mathewhe/aqua_rat huggingface dataset:
Question: Each week, Harry is paid X dollars per hour for the first 30 hours and 1.5X dollars for each additional hour worked that week. Each week, James is paid X dollars per hour for the first 40 hours and 2X dollars for each additional hour worked that week. Last week James worked a total of 53 hours. If Harry and James were paid the same amount last week, how many hours did Harry work last week?
(A) 35
(B) 36
(C) 37
(D) 38
(E) 54
Rationale: Amount earned by James = 40*x + 13*2x = 66x
Therefore, Amount earned by Harry = 66x
But we know the amount Harry earned assuming working y hours (y>30) is 30*x + (y-30)*1.5x
[[We know y>30 because in 30h the most Harry could earn is 30x, but he has earned 66x]]
So x*(1.5y -45 +30) = 66x
Or x*(1.5y - 15) = 66x
So 1.5y - 15 = 66
So 1.5y = 81
So y = 54
Answer is E
Answer: (E) 54
Question: A card is drawn from a pack of 52 cards. The probability of geƫng a queen of club or a king of heart is
(A) 1/13
(B) 2/13
(C) 1/26
(D) 1/52
(E) None of these
Rationale: Explanation:
Total number of cases = 52
Favourable cases = 2
Probability = 2/56 = 1/26
Answer: C
Answer: (C) 1/26
Question: Two trains start together to travel to a certain destination,one at speed of 55 km/hr and another at 65 km/hr. The former arrives 3 hours after the latter. What is the total distance.
(A) 768 km.
(B) 887 km.
(C) 9002.5 km.
(D) 1002 km.
(E) 1072.5 km.
Rationale: A _________________X Km_______________________B
Let both trains starts from A. Distance is X km. Faster trains take t hour and other one takes (t -3) hours.
For both trains distance is same to travel.
Speed of faster train /speed of slower train = time taken by slower train /time taken by faster train
65/55 = (t +3)/t
13t = 11t + 33
2t = 33
t = 16.5 hours.
Total distance = s *t = 65 * 16.5 = 1072.5 km.
ANSWER :OPTION E
Answer: (E) 1072.5 km.
Question: If a code word is defined to be a sequence of different letters chosen from the 10 letters A, B, C, D, E, F, G, H, I, and J, what is the ratio of the number of 8-letter code words to the number of 6-letter code words?
(A) 5 to 4
(B) 3 to 2
(C) 12 to 1
(D) 5 to 1
(E) 6 to 1
Rationale: Number of ways to form 8-letter code: 10!/2! = 10*9*8*7*6*5*4*3
Number of ways to form 6-letter code: 10!/4! = 10*9*8*7*6*5
Ratio: 12 to 1
Answer : C
Answer: (C) 12 to 1
Question: Donald plans to invest x dollars in a savings account that pays interest at an annual rate of 8% compounded quarterly. Approximately what amount is the minimum that Donald will need to invest to earn over $100 in interest within 6 months?
(A) 1500
(B) 1750
(C) 2000
(D) 2500
(E) 3000
Rationale: Compound interest formula
A = P ( 1+r/n)power nt
given, n= 4 (quaterly);r =.08
the approach is substitution,
our interest requirement is 100$ after 6 months, 2 compounding period. interest per compounding period is 2%
lets take 1500, after 3 months interest accumulated is 30$, total amount is 1530
after 6 months, interest is 30.6$ and total is 1560.6$, so not 1500
1500 & 1750 have a difference of 250$ only , but the expected interest different is around 40$ hence you can straightaway rule out 1750
2000 is again can be ruled out as approx 4% interest yeilds only 80$
2500$ is a good bet, first 3 months it earns 50$ as interest, next 3 months it will earn 51$ as interest.
hence answer is D
Answer: (D) 2500
Question: How many paying stones, each measuring 2 1/2 m * 2 m are required to pave a rectangular court yard 30 m long and 16 1/2 m board?
