mathewhe/aqua_rat huggingface dataset:
Question: Mira is making telescopes, each consisting of 2 lenses, 1 tube, and 1 eyepiece. Lenses can be purchased only in packs of 50, tubes only in packs of 10, and eyepieces only in packs of 30. However, half of the lenses in each pack are not usable for telescopes. If all parts are used only for the telescopes what is the minimum number of lenses Mira must purchase to make a set of telescopes with no leftover components other than the unusable lenses?
(A) 75
(B) 150
(C) 300
(D) 500
(E) 2400
Rationale: I'd use backsolving for this question.
Check E:
2400 lenses = 1200 usable lenses = 600 tubes = 600 eyepieces. We CAN buy 600 tubes and 600 eyepieces, so that not to have leftovers.
Answer: E.
Answer: (E) 2400
Question: A dealer purchases 15 articles for Rs. 25 and sells 12 articles for Rs. 30. Find the profit percentage?
(A) 88%
(B) 50%
(C) 87%
(D) 66%
(E) 54%
Rationale: L.C.M of 15 and 12 = 60
CP of 60 articles = Rs. 100 (25 * 4)
SP of 60 articles = Rs. 150 (30 * 5)
Profit percentage = (150 - 100)/100 * 100 = 50%
Answer: B
Answer: (B) 50%
Question: A FIVE DIGIT NUMBER DIVISIBLE BY 3 IS TO BE FORMED USING THE DIGITS 0, 1, 2, 3, 4 and 5 WITHOUT REPETITIONS. THAT TOTAL NO OF WAYS IT CAN BE DONE IS?
(A) 122
(B) 210
(C) 216
(D) 217
(E) 220
Rationale: First step:
We should determine which 5 digits from given 6, would form the 5 digit number divisible by 3.
We have six digits: 0,1,2,3,4,5. Their sum=15.
For a number to be divisible by 3 the sum of the digits must be divisible by 3. As the sum of the six given numbers is 15 (divisible by 3) only 5 digits good to form our 5 digit number would be 15-0=(1,2,3,4,5) and 15-3=(0,1,2,4,5). Meaning that no other 5 from given six will total the number divisible by 3.
Second step:
We have two set of numbers:
1,2,3,4,5 and 0,1,2,4,5. How many 5 digit numbers can be formed using this two sets:
1,2,3,4,5 --> 5! as any combination of these digits would give us 5 digit number divisible by 3. 5!=120.
0,1,2,4,5 --> here we can not use 0 as the first digit, otherwise number won't be any more 5 digit and become 4 digit. So, total combinations 5!, minus combinations with 0 as the first digit (combination of 4) 4! --> 5!-4!=96
120+96=216
Answer: C.
Answer: (C) 216
Question: A grocer has a sale of Rs. 2500, Rs. 4000, Rs. 3540 for 3 consecutive months. How much sale must he have in the fourth month so that he gets an average sale of Rs. 2890?
(A) Rs.3500
(B) Rs. 1520
(C) Rs. 4996
(D) Rs. 4000
(E) Rs. 900
Rationale: Total sale for 5 months = Rs. ( 2500 + 4000 + 3540) = Rs. 10040.
Required sale = Rs. [ (2890 x 4) -10040 ]
= Rs. (11560 - 10040)
= Rs. 1520.
B)
Answer: (B) Rs. 1520
Question: A man reaches his office 20 min late, if he walks from his home at 3 km per hour and reaches 30 min early if he walks 4 km per hour. How far is his office from his house ?
(A) 50 km
(B) 80 km
(C) 20 km
(D) 10 km
(E) 30 km
Rationale: Explanation:
Let distance = x km.
Time taken at 3 kmph : dist/speed = x/3 = 20 min late.
time taken at 4 kmph : x/4 = 30 min earlier
difference between time taken : 30-(-20) = 50 mins = 50/60 hours.
x/3- x/4 = 50/60
x/12 = 5/6
x = 10 km.
