mathewhe/aqua_rat huggingface dataset:
Question: If Josh, Doug, and Brad have a total of $68 between them, and Josh has two times as much money as Brad but only three-fourths as much as Doug, how much money does Brad have?
(A) $10
(B) $24
(C) $26
(D) $12
(E) $36
Rationale: Josh+Doug+Brad = 68 ; Josh = 2 Brad, Josh =3/4 Doug
Josh+1/2 Josh+ 4/3 Josh = 68 (substituted the given values)
Josh = 24. 24= 3/4 Doug => Doug =32
Josh+Doug+Brad = 68
24 + 32 + Brad = 68
Brad = 12
Answer is D.
Answer: (D) $12
Question: WILLIAM has 13 ten-dollar bills, 11 five-dollar bills, and 17 one-dollar bills. If WILLIAM needs to pay exactly $128, what is the least number of bills he will need to use?
(A) 567
(B) 11
(C) 22
(D) 46
(E) 16
Rationale: 128 is the total sum of money.
as we have 13 10 dollar bills so the closest we can get to 128 using the 10 dollar bills is by using 12 * 10 dollar bils
128-120 = 8
so now we need to get 8 from either 5 dollar bills or 1 dollar bills
8 - 5 (use only 1 5 dollar bill) = 3
so we can get 3 from using 3 $1 bills.
Hence 16 ( 12+1+3 )
ANSWER IS E
Answer: (E) 16
Question: A train 200 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is?
(A) 28
(B) 50
(C) 77
(D) 22
(E) 12
Rationale: Speed of the train relative to man = (200/10) m/sec = (20) m/sec. [(20) * (18/5)] km/hr = 72 km/hr. Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr. x - 5 = 72 ==> x
= 77 km/hr.Answer:C
Answer: (C) 77
Question: A train 280 m long, running with a speed of 63 km/hr will pass a tree in?
(A) 21 sec
(B) 16 sec
(C) 71 sec
(D) 18 sec
(E) 28 sec
Rationale: Speed = 63 * 5/18 = 35/2 m/sec
Time taken = 280 * 2/35
= 16 sec
Answer: B
Answer: (B) 16 sec
Question: Lines y=4√5·x−2 and y=3√5·x−1 intersect at what height above the x axis?
(A) 0
(B) 2√5
(C) 2
(D) 3√5
(E) 12√5
Rationale: Solve two equations for y
y=4√5·x−2
y=3√5·x−1
Set the two equations equal to each other and solve for x
4√5·x−2=3√5·x−1
√5·x = 1
x = 1/√5
Plug x = 1/√5 into any one of the original equations to find the y value (height above x axis) where the two lines intersect
y=4√5·x−2
y=4√5·(1/√5)−2
y=4·1 - 2
y = 4 - 2
y = 2
Final answer:
C) 2
Answer: (C) 2
Question: 12 men take 18 days to complete a job whereas 12 women in 18 days can complete 1â„4 of the same job. How many days will 10 men and 8 women together take to complete the same job?
(A) 6
(B) 13 1â„2
(C) 18
(D) Data inadequate
(E) None of these
Rationale: 12 M Ã— 18 = 12 W Ã— 18 Ã— 4â„1
\ w = 1/4 M
10M + 8W = 10M + 8 Ã— 1â„4M = 12 M
\12 men can complete the same work
in 12Ã—18/12=18days
Answer C
Answer: (C) 18
Question: find value for x from below equation?
x + 1 = -3
(A) -2
(B) -4
(C) -1
(D) -5
(E) 1
Rationale: 1. Subtract 1 from both sides:
x + 1 - 1 = -3 - 1
2. Simplify both sides:
x = -4
B
Answer: (B) -4
Question: Out of 15 consecutive numbers, 2 are chosen at random. The probability that they are both odds or both primes is
(A) 10/17
(B) 10/19
(C) 46/105
(D) 11/15
(E) Cannot be determined
Rationale: There is no definite formula for finding prime numbers among 15 consecutive numbers. Hence the probability cannot be determined.