(A) 99
(B) 626
(C) 27
(D) 26
(E) 28
Rationale: 30 * 33/2 = 5/2 * 2 * x => x
= 99
Answer: A
Answer: (A) 99
Question: If 30% of a class averages 95% on a test, 50% of the class averages 79% on the test, and the remainder of the class averages 60% on the test, what is the overall class average? (Round final answer to the nearest percent).
(A) 76%
(B) 77%
(C) 78%
(D) 79%
(E) 80%
Rationale: This question is a Weighted Average question with a series of dependent variables.
The remaining portion of the class represents 100% - 30% - 50% = 20% of the class
Converting the portions of the class population to decimal weights, we find:
Class Average = 0.30x95 + 0.50x79 + 0.20x60 = 80
The class average (rounded) is 80%
Final Answer
E) 80%
Answer: (E) 80%
Question: A merchant marks goods up by 75% and then offers a discount on the marked price. The profit that the merchant makes after offering the discount is 5%. What % discount did the merchant offer?
(A) 20%
(B) 25%
(C) 35%
(D) 40%
(E) 45%
Rationale: Let P be the original price of the goods and let x be the rate after the markup.
(1.75P)*x = 1.05P
x = 1.05/1.75 = 0.6 which is a discount of 40%.
The answer is D.
Answer: (D) 40%
Question: 1!+2!+3!+4!+5!+.100! is divided by 24. Find the remainder from this?
(A) 4
(B) 6
(C) 9
(D) 10
(E) 11
Rationale: By applying rule 2, we divide the terms of the above expression individually, and add them to get the final remainder. But from 4! onwards all the terms leave a remainder 0 when divided by 24.
So the remainder = 1 + 2 + 6 + 0 + 0....... =
C
Answer: (C) 9
Question: A train running at the speed of 120 km/hr crosses a pole in 9 seconds. Find the length of the train.
(A) 100 meter
(B) 150 meter
(C) 200 meter
(D) 250 meter
(E) 300 meter
Rationale: Speed = 120*(5/18) m/sec = 200/6 m/sec
Length of Train (Distance) = Speed * Time
(200/6) * 9 = 300 meter
Answer:E
Answer: (E) 300 meter
Question: HOW MANY KGS OF TEA WORTH RS.25/KG MUST BE BLENDED WITH 30 KGS OF TEA WORTH RS.30/KG SO THAT BY SELLING THE BLENDED VARIETY AT RS.30/KG THERE SHOULD BE A GAIN OF 5%
(A) 36
(B) 40
(C) 32
(D) 12
(E) 45
Rationale: (x+30)*30=(105/100)(25x+30*30)
Solving we get 12.
Answer is D.
Answer: (D) 12
Question: judith is practicing her dance steps along with her friends. In a particular sequence, all of them form a row. At that point, judithis standing on the 6th position from either end of the row.
Can you find out how many girls are practicing together?
(A) 4
(B) 9
(C) 11
(D) 6
(E) 8
Rationale: As judith is 6th from either end of the row, it means that 5 girls are on one of her sides and 5 are present on the other.
5 + 5 + 1(judith herself) = 11.
Hence, 11 girls are practicing the dance together.
correct answer is C)11
Answer: (C) 11
Question: A bus leaves Los Angeles at 7:00 a.m. traveling north at 80 miles per hour. At 12:00 p.m. a plane leaves Los Angeles traveling north at 380 miles per hour. At what time will the plane overtake the bus?
(A) 1:45 p.m.
(B) 1:20 p.m.
(C) 12:25 p.m.
(D) 12:40 p.m.
(E) 2:10 p.m.
Rationale: At 12:00pm, the bus is 400 miles ahead of plane
The plane travels at 380 mph, which gains 300 mph on bus
400/300= 4/3 hours = 80 minutes
12:00 + 0:80 = 1:20
The plane will overtake bus at 01:20pm
Answer:B
Answer: (B) 1:20 p.m.
Question: The first three terms of a proportion are 3, 9 and 12. The fourth term is?
(A) 15
(B) 87
(C) 16
(D) 36
(E) 12
Rationale: (9*12)/3 = 36
Answer: D
Answer: (D) 36
Question: If 5x + 3 = 10x – 17, what is the value of x?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: solve for x:
5x+3=10x-17
20=5x
4=x
correct answer D)4
Answer: (D) 4
Question: Mike earns $14 per hour and Phil earns $7 per hour. Approximately how much less, as a percentage, does Phil earn than Mike per hour?