Answer: D
Answer: (D) 10 km
Question: Sarah operated her lemonade stand Monday through Friday over a two week period and made a total profit of 350 dollars. On hot days she sold cups of lemonade for a price that was 25 percent higher than the regular days. Each cup she sold had a total cost of 75 cents and Sarah did not incur any other costs. If every day she sold exactly 32 cups and 4 of the days were hot, then what was the price of 1 cup on a hot day?
(A) $ 1.50
(B) $ 1.88
(C) $ 2.09
(D) $ 2.50
(E) $ 3.25
Rationale: 6 regular days --> sales = 6*32*x = 192x;
4 hot days --> sales = 4*32*(1.25x) = 160x;
Total sales = 192x+160x = 352x.
Total cost = 10*32*0.75 = 240.
Profit = 352x - 240 = 350 --> x=1.676.
1.25x=~2.09.
Answer: C.
Answer: (C) $ 2.09
Question: A rectangular farm has to be fenced one long side, one short side and the diagonal. If the cost of fencing is Rs.10 per meter. The area of farm is 1200 m2 and the short side is 30 m long. How much would the job cost?
(A) 1788
(B) 1200
(C) 2789
(D) 1776
(E) 1999
Rationale: l * 30 = 1200 è l = 40
40 + 30 + 50 = 120
120 * 10 = 1200
Answer: B
Answer: (B) 1200
Question: A reduction of 40% in the price of bananas would enable a man to obtain 65 more for Rs.40, what is reduced price per dozen?
(A) 1.95
(B) 2.95
(C) 4.95
(D) 3.95
(E) 5.95
Rationale: 40*(40/100) = 16 --- 65
? --- 12 => Rs.2.95
Answer: B
Answer: (B) 2.95
Question: A train 120 m in length crosses a telegraph post in 6 seconds. The speed of the train is?
(A) 72 kmph
(B) 88 kmph
(C) 54 kmph
(D) 18 kmph
(E) 19 kmph
Rationale: S = 120/6 * 18/5
= 72 kmph
Answer: A
Answer: (A) 72 kmph
Question: If (1 – 1.25)N = 5, then N =
(A)  −20
(B)  −140
(C)  −4
(D)  4
(E)  400
Rationale: (1 – 1.25)N = 5
Simplify to get: -0.25N = 5
Rewrite as (-1/4)N = 5
Multiply both sides by -4 to get: N = -20
Answer: A
Answer: (A)  −20
Question: A and B together can complete work in 5 days. A alone starts working and leaves it after working for 3 days completing only half of the work. In how many days it can be completed if the remaining job is undertaken by B?
(A) 4
(B) 8
(C) 15
(D) 6
(E) 7
Rationale: Explanation:
(A+B) one day work =1/5
now A does half of the work in 3 days so A can complete the whole work in 6 days
A’s one day work =1/6
B’s one day work=1/5 - 1/6= 1/30
B alone can complete the work in 30 days so half of the work in 15 days
Answer: Option C
Answer: (C) 15
Question: 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?
(A) 337
(B) 278
(C) 221
(D) 860
(E) 121
Rationale: Explanation:
CP = SP + 1CP = SP - g
800 + x = 980 - 2x
3x = 180 => x = 60
CP = 800 + 60 = 860
Answer:D
Answer: (D) 860
Question: Suppose 7 students are staying in a hall in a hostel and they are allotted 7 beds. Among them, Parvin does not want a bed next to Anju because Anju snores. Then, in how many ways can you allot the beds?
(A) 600
(B) 620
(C) 670
(D) 690
(E) 700
Rationale: Suppose Anju is allotted bed number 1.
Then, Parvin cannot be allotted bed number 2.
So Parvin can be allotted a bed in 5 ways.
After allotting a bed to Parvin, the remaining 5 students can be allotted beds in 5! ways.
So, in this case the beds can be allotted in 5×5!=6005×5!=600 ways.
Option is A
Answer: (A) 600
Question: A man is 22 years older than his son. In two years, his age will be twice the age of his son. What is the present age of his son?
(A) 23 years
(B) 22 years
(C) 21 years
(D) 20 years
(E) 19 years
Rationale: Let present age of the son =x years
Then, present age the man =(x+22) years
Given that, in 2 years, man's age will be twice the age of his son
â‡’(x+22)+2=2(x+2)
â‡’x=20
ANSWER:D
Answer: (D) 20 years
Question: Which of the following is a prime number ?
