who order dessert don't order coffee. What is the probability Y that the next couple the maitre 'd seats will not order dessert? | [
"A) 20%",
"B) 25%",
"C) 40%",
"D) 60%",
"E) 75%"
] | could you use a venn diagram and just go with the number 100.
60 people order dessert and coffee... which is the union of D and C.
Y=2/10 of D aren't in D U C = so 8/10 of D are in DUC which means =60 =8/10D. So D in total=75, and 15 D's aren't in D union C. which means 25 people are in C only + Neither.
B 25% | B |
deepmind/aqua_rat | Maths-Algebra | A train passes a station platform in 36 seconds and a man standing on the platform in 10 seconds. If the speed of the train is 72 km/hr, what is the length of the platform? | [
"A)338",
"B)240",
"C)520",
"D)267",
"E)191"
] | Speed = (72 * 5/18) m/sec = 20 m/sec. Length of the train = (20 x 10)m = 200 m. Let the length of the platform be x meters. Then, (x + 200)/36 = 20 ==> x + 200 = 720 ==> x = 520 m.
Answer: C | C |
deepmind/aqua_rat | Maths-Algebra | A grocer stacked oranges in a pile. The bottom layer was rectangular with 3 rows of 7 oranges each. In the second layer from the bottom, each orange rested on 4 oranges from the bottom layer, and in the third layer, each orange rested on 4 oranges from the second layer. Which of the following is the maximum number of oranges that could have been in the third layer? | [
"A) 5",
"B) 4",
"C) 3",
"D) 2",
"E) 1"
] | Bottom Layer = 7 x 3 = 21
IInd Layer = (7-1) x (3-1) = 12
IIIrd Layer = (6-1) x (2-1) = 5
Answer = 5 = A | A |
deepmind/aqua_rat | Maths-Algebra | Best friends Sprite and Icey have are playing a game of marbles. They invite 2 of their friends to play with them. There are 36 marbles in the bag. If all 4 people are playing, how many marbles does each person get? | [
"A)3",
"B)9",
"C)5",
"D)6",
"E)7"
] | Answer= B
36 / 4 = 9
Answer= B | B |
deepmind/aqua_rat | Maths-Algebra | If 5^r is a factor of 30!, which of the following is the maximum possible value of r? | [
"A)4",
"B)5",
"C)6",
"D)7",
"E)8"
] | 5^r is a factor of 30! We need the maximum value of r
Or in other words, we need the maximum power of 5 in 30!
Powers of 5 in 30! = [30/5] + [30/25] = 7, where [x] is the integral part of x
Other way is to calculate the number of 5's in 30!
In the multiplication upto 30, we will encounter: 5, 10, 15, 20,25, 30
Each of 5, 10, 15, 20, 30 contain one power of 5
25 contains 2 powers of 5.
Hence total powers of 5 in 30!= 5 + 2 = 7
Correct option: D | D |
deepmind/aqua_rat | Maths-Algebra | In a 1000 m race, A beats B by 50 m and B beats C by 100 m. In the same race, by how many meters does A beat C? | [
"A)145",
"B)266",
"C)276",
"D)027",
"E)266"
] | By the time A covers 1000 m, B covers (1000 - 50) = 950 m.
By the time B covers 1000 m, C covers (1000 - 100) = 900 m.
So, the ratio of speeds of A and C =
1000/950 * 1000/900 = 1000/855 So, by the time A covers 1000 m, C covers 855 m.
So in 1000 m race A beats C by 1000 - 855 = 145 m.
Answer: A | A |
deepmind/aqua_rat | Maths-Algebra | In how many ways can you line up 7 wrestlers in a row if one of them, The Undertaker, cannot be in the middle or at the either end? | [
"A)1,570",
"B)2,880",
"C)90",
"D)192",
"E)5,300"
] | Since The Undertaker cannot be placed in the middle or at either end (3 spots), then he can choose 4 spots to sit. The remaining 6 apples can be placed in in 6! ways. Thus the # of arrangements is 4*6! = 2,880.
Answer: B. | B |
deepmind/aqua_rat | Maths-Algebra | Benny goes to the market for buying some apples to be distributed between her nine kids equally.She takes 360 dollars with her .The cost of each apple is 4 dollars .How many apples does she buy to share them equally between her nine kids? | [
"A)8",
"B)9",
"C)3",
"D)7",
"E)10"
] | cost of each apple = 4 dollars
Apples that Benny can buy with the amount she has=360/4 = 90.