(A) 25%
(B) 32.5%
(C) 37%
(D) 50%
(E) 40%
Rationale: What % less of 14 is 7
let it be x % less ,then
=14(1-x/100)=7
1-x/100=7/14
x=100/2
x=50%
Ans D
Answer: (D) 50%
Question: A certain amount earns simple interest of Rs. 1200 after 10 years. Had the interest been 2% more, how much more interest would it have earned?
(A) Rs. 25
(B) None of these
(C) Rs. 120
(D) Rs. 100
(E) Cannot be determined
Rationale: Explanation :
Since we do not have the principal and rate of interest, we can not find out the required details.
Answer : Option D
Answer: (D) Rs. 100
Question: X and Y run a 100m race,where X beats Y by 20 m. To do a favor to Y, X starts 10m behind the starting line in a second 100m race. Both run at the same previous speed. Which of the following is true?
(A) X Beats Y by 2m
(B) X Beats Y by 0.5 m
(C) X Beats Y by 4 m
(D) X Beats Y by 4 m
(E) Y Beats X by 10m
Rationale: Let's suppose that the speed of X is 10m/s and that the speed of Y is 8 m/s.
So, in the first race, the results are the following:
X crosses the finish line in 10s. In other words, X has run 100m in 10 s.
In 10s, Y has run 80 meters.
Therefore, there is the difference of 20 meters mentioned in the question.
Now, let's review the second race.
In 12 seconds, X can complete the 100 meters race. We have to remember that X is 4 meters behind the starting line.
But in 12 seconds, Y has covered (96 ) =96 meters. Also, it is important to notice that in 12 seconds Y cannot arrive to the finish line.
So, 100 - 96 = 4 meter
Answer: D
Answer: (D) X Beats Y by 4 m
Question: By selling a house for Rs.45000, it was found that 1/8 of the outlay was gained, what ought the selling to price to have been in order to have lost 5 p.c?
(A) 54670
(B) 12300
(C) 38000
(D) 43200
(E) 45000
Rationale: Option C
Explanation:
CP + CP/8 = 45000
CP = 40000
SP = 40000*(95/100) = 38000
Answer: (C) 38000
Question: Hitesh is 40 years old and Ronnie is 60 years old. How many years ago was the ratio of their ages 3 : 5?
(A) 5 years
(B) 10 years
(C) 20 years
(D) 37 years
(E) None
Rationale: Solution
Suppose, the ratio was 3 : 5, x years ago.
Then,	40 - x / 60 - x
= 3 / 5.
‹=›5(40-x)=3(60-x)
‹=›2x= 20
‹=›x= 10
Answer B
Answer: (B) 10 years
Question: If ab represents a positive two digit number, where a and b are single digit integers, which of the following cannot be true?
(A) a+b =9
(B) (a)(b)=9
(C) a-b = 9
(D) b-a= 9
(E) a/b = 9
Rationale: (A) ab = 45 or 63 or 27
(B) ab = 33 or 19
(C) 90
(D) impossible
(E) ab = 91
(D) is impossible because 09 is not a valid two digit number --- if there's a zero in the ten's place, that's just 9, a single digit number. Therefore, no valid two digit number would satisfy (D).
ans D
Answer: (D) b-a= 9
Question: If n is a positive integer, what is the remainder when (7^(3n+3))(6^n) is divided by 10?
(A) 1
(B) 2
(C) 4
(D) 6
(E) 8
Rationale: This one took me bout 3 1/2 min. Just testin numbers and what not.
First notice that n is positive. Save time by noticing thatI worked out one solution where n=0 only to find that thats not an option :p.
1-7 stands for ^1 thru 7
1: 7*1=7
2: 7*7=9
3: 7*9=3
4: 7*3=1
5: 7*1=7
6: 7*7=9
7: 7*9=3
Pattern repeats every @ 5. Notice every ^4 or multiple of 4 is always going to be 1. This is just for future notice for similar problems.
so 7^4n+3 ---> if n=1 then its ((7^7)*6))/10 which can say is going to be 3*8--> 18/10 --> R=8
Now from here if id double check just to make sure.