(A) 2
(B) 1
(C) 5
(D) 4
(E) 3
Rationale: 2 is a prime number. A prime number is a natural number greater than 1 which has no positive divisors other than 1 and itself. Hence the primer numbers are 2,3,5,7,11,13,17,...
Answer is A.
Answer: (A) 2
Question: Find the greatest number which on dividing 1657 and 2037 leaves remainders 6 and 5 respectively.
(A) 121
(B) 124
(C) 127
(D) 122
(E) 129
Rationale: Required number = H.C.F. of (1657 - 6) and (2037 - 5) = H.C.F. of 1651 and 2032
_______
1651 ) 2032 ( 1 1651
1651_______
381 ) 1651 ( 4
1524_________
127 ) 381 ( 3
381
0
Required number = 127.
Answer is C.
Answer: (C) 127
Question: Two kinds of Vodka are mixed in the ratio 1:2 and 2:1 and they are sold fetching the profit 30% and 20% 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) 18%
(B) 20%
(C) 21%
(D) 23%
(E) Cannot be determined
Rationale: Answer: D.
Answer: (D) 23%
Question: If a and b are two-digit integers such that a > 20 and b<60, which of the following is closest to the maximum possible value of ab ?
(A)  700
(B)  2,800
(C)  5,841
(D)  7,000
(E)  28,000
Rationale: To get the maximum possible value of ab, we need maximize the value of both a and b
max a can be = 99 (given a is a two-digit integer > 20)
max b can be = 59 (given b is a two-digit integer < 60)
xy = 99*59 = 5841
Answer (C)
Answer: (C)  5,841
Question: A jar is filled with red, white, and blue tokens that are equivalent except for their color. The chance of randomly selecting a red token, replacing it, then randomly selecting a white token is the same as the chance of randomly selecting a blue token. If the number of tokens of every color is a multiple of 4, what is the smallest possible total number of tokens in the jar?
(A)  9
(B)  12
(C)  15
(D)  18
(E)  21
Rationale: (Red / Total Coins)*(White / Total Coins) = (Blue / Total Coins)
i.e. Red*White = Blue*Total Coins
Let, Red = 3a
White = 3b
Blue = 3c
Total Coins = 3(a+b+c)
i.e. 3a * 3b = 3c*3(a+b+c)
i.e. a*b = c*(a+b+c)
For smallest values of a, b and c
2*3 = 1*(1+2+3)
i.e. Minimum Total Coins = 3*(1+2+3) = 18
Answer: Option C
Answer: (C)  15
Question: Line m lies in the xy-plane. The y-intercept of line m is -2, and line m passes through the midpoint of the line segment whose endpoints are (2, 8) and (12,2). What is the slope of line m?
(A) -2
(B) -1
(C) 0
(D) 1
(E) 2
Rationale: The midpoint of (2,8) and (12,2) is (7,5).
The slope of a line through (0,-2) and (7,5) is (5-(-2))/(7-0) = 7/7 = 1
The answer is D.
Answer: (D) 1
Question: A straight pipe 7 yard in length was marked off in fourths and also in thirds. If the pipe was then cut into separate pieces at each of these markings, which of the following gives all the different lengths of the pieces, in fractions of a yard?
(A)  1/6 and 1/4 only
(B)  1/4 and 1/3 only
(C)  1/6, 1/4, and 1/3
(D)  1/12, 1/6 and 1/4
(E)  1/12, 1/6, and 1/3
Rationale: Since we want to find the fractions, we can assume some other length of the pipe which will make calculation easier. Take the length of the pipe to be 12-meter long (the least common multiple of 3 and 4.
In this case the branch would be cut at3,4, 6,8, and 9meters (in black are given fourths of the length and in red thirds of the length).
Distinct lengths would be: 3=3/12=1/3, 4-3=1=1/12and 6-4=2=2/12=1/6meters long pieces.
Answer: E.