ANSWER:E
Answer: (E) Cannot be determined
Question: Walking 7/6 of his usual rate, a boy reaches his school 4 min early. Find his usual time to reach the school?
(A) 11
(B) 15
(C) 16
(D) 28
(E) 19
Rationale: Speed Ratio = 1:7/6 = 6:7
Time Ratio = 7:6
1 -------- 7
4 --------- ? è 28 m
Answer: D
Answer: (D) 28
Question: The difference between the compound interest and simple interest on a certain sum of money at 5% per annum for 2 years is 45. Then the original sum is?
(A) Rs.16500/-
(B) Rs.17000/-
(C) Rs.18000/-
(D) Rs.19000/-
(E) Rs.20000/-
Rationale: For 2 years = (1002D)/R2
= (1002 × 45)/(5 × 5) = (10000 × 45)/25 = Rs.18000/-
C
Answer: (C) Rs.18000/-
Question: Reena took a loan of Rs. 2000 with simple interest for as many years as the rate of interest. If she paid Rs. 720 as interest at the end of the loan period, what was the rate of interest?
(A) 6
(B) 7
(C) 8
(D) 9
(E) 10
Rationale: Let rate = R% and time = R years.
=(2000xRxR)/100 =720
=20Rsquare =720
R Square = 720/20 =36
R= 6
ANSWER :A
Answer: (A) 6
Question: How many seconds will a 900 metre long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr?
(A) 25
(B) 30
(C) 40
(D) 45
(E) 54
Rationale: Relative speed of the train=63-3=60kmph=60*5/18=50/3 m/sec
t=900*3/50=54sec
ANSWER:E
Answer: (E) 54
Question: In three annual examinations, of which the aggregate marks of each was 500, a student secured
average marks 45% and 55% in the first and the second yearly examinations respectively. To secure 70% average total marks, it is necessary for him in third yearly examination to secure marks :
(A) 300
(B) 350
(C) 400
(D) 450
(E) 550
Rationale: total marks:1500 for three exams
70% of 1500=1050
first exam marks=45% of 500=225
second exam marks=55% of 500=275
let X be the third exam marks
225 + 275 + X =1050
X=550
ANSWER:E
Answer: (E) 550
Question: In a division sum, the remainder is 0. As student mistook the divisor by 12 instead of 21 and obtained 35 as quotient. What is the correct quotient ?
(A) 0
(B) 12
(C) 13
(D) 20
(E) 25
Rationale: 12*35=420
420%21=20
ANSWER:D
Answer: (D) 20
Question: A fruit seller had some Mangoes. He sells 50% oranges and still has 500 Mangoes. How many Mangoes he had originally?
(A) 800
(B) 850
(C) 900
(D) 1000
(E) 1050
Rationale: He sells 50% of oranges and still there are 500 oranges remaining.
= 50% of oranges = 500
Total oranges x (50/100)= 500
= Total oranges =500×100/50=1000
answer :D
Answer: (D) 1000
Question: n is a positive integer and k is the product of all integers from 1 to n inclusive. If k is a multiple of 1600, then what is the smallest possible value of n?
(A) 6
(B) 8
(C) 10
(D) 12
(E) 15
Rationale: 1600=2^6*5^2
2^6 means that n must be at least 8. That is, we need 2, 2*2, 6, and 2*2*2.
5^2 means that n must be at least 10. That is, We need 5 and 10.
The answer is C.
Answer: (C) 10
Question: Analyze the number square carefully and find out what number fits in place of question mark.
35	20	14
27	12	18
5	2	?
(A) 19
(B) 23
(C) 21
(D) 22
(E) 20
Rationale: E
20 fits in place of question mark.
This is because (number in first column) / (number in second column) * 8 = number in third column.
Here (left number / middle number) * 8 = right number
E.g. (35 / 20) * 8 = (7/4) * 8 = 7 x 2 = 14
The same process can be used to find out the missing digit.
Answer: (E) 20
Question: A business school club, Friends of Foam, is throwing a party at a local bar. Of the business school students at the bar, 40% are first year students and 60% are second year students. Of the first year students, 50% are drinking beer, 30% are drinking mixed drinks, and 20% are drinking both. Of the second year students, 30% are drinking beer, 30% are drinking mixed drinks, and 20% are drinking both. A business school student is chosen at random. If the student is drinking beer, what is the probability that he or she is also drinking mixed drinks?