7^4(2)+3*6^2 ---> 7^11*36 or we can just say again 7^11*6 (b/c we are only interested in the units digit).
Since ^12 is going to be 1 that means ^11 is going to be 3 (as taken from our pattern)
so again 3*6=18/10 ---> R =6.
D or J in this problem.
Answer: (D) 6
Question: The weights of three boys are in the ratio 4 : 5 : 6. If the sum of the weights of the heaviest and the lightest boy is 47 kg more than the weight of the third boy, what is the weight of the lightest boy?
(A) 87.6 kg
(B) 37.6 kg
(C) 98.6 kg
(D) 65.6 kg
(E) 87 kg
Rationale: Let the weights of the three boys be 4k, 5k and 6k respectively.
4k + 6k = 5k + 47
=> 5k = 47 => k = 9.4
Therefore the weight of the lightest boy
= 4k = 4(9.4) = 37.6 kg.
Answer:B
Answer: (B) 37.6 kg
Question: Find the area of a parallelogram with base 21 cm and height 11 cm?
(A) 231
(B) 284
(C) 288
(D) 255
(E) 122
Rationale: Area of a parallelogram = base * height
= 21 * 11
= 231 cm2
Answer: A
Answer: (A) 231
Question: Find the value of 1/(3+1/(3+1/(3-1/3)))
(A) 21/29
(B) 27/89
(C) 89/21
(D) 29/21
(E) None
Rationale: 1/[3 + (1/(3+1/(3 - 1/3)))]
=> 1/[3 + 1/(3 + 1/(8/3))]
=> 1/[3 + 1/(3 + 3/8)]
=> 1/[3 + 8/27]
=> 1/(89/27)
=> 27/89
B
Answer: (B) 27/89
Question: X starts a business with Rs.45000. Y joins in the business after 3 months with Rs.30000. What will be the ratio in which they should share the profit at the end of the year?
(A) 1:2
(B) 2:1
(C) 3:2
(D) 2:3
(E) 5:3
Rationale: Ratio in which they should share the profit
= Ratio of the investments multiplied by the time period
=45000×12:30000×9
=45×12:30×9
=3×12:2×9
=2:1
Answer is B.
Answer: (B) 2:1
Question: Ratio between two numbers is 3: 4 and their sum is 420. Find the smaller number?
(A) 240
(B) 180
(C) 160
(D) 140
(E) 150
Rationale: Explanation:
3x + 4x = 420
x = 60 => 3x = 180
ANSWER IS B
Answer: (B) 180
Question: On average, the boys in the class have 56 pens and the girls have 32 pens. If the overall class average is 41 pens, what is the ratio of boys to girls in the class?
(A) 1/3
(B) 3/4
(C) 3/2
(D) 2/3
(E) 3/5
Rationale: (32G + 56B) / (G+B) = 41
32G + 56B = 41(G+B)
15B=9G
B/G = 3/5
The answer is E.
Answer: (E) 3/5
Question: Ms. Martha invested in Fund W and Fund B. The total amount she invested, in both funds combined, was $100,000. In one year, Fund W paid 23% and Fund B paid 17%. The interest earned in Fund B was exactly $200 greater than the interest earned in Fund W. How much did Ms. Morris invest in Fund W?
(A)  $32,000
(B)  $36,000
(C)  $40,000
(D)  $42,000
(E)  $45,000
Rationale: 0.17B-0.23W = 200 | * 100
17B-23W=20,000
W+B=100,000
B=100,000 - W
17(100,000 - W) - 23W = 20,000
1,700,000 - 17W - 23W = 20,000
1,680,000 = 40W
divide by 40
first two digits: 42...so answer is D.
Answer: (D)  $42,000
Question: In a class there are 20 boys and 25 girls. In how many ways can a boy and a girl be selected?