Answer: (E)  1/12, 1/6, and 1/3
Question: A father said his son , " I was as old as you are at present at the time of your birth. " If the father age is 32 now, the son age 5 years back was
(A) 11
(B) 17
(C) 11
(D) 19
(E) 99
Rationale: Let the son's present age be x years .Then, (32 - x) = x x= 16.
Son's age 5 years back = (16 - 5) = 11 years
Answer: A
Answer: (A) 11
Question: How many integers k greater than 100 and less than 1100 are there such that if the hundreds and the unit digits of k are reversed, the resulting integer is k + 99?
(A) 50
(B) 60
(C) 70
(D) 80
(E) 90
Rationale: Not sure if this is the shortest.. But this is how I did this
There are 9 sets of integers with hundreds and units digits exchanged that satisfies k + 99.
1. 102 | 201 (satisfies k+99, where k = 102)
2. 203 | 302 (satisfies k+99, where k = 203)
3. ...
4. ...
5. ...
6. ...
7. 708 | 807
8. 809 | 908
9. 910 | 1001
Each set has 10 such numbers.
1. 102 | 201 (still k+99 holds good)
2. 112 | 211
3. 122 | 221
4. 132 | 231
5. ...
6. ...
7. ...
8. ...
9. 182 | 281
10. 192 | 291
Therefore, 9 sets with 10 such number in each set will give 9 x 10 = 90 integers.
E
Answer: (E) 90
Question: Compound interest of Rs.6000 at 10% per annum for 1 1/2years will be (interest compounded half yearly).
(A) Rs.473
(B) Rs.374
(C) Rs.495
(D) Rs.945
(E) None of the above
Rationale: 10% interest per annum will be 5% interest half yearly for 3 terms( 1 1/2 years)
So compound interest=6000[1+(5/100)]^3 - 6000=6000[(21/20)^3 -1]
=6000(9261-8000)/8000
=6*1261/8
=945
ANSWER:D
Answer: (D) Rs.945
Question: The speed of a boat in upstream is 50 kmph and the speed of the boat downstream is 90 kmph. Find the speed of the boat in still water and the speed of the stream?
(A) 10
(B) 40
(C) 88
(D) 66
(E) 23
Rationale: Speed of the boat in still water = (50+90)/2 = 70 kmph. Speed of the stream = (90-50)/2 = 20 kmph. Answer:B
Answer: (B) 40
Question: On a map the distance between two mountains is 312 inches. The actual distance between the mountains is 140 km. Ram is camped at a location that on the map is 34 inch from the base of the mountain. How many km is he from the base of the mountain?
(A) 14.83
(B) 14.81
(C) 14.8
(D) 15.25
(E) 14.12
Rationale: Explanation:
Since 312 inch = 140 km
So 1 inch = 140/312 km
So 34 inch = (140 Ã— 34)/ 312 = 15.25 km
Answer: D
Answer: (D) 15.25
Question: If the simple interest on Rs. 8010 amount to Rs $3364.20 in 6 Years, calculate the rate percent?
(A) 5%
(B) 6%
(C) 7%
(D) 3%
(E) 9%
Rationale: 3364.20 = (8010*6*R)/100
R = 7%
Answer: C
Answer: (C) 7%
Question: During the first week of performances of a certain play, 5,400 tickets were sold, all at reduced price. During the remaining weeks of performances, 5 times as many tickets were sold at full price as were sold at reduced price. If the total number of tickets sold Q was 25,200, how many of them were sold at full price?
(A) 21,000
(B) 19,800
(C) 16,500
(D) 15,800
(E) 8,700
Rationale: Given:
The question tells us about the number of tickets sold in the first week at reduced price = 5,400. It also tells us that during the remaining weeks, the number of tickets sold at full price was 5 times the no. of tickets sold at reduced price. The total tickets sold was 25,200, and we are asked to find the number of tickets that where sold at full price.
Approach:
The question asks us to find the number of ticket sold at full price. We know that the number of tickets sold at full price was 5 times the no. of tickets sold at reduced price in remaining weeks. Hence, assuming tickets sold at reduced price in remaining weeks to be x would give us the no. of tickets sold at full price to be 5x.