(A) 2/5
(B) 4/7
(C) 10/19
(D) 7/24
(E) 7/10
Rationale: Suppose there are 100 students
Group A : 40% = 40 students
50% drink beer = 20
30% mixed = 12
20% both = 8
Group B 60% = 60
30% beer= 18
30% mixed = 18
20% both= 12
now we need both ( beer + mixed = both)
probability = total beer drinker = 20+18 =38 and both = 20
thus 20/38 = 10/19
Hence C
Answer: (C) 10/19
Question: From a bunch of eight keys, three particular keys have to be used to open a combination lock, such that the second key can be used only after the first key and the third key can be used only after the second key. What are the chances of opening the lock in a random selection of three keys?
(A) 1/120
(B) 1/180
(C) 1/336
(D) 1/480
(E) 1/720
Rationale: The probability is 1/8*1/7*1/6 = 1/336.
The answer is C.
Answer: (C) 1/336
Question: A warehouse had a square floor with area 10,000 sq.meters. A rectangular addition was built along one entire side of the warehouse that increased the floor by one-half as much as the original floor. How many meters did the addition extend beyond the original buildings ?
(A) 10
(B) 20
(C) 50
(D) 100
(E) 500
Rationale: as L*B=10000 ie for square L=B=100m
THEN,
IF A RECTANGULAR ADDITIONALLY WAS BUILT ALONG ONE ENTIRE SIDE IT ENSURES THAT ONE SIDE MUST BE REMAIN SAME AS THE SQUARE
HENCE EQUATION BECOMES
(100+X)100=10000+(1/2)*10000
(100+X)100=15000
X=50
ANSWER:C
Answer: (C) 50
Question: A 425 meter long train crosses a platform in 55 seconds while it crosses a signal pole in 40 seconds. What is the length of the platform?
(A) 155.68
(B) 160
(C) 159.38
(D) 180
(E) 175
Rationale: Speed = [425 / 40 m/sec = 42.5/4 m/sec.
Let the length of the platform be x meters.
Then, x + 425 / 55= 42.5/4
4(x + 425) = 2337.5 è x =159.38 m. Answer: C
Answer: (C) 159.38
Question: In a certain city, 60 percent of the registered voters are Democrats and the rest are Republicans. In a mayoral race, if 85 percent of the registered voters who are Democrats and 20 percent of the registered voters who are Republicans are expected to vote for Candidate A, what percent of the registered voters are expected to vote for Candidate A ?
(A) 50%
(B) 59%
(C) 54%
(D) 55%
(E) 57%
Rationale: Say there are total of 100 registered voters in that city. Thus 60 are Democrats and 40 are Republicans.
60*0.85=51 Democrats are expected to vote for Candidate A;
40*0.20=8 Republicans are expected to vote for Candidate A.
Thus total of 51+8=59 registered voters are expected to vote for Candidate A, which is 59% of the total number of registered voters.
Answer: B.
Answer: (B) 59%
Question: Find the principle on a certain sum of money at 5% per annum for 2 2/5 years if the amount being Rs.1008?
(A) 900
(B) 2217
(C) 2889
(D) 2777
(E) 2991
Rationale: 1008 = P [1 + (5*12/5)/100]
P= 900
Answer: A
Answer: (A) 900
Question: A textile manufacturing firm employees 56 looms. It makes fabrics for a branded company. The aggregate sales value of the output of the 56 looms is Rs 5,00,000 and the monthly manufacturing expenses is Rs 1,50,000. Assume that each loom contributes equally to the sales and manufacturing expenses are evenly spread over the number of looms. Monthly establishment charges are Rs 75000. If one loom breaks down and remains idle for one month, the decrease in profit is:
(A) 13000
(B) 6250
(C) 10000
(D) 5000
(E) None of these
Rationale: Explanation :
Profit = 5,00,000âˆ’(1,50,000+75,000) =Rs. 2,75,000.
Since, such