(A) 176 ways
(B) 500 ways
(C) 178 ways
(D) 198 ways
(E) 156 ways
Rationale: We can select one boy from 20 boys in 20 ways.
We select one girl from 25 girls in 25 ways
We select a boy and girl in 20 * 25 ways i.e.,
= 500 ways.
Answer:B
Answer: (B) 500 ways
Question: A pharmaceutical company received $3 million in royalties on the first $20 million in sales of and then $9 million in royalties on the next $108 million in sales. By approximately what percentage did the ratio of royalties to sales decrease from the first $20 million in sales to the next $104 million in sales?
(A) 8%
(B) 15%
(C) 45%
(D) 42%
(E) 56%
Rationale: (9/104)/(3/20) = 30/54 = 57,6% it means that 9/108 represents only 57,6%. Therefore a decrease of 42%.
Answer D
Answer: (D) 42%
Question: A man can do a piece of work in 10days, but with the help of his son, he can do it in 4 days. In what time can the son do it alone?
(A) 13/2
(B) 17/3
(C) 15/2
(D) 20/3
(E) 9
Rationale: Son's 1day's work = (1/4)-(1/10) = 3/20
The son alone can do the work in 20/3 days
Answer is D
Answer: (D) 20/3
Question: A speaks truth in 75% of cases and B in 80% of cases. In what percentage of cases are they likely to contradict each other, narrating the same incident
(A) 35/900
(B) 35/100
(C) 35/101
(D) 35/109
(E) 35/122
Rationale: Explanation:
Let A = Event that A speaks the truth
B = Event that B speaks the truth
Then P(A) = 75/100 = 3/4
P(B) = 80/100 = 4/5
P(A-lie) = = 1/4
P(B-lie) = = 1/5
Now, A and B contradict each other =[A lies and B true] or [B true and B lies]
= P(A).P(B-lie) + P(A-lie).P(B)
=
= = 35%
Answer: B) 35/100
Answer: (B) 35/100
Question: In an examination, a student scores 4 marks for every correct answer and loses 1 mark for every wrong answer. If he attempts all 80 questions and secures 120 marks, How many questions does he answer correctly?
(A) 20
(B) 10
(C) 30
(D) 50
(E) 40
Rationale: Let the number of correct answers be x
Then, number of wrong answers = (80 - x)
4x – (80 - x) = 120
=> 4x – 80 + x = 120
=> 5x = 200
=> x = 200/5 = 40
i.e., he does 40 questions correctly
Answer is E.
Answer: (E) 40
Question: There are 50 students in a class. If 6% are absent on a particular day, find the number of students present in the class.
(A) 47
(B) 36
(C) 28
(D) 12
(E) 11
Rationale: Number of students absent on a particular day = 6 % of 50
i.e., 6/100 × 50 = 3
Therefore, the number of students present = 50 - 3 = 47 students.
Answer: A
Answer: (A) 47
Question: A 7" cube is painted in all its faces and then it is cut down into 1" blocks. How many 1" blocks
are there even without a single face being painted?
(A) 81
(B) 100
(C) 125
(D) 144
(E) 225
Rationale: The unpainted blocks are the interior blocks.
These blocks form a 5" cube on the inside.
The number of unpainted blocks is 5*5*5 = 125 blocks.
The answer is C.
Answer: (C) 125
Question: The capacity of a tank of dimensions (8m x 6m x 2.5m)is
(A) 120 litres
(B) 1200 litres
(C) 12000 litres
(D) 120000 litres
(E) None of these
Rationale: Explanation:
capacity of atank =volume of tank
= (8 x 100 x 6 x 100 x 2.5 x 100)/1000 litres
= 120000 litres
Answer: D
Answer: (D) 120000 litres
Question: Meg and Bob are among the 7 participants in a cycling race. If each participant finishes the race and no two participants finish at the same time, in how many different possible orders can the participants finish the race so that Meg finishes ahead of Bob?
(A) 24
(B) 30
(C) 60
(D) 2220
(E) 120
Rationale: Total # of ways the race can be finished is 7!. In half of the cases Meg finishes ahead of Bob and in other half Bob finishes ahead of Meg. So, ways Meg to finish ahead of Bob is 7!/2=2220.