Tickets sold in first week + Tickets sold in remaining weeks = Total no. of tickets soldi.e.
Tickets sold in first week + Tickets sold at full price in remaining weeks + Tickets sold at reduced price in remaining weeks = Total no. of tickets sold
We know the no. of tickets sold during first week and the total no. of tickets sold. We will use this relation to get to our answer.
Working Out:
Tickets sold in first week + Tickets sold at full price in remaining weeks + Tickets sold at reduced price in remaining weeks = Total no. of tickets sold
Substituting values in the equation, we get
5,400 + 5x + x = 25,200
x= 3,300
Tickets sold at full price = 5x = 16,500
Answer: Option C
Answer: (C) 16,500
Question: When positive integer k is divided by 5, the remainder is 2. When k is divided by 6, the remainder is 5. If k is less than 38, what is the remainder when k is divided by 7?
(A) 2
(B) 4
(C) 3
(D) 5
(E) 6
Rationale: Cant think of a straight approach but here is how I solved it:
K is divided by 5 and remainder is 2. This means k = 5n + 2 (n is an integer)
so the possible values of K = {2, 7, 12, 17, 22, 27, 32, 37} (less than 38)
Secondly, if K is divided by 6, the remainder is 5 => k= 6m + 5
so the possible value set for k = {5, 11, 17, 23, 29,35} (less than 38)
17 is the only common number in both the sets. Hence k = 17
Answer : C
Answer: (C) 3
Question: Two drivers began their journey with the same amount of petrol in their cars at the same time. The only difference is that the first driver�s car could drive 4 hours in that amount of petrol and the second one could drive 5 hours.
However, they only drove for some time and found that the amount of petrol that was left in one of the cars was four times the petrol left in the other one.
For how long had they driven at this point of time?
(A) 3.75 hours
(B) 5.45 hours
(C) 7.10 hours
(D) 4.75 hours
(E) 3.33 hours
Rationale: A
3.75 hours
While you can solve it as you like, a simple mathematical equation can be used to find out.
Let M be the amount of petrol initially.
Let N be the time for which they drove.
According to the question, the amount of petrol used by first car in N hours = MN / 4
The amount of petrol used by second car in N hours = MN / 5
Hence, the amount of petrol left in the first car = (M - MN / 4)
The amount of petrol left in the second car = (M - MN / 5)
AS per the details given in the question, we can form the below equation:
M - MN / 5 = 4(M - MN / 4)
N = 15 / 4 or 3.75 hours.
Hence, both the drivers have driven the car for 3.75 hours at that particular time.
Answer: (A) 3.75 hours
Question: A rectangular field is to be fenced on three sides leaving a side of 20 feet uncovered.If the area of the field is 680 sq.ft, how many feet of fencing will be required?
(A) 44ft
(B) 88ft
(C) 22ft
(D) 11ft
(E) 66ft
Rationale: Given that length and area, so we can find the breadth.
Length x Breadth = Area
20 x Breadth = 680
Breadth = 34 feet
Area to be fenced = 2B + L = 2 (34) + 20 = 88 feet
Answer: B) 88ft
Answer: (B) 88ft
Question: Three bells chime at intervals of 18 min., 24 min. and 32 min. respectively. At a certain time they begin together. What length L of time will elapse before they chime together again?
(A) 2 hr. and 24 min.
(B) 4 hr. and 48 min.
(C) 1 hr. and 36 min.
(D) 5 hr.
(E) 2 hr.
Rationale: It should be simple. All the three bells will chime again together whenver their time intervals intersect eachother.
So the LCM of the three time intervals (18, 24,32) would be the answer.
LCM (18, 24, 32) L= 288 => 4 hours 48 mins.B
Answer: (B) 4 hr. and 48 min.
Question: Last year Elaine spent 20% of her annual earnings on rent. This year she earned 15% more than last year and she spent 25% of her annual earnings on rent. The amount she spent on rent this year is what percent of the amount spent on rent last year?
(A)  152.5
(B)  143.75
(C)  155.5
(D)  165.5
(E)  117.5
Rationale: For this it is easiest to use simple numbers. Let's assume that Elaine's annual earnings last year were $100.