Apples that each kid gets evenly = 90/9 =10 Apples.
So the answer is E=10 | E |
deepmind/aqua_rat | Maths-Algebra | What amount does an investor receive if the investor invests $3000 at 10% p.a. compound interest for two years, compounding done annually? | [
"A)$3420",
"B)$3630",
"C)$3870",
"D)$4040",
"E)$4220"
] | A = (1 + R/100)^n * P
(1.1)^2 * 5000 = 1.21 * 5000 = 3630
The answer is B. | B |
deepmind/aqua_rat | Maths-Algebra | Will must choose a 2-character computer password, consisting of 1 letter from the alphabet and 1 distinct digits, in any order.From how many different passwords can Will choose? | [
"A)520",
"B)1560",
"C)4,680",
"D)7,020",
"E)14,040"
] | 26C1*10C1 = 260
=> 260 * 2 ! = 520
Option E is correct answer...but OA is A. | A |
deepmind/aqua_rat | Maths-Algebra | A train running at a speed of 60 kmph crosses a pole in 6 seconds.What is the length of the train? | [
"A)120 m",
"B)180 m",
"C)100 m",
"D)150 m",
"E)160 m"
] | 60 kmph=50/3 m/sec
50/3*6=100 m
ANSWER:C | C |
deepmind/aqua_rat | Maths-Algebra | P is able to do a piece of work in 10 days and Q can do the same work in 12 days. If they can work together for 5 days, what is the fraction of work left? | [
"A)7/12",
"B)5/12",
"C)1/12",
"D)3/12",
"E)1/2"
] | Explanation :
Amount of work P can do in 1 day = 1/10
Amount of work Q can do in 1 day = 1/12
Amount of work P and Q can do in 1 day = 1/10+ 1/12 = 11/60
Amount of work P and Q can together do in 5 days = 5 × (11/60) =11/12
Fraction of work left = 1 – 11/12= 1/12
Answer : Option C | C |
deepmind/aqua_rat | Maths-Algebra | Two equilateral triangles of side 12cm are placed one on top of another, such that a 6 pointed star is formed .if the six verticals lie on a circle what is the area of the circle not enclosed by the star ? | [
"A)68",
"B)83",
"C)57",
"D)61",
"E)62"
] | area of star = √3/4 * (12)^2 + 3* √3/4 *(12/3)^2 = 48√3
if r be radius of circle then r=6/cos30 => r=12/√3 => r^2=48
area of circle = pi*48
area of the circle not enclosed by the star = 48*pi - 48√3 =48(3.14-1.732)= 68(approax)
ANSWER:A | A |
deepmind/aqua_rat | Maths-Algebra | Find the odd man out
253, 136, 352, 329, 631, 244 | [
"A)329",
"B)136",
"C)352",
"D)631",
"E)531"
] | The sum all three digits comes to 10 except 329
ANSWER:A | A |
deepmind/aqua_rat | Maths-Algebra | 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? | [
"A)12 days",
"B)15 days",
"C)18 days",
"D)20 days",
"E)22 days"
] | A’s two day’s work = 2/20 = 1/10
(A + B + C)’s one day’s work = 1/20 + 1/30 + 1/60 = 6/60 = 1/10
Work done in 3 days = (1/10 + 1/10) = 1/5
Now, 1/5 work is done in 3 days
Therefore, Whole work will be done in (3 x 5) = 15 days.
ANSWER:C | C |
deepmind/aqua_rat | Maths-Algebra | The sum of ages of 5 children born at the intervals of 3 years each is 50 years. What is the age of the youngest child? | [
"A)4years",
"B)5years",
"C)6years",
"D)7years",
"E)8years"
] | Let the ages of children be x, (x + 3), (x + 6), (x + 9) and (x + 12) years.
Then, x + (x + 3) + (x + 6) + (x + 9) + (x + 12) = 50
5x = 20
x = 4.
Age of the youngest child = x = 4 years.
answer :A | A |
deepmind/aqua_rat | Maths-Algebra | A tradesman is marketing his goods 20% above the cost price of the goods. He gives 10% discount on cash payment, find his gain percent. | [
"A)12%",
"B)8%",
"C)15%",
"D)18%",
"E)None of these"
] | Let the C.P. of the goods be 100
⇒ Marked price of the goods = 120
Discount = 10% ⇒ S.P. is 90% of 120 = 108
∴ Gain = (108 – 100) i.e. 8%.