Answer: D.
Answer: (D) 2220
Question: At Deluxe paint store, Fuchsia paint is made by mixing 5 parts of red paint with 3 parts of blue paint. Mauve paint is made by mixing 3 parts of red paint with 5 parts blue paint. How many liters of blue paint must be added to 24 liters of Fuchsia to change it to Mauve paint?
(A) 9
(B) 12
(C) 15
(D) 16
(E) 18
Rationale: in 24 liters, Red = 5/8 * 24 = 15 and Blue = 9
so, 15/(9+x) = 3/5
or, x = 16 (Answer D)
Answer: (D) 16
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 400 sq.ft, how many feet of fencing will be required ?
(A) 60feet
(B) 50feet
(C) 40feet
(D) 30feet
(E) 5feet
Rationale: Explanation:
We are given with length and area, so we can find the breadth.
as Length * Breadth = Area
=> 20 * Breadth = 400
=> Breadth = 20 feet
Area to be fenced = 2B + L = 2*20 + 20
= 60 feet
Answer: Option A
Answer: (A) 60feet
Question: Find the value of 3/11 × [(1 + 1/3) (1 + 1/4) …………. (1 + 1/120)] is ?
(A) 11
(B) 12
(C) 14
(D) 15
(E) 16
Rationale: 3/11 × [(1 + 1/3) (1 + 1/4) ....... (1 + 1/120)]
3/11 × [4/3 + 5/4 × ........ 121/120]
3/11 × 4/3 × 5/4 × .... 121/120
121/11 = 11.
A)
Answer: (A) 11
Question: The CI on Rs. 30,000 at 7% per year is Rs. 4347. The period is?
(A) 1 years
(B) 2 years
(C) 3 years
(D) 4 years
(E) 5 years
Rationale: Amount = Rs. (30000 + 4347) = Rs. 34347.
Let the time be n years.
Then, 30000 1 + 7 n = 34347
100
107 n = 34347 = 11449 = 107 2
100 30000 10000 100
n = 2 years
B
Answer: (B) 2 years
Question: 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?
(A) 30, 40
(B) 25, 30
(C) 50, 60
(D) 20, 40
(E) 20, 60
Rationale: 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
Answer: (A) 30, 40
Question: A train passes a man standing on the platform. If the train is 60 meters long and its speed is 72 kmph, how much time it took in doing so?
(A) 6 ½ sec
(B) 4 ½ sec
(C) 6 sec
(D) 3 sec
(E) 2 ½ sec
Rationale: D = 60
S = 72 * 5/18 = 20 mps
T = 60/20 = 3 sec
Answer: D
Answer: (D) 3 sec
Question: If PINTU is coded as 79523 in a certain code language, how would you code DUMBO in the same language?
(A) 43426
(B) 14236
(C) 13436
(D) 14263
(E) 15263
Rationale: 1 2 3 4 5 6 7 8 9
a b c d e f g h i
j k l m n o p q r
s t u v w x y z
sooo...DUMBO is 43426...
ANSWER:A
Answer: (A) 43426
Question: The H.C.F of two numbers is 11 and their L.C.M is 7700. If one of the numbers is 275, then the other is:
(A) 279
(B) 283
(C) 308
(D) 318
(E) 328
Rationale: Other number = (11 * 7700)/275 = 308.
ANSWER:C
Answer: (C) 308
Question: A delegation of 5 members has to be formed from 3 ladies and 5 gentlemen. In how many ways the delegation can be formed, if 2 particular ladies are always included in the delegation?
(A) 20
(B) 99
(C) 88
(D) 77
(E) 61
Rationale: There are three ladies and five gentlemen and a committee of 5 members to be formed.
Number of ways such that two ladies are always included in the committee = ⁶C₃ = (6 * 5 * 4)/6
= 20.