She would've spent $20 of this on rent.
This year she earned 15% more, or $115.
She would've spent 25% of this on rent, or $28.75
Do $34.5/$20
This will give you 143.75%
B is the correct answer.
Answer: (B)  143.75
Question: The length of the bridge, which a train 150 meters long and travelling at 45 km/hr can cross in 30 seconds, is?
(A) 328
(B) 279
(C) 225
(D) 288
(E) 211
Rationale: Speed = (45 * 5/18) m/sec = (25/2) m/sec. Time = 30 sec. Let the length of bridge be x meters. Then, (150 + X)/30 = 25/2 ==> 2(150 + X) = 750 ==> X = 225 m.Answer: C
Answer: (C) 225
Question: A box contains 20 balls, numbered from 1 to 20. If three balls are selected at random and with replacement from the box, what is the probability that the sum of the three numbers on the balls selected from the box will be odd?
(A) 1/4
(B) 3/8
(C) 1/2
(D) 5/8
(E) 3/4
Rationale: I don't think order matters in this case, because 2 + 2 + 1 = 2 + 1 + 2
My answer is: 1/4
A
Answer: (A) 1/4
Question: The average temperature for Monday, Tuesday, Wednesday and Thursday was 48 degrees and for Tuesday, Wednesday, Thursday and Friday was 40 degrees. If the temperature on Monday was 42 degrees. Find the temperature on Friday?
(A) 8
(B) 9
(C) 10
(D) 12
(E) 16
Rationale: M + Tu + W + Th = 4 * 48 = 192
Tu + W + Th + F = 4 * 40 = 160
M = 42
Tu + W + Th = 192 -42 = 150
F = 160 – 150 = 10
ANSWER:C
Answer: (C) 10
Question: On a certain date, Pat invested $10,000 at x percent annual interest, compounded annually. If the total value of the investment plus interest at the end of 12 years will be $40,000, in how many years, the total value of the investment plus interest will increase to $240,000?
(A) 27
(B) 16
(C) 18
(D) 20
(E) 24
Rationale: if i were to choose during the test, would go for 18 or 20. probably 18 cuz it wont take too long to get the value doubled....
I found a method: Rule of 72.
Given an x% return, it takes 10,000 to quadralope 12 years.
So according to the rule: 72/x is the no of years 10,000.00 took to double 20,000.00.
Again, 20,000.00 took to double 40,000.00 same (72/x) no of years.
72/x+ 72/x = 12
x = 12% (though rate here is not very much required).
Again, 40,000.00 takes the same (72/x) no of years to double 240,000.00.
72/x = 6 years.
So altogather:
10,000 - 20,000 = 6 years
20,000 - 40,000 = 6 years
40,000 - 80,000 = 6 years
80,000 - 160,000 = 6 years
160,000 - 240,000 = 3 years
total 27 years.
Answer A
Answer: (A) 27
Question: Using all the letters of the word "NOKIA", how many words can be formed, which begin with N and end with A?
(A) 3
(B) 6
(C) 24
(D) 120
(E) 12
Rationale: Explanation:
There are five letters in the given word.
Consider 5 blanks ....
The first blank and last blank must be filled with N and A all the remaining three blanks can be filled with the remaining 3 letters in 3! ways.
The number of words = 3! = 6.
ANSWER IS B
Answer: (B) 6
Question: If â€˜NAGALANDâ€™ is coded as â€˜EAGACAEDâ€™, then â€˜ODISHAâ€™ is coded as
(A) FDIHJA
(B) FIDHAJ
(C) FDIHAJ
(D) FIDJHA
(E) FDIJHA
Rationale: M=13,1+3=4=D
A=1=A
SIMILARLY,
O=15=F
D=4=D
I=9=I
S=19=1+9=10=J
H=8=H
A=1=A
SO ANS IS
FDIJHA
ANSWER:E
Answer: (E) FDIJHA
Question: A certain ski shop sells pairs of gloves in 11 different colors. If one pair of each color is dropped in a bag and a store clerk reaches in to draw two individual gloves simultaneously and at random, what is the probability that she draws two gloves of the same color?