Answer B | B |
deepmind/aqua_rat | Maths-Algebra | A teacher gave the same test to three history classes: A, B, and C. The average (arithmetic mean) scores for the three classes were 65, 90, and 77, respectively. The ratio of the numbers of students in each class who took the test was 4 to 6 to 5, respectively. What was the average score for the three classes combined? | [
"A)74",
"B)75",
"C)76",
"D)77",
"E)79"
] | ratio is 4:6:5 , numbers are 4x, 6x, 5x
total scores of each class is (65*4x + 6x * 90 + 77*5x) = 260x+540x+385x = 1185x
total number of students = 15x
average = 1185x/15x = 79
E is the answer | E |
deepmind/aqua_rat | Maths-Algebra | The average weight of 10 students decreases by 6 kg when one of them weighing 120 kg is replaced by a new student. The weight of the student is | [
"A)62 kg",
"B)60 kg",
"C)70 kg",
"D)72 kg",
"E)None of these"
] | Explanation :
Let the weight of student be x kg.
Given, Difference in average weight = 6 kg
=> (120-x)/10 = 6
=> x = 60
Answer : B | B |
deepmind/aqua_rat | Maths-Algebra | At milk factory, each employee working the second shift produced 2/3 as many widgets as each employee working the first shift. If the first shift has 3/4 as many employees, what fraction of the total widgets did the second shift produce? | [
"A)8/17",
"B)1/2",
"C)8/9",
"D)9/8",
"E)17/8"
] | At milk factory, Let the first shift have 3 employee and each produce 3 widgets, so the total number of widgets produced by the first shift is 3*3=9;
Then the second shift would have 4 employees and each second shift employee would produce 3*2/3=2 widgets, so the total number of widgets produced by the second shift employees would be 4*2=8;
The ratio of the second shift production to the total is 8/(9+8)=8/17.
Answer: A. | A |
deepmind/aqua_rat | Maths-Algebra | The price of a jacket is reduced by 10%. During a special sale the price of the jacket is reduced another 30%. By approximately what percent must the price of the jacket now be increased in order to restore it to its original amount? | [
"A)32.5",
"B)58.7",
"C)48",
"D)65",
"E)67.5"
] | 1) Let the price of jacket initially be $100.
2) Then it is decreased by 10% , therefore bringing down the price to $90.
3) Again it is further discounted by 30%, therefore bringing down the price to $63.
4) Now 67.5 has to be added byX %in order to equal the original price.
63 + ( X% ) 63 = 100.
Solving this eq for X, we get X = 58.7
Ans is B | B |
deepmind/aqua_rat | Maths-Algebra | An author received $0.80 in royalties for each of the first 100,000 copies of her book sold, and $0.80 in royalties for each additional copy sold. If she received a total of $260,000 in royalties, how many copies of her book were sold? | [
"A)130,000",
"B)300,000",
"C)325,000",
"D)400,000",
"E)420,000"
] | Total royalties for first 100.000 books = .8*100,000= 80,000
Total royalties for the rest of the books = 260,000-80,000 = 180,000
Remaining books = 180,000/0.8 = 225,000
Total books = 225,000+100,000 = 325,000 Answer C | C |
deepmind/aqua_rat | Maths-Algebra | If P represents the product of the first 16 positive integers, then P is not a
multiple of: | [
"A)a) 99",
"B)b) 84",
"C)c) 133",
"D)d) 65",
"E)e) 57"
] | a) 99 = 9*11
b) 84 = 4*7*3
c) 133 =19*7
d) 65 = 5*13
e) 57 =19*3
since 19 is not there in first 15 positive numbers it is the only possibility
C | C |
deepmind/aqua_rat | Maths-Algebra | A person sold two cows each for Rs.9900. If he gained 10% on one and lost 20% on the other, then which of the following is true ? | [
"A)He lost Rs. 200",
"B)He gained Rs. 200",
"C)Neither he gained nor lost",
"D)None of the above",
"E)He gained Rs. 300"
] | Explanation:
In first he got Rs. 990
But in second he lost Rs. 1980
So he lost Rs. 990.
ANSWER IS D | D |
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