Answer:A
Answer: (A) 20
Question: Two trains travel in opposite directions at 36 kmph and 45 kmph and a man sitting in slower train passes the faster train in 16 seconds. The length of the faster train is
(A) 80 m
(B) 100 m
(C) 120 m
(D) 180 m
(E) None
Rationale: Solution
Relative Speed	= (36 + 45) km/hr
= (81 x 5/18) m/sec
= (45/2) m/sec
Length of the train	= (45 / 2 x 16) m
= 360 m.
Answer E
Answer: (E) None
Question: Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {1, 2, 3, 4}.Find A'
(A) {2,5}
(B) {3,4}
(C) {5,6}
(D) {7,8}
(E) {5,6,7,8,9}
Rationale: U = {1, 2, 3, 4, 5, 6, 7, 8, 9}
A = {1, 2, 3, 4}
correct answer :A'= {5, 6, 7, 8, 9}
E
Answer: (E) {5,6,7,8,9}
Question: At a certain company, each employee has a salary grade s that is at least 1 and at most 5. Each employee receives an hourly wage p, in dollars, determined by the formula p = 11.50 + 0.25(s – 1). An employee with a salary grade of 5 receives how many more dollars per hour than an employee with a salary grade of 1?
(A) $0.50
(B) $1.00
(C) $1.25
(D) $1.50
(E) $1.75
Rationale: OA is definitely wrong. The answer should be E.
Answer: (E) $1.75
Question: At steel 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
Rationale: At steel 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.
Answer: (A) 8/17
Question: A space shuttle orbits the earth at about 6 kilometers per second. This speed is equal to how many kilometers per hour?
(A)  480
(B)  2,880
(C)  21,600
(D)  28,800
(E)  48,000
Rationale: Seconds in 1 hours:
60s in 1 min
60 min in 1 hr
60*60=3600 sec in 1 hr
6*3600=21,600
Answer: C
Answer: (C)  21,600
Question: What approximate value should come in place of the question mark (?) in the following equation?50.02 Ã— 12.65 â€“ 37.50 Ã— 10.55 = (50 + ?) Ã— 4
(A) 10.282
(B) 9.282
(C) 9.5
(D) 8.282
(E) 9.1
Rationale: Solve using approximation
Answer B
Answer: (B) 9.282
Question: A towel, when bleached, was found to have lost 20% of its length and 10% of its breadth. The percentage of decrease in area is ?
(A) 88%
(B) 38%
(C) 68%
(D) 28%
(E) 24%
Rationale: Let original length = x
and original width = y
Decrease in area will be
=xy−(80x100×90y100)=(xy−1825xy)=725xyDecrease = (7xy25xy×100)%=28%
Answer: D
Answer: (D) 28%
Question: A coin is tossed live times. What is the probability that there is at the least one tail?
(A) 31/32
(B) 31/39
(C) 37/32
(D) 11/32
(E) 31/82
Rationale: Let P(T) be the probability of getting least one tail when the coin is tossed five times.
= There is not even a single tail.
i.e. all the outcomes are heads.
= 1/32 ; P(T) = 1 - 1/32
= 31/32
Answer:A
Answer: (A) 31/32
Question: A 10 meter long wire is cut into two pieces. If the longer piece is then used to form a perimeter of a square, what is the probability that the area of the square will be more than 4 if the original wire was cut at an arbitrary point?
(A) 1/6
(B) 1/5
(C) 3/10
(D) 1/3
(E) 4/10
Rationale: A square with an area of 4 has a perimeter of 8.
For the area to be >4, the longer piece must be >8.
The wire must be cut within 2 meters from either end.
The probability of this is 4/10 = 2/5.
The answer is E.
Answer: (E) 4/10
Question: Jim’s Taxi Service charges an initial fee of $2.25 at the beginning of a trip and an additional charge of $0.35 for each 2/5 of a mile traveled. What is the total charge for a trip of 3.6 miles?
(A) $3.15
(B) $4.45
(C) $4.80
(D) $5.05
(E) $5.40
Rationale: Let the fixed charge of Jim’s Taxi Service = 2.25 $
and charge per 2/5 mile(.4 mile) = .35$
Total charge for a trip of 3.6 miles = 2.25 + (3.6/.4) * .35
= 2.25 + 9*.35
= 5.4 $
Answer E
Answer: (E) $5.40