(A) 1/144
(B) 1/143
(C) 1/21
(D) 1/23
(E) 1/12
Rationale: there are 11 different colours sothere are 11 pairs of gloves dropped..
first can be any of 22..so 22/22..
second has to be its pair, which will be just one out of remaining 21.. 1/21..
overall prob=22/22*1/21= 1/21..
C
Answer: (C) 1/21
Question: If 40% of a number is equal to two-third of another number, what is the ratio of first number to the second number?
(A) 1:2
(B) 2:3
(C) 5:3
(D) 3:7
(E) 9:13
Rationale: Let 40% of A = 2/3 B
then 40A/100 = 2B/3
2A/5 = 2B/3
A/B = 5/3
A:B = 5:3
Answer is C
Answer: (C) 5:3
Question: Last month, John rejected 0.7% of the products that he inspected and Jane rejected 0.8 percent of the products that she inspected. If total of 0.75 percent of the products produced last month were rejected, what fraction of the products did Jane inspect?
(A) 1/6
(B) 1/2
(C) 5/8
(D) 5/6
(E) 15/16
Rationale: X - fraction of products Jane inspected
(1 - X) - fraction of products John inspected
0.8(X) + 0.7(1-X) = 0.75
0.1X = 0.75 - 0.7
X = 0.05/0.1
X = 1/2
Therefore the answer is B: 1/2.
Answer: (B) 1/2
Question: A student chose a number, multiplied it by 2, then subtracted 138 from the result and got 112. What was the number he chose?
(A) 123
(B) 267
(C) 125
(D) 267
(E) 120
Rationale: Let xx be the number he chose, then
2â‹…xâˆ’138=112
x=125
Answer:C
Answer: (C) 125
Question: A trader has 1600Kg of sugar. He sells a part at 8% profit and the rest at 12% profit. If he gains 11%
on the whole , find the quantity sold at 12%.
(A) 1200 Kg
(B) 1400 Kg
(C) 1600 Kg
(D) 800 Kg
(E) None of these
Rationale: Explanation :
By the rule of alligation, we have
% Profit by selling part1 % Profit by selling part2
8 12
Net % Profit
11
12 - 11 = 1 11 - 8 = 3
=>Quantity of part1 : Quantity of part2 = 1 : 3
Given that total quantity = 1600 Kg
Hence quantity of part2 (quantity sold at 12%) = 1600×34=1200
Answer : Option A
Answer: (A) 1200 Kg
Question: Tom planted vegetables in a rectangular garden that was 24 feet long and 15 feet wide. He used
1/3 of the area for corn and 1/5 of it for peas. How many square feet are left for other vegetables?
(A) 165 sq. ft.
(B) 166 sq. ft.
(C) 167 sq. ft.
(D) 168 sq. ft.
(E) 169 sq. ft.
Rationale: area of garden is 24 x 15 = 360 sq. ft.
1/3 x 360 = 120 sq. ft. for corn
1/5 x 360 = 72 sq. ft. for peas
120 + 72 = 192 sq. ft. used
360 - 192 = 168 sq. ft. left over
correct answer D
Answer: (D) 168 sq. ft.
Question: Six bells commence tolling together and toll at the intervals of 2,4,6,8,10,12 seconds resp. In 60 minutes how many times they will toll together.
(A) 15
(B) 16
(C) 30
(D) 31
(E) 32
Rationale: Explanation:
LCM of 2-4-6-8-10-12 is 120 seconds, that is 2 minutes.
Now 60/2 = 30
Adding one bell at the starting it will 30+1 = 31
Option D
Answer: (D) 31
Question: 0.003 * ? * 0.0003 = 0.00000027
(A) 9
(B) 3
(C) 0.3
(D) 0.03
(E) None of these
Rationale: Explanation:
0.003 * ? * 0.0003 = 0.00000027
3/1000 * ? * 3/10000 = 3/1000 * 3/1000 * 3/100
? = 3/10 = 0.3
ANSWER IS C
Answer: (C) 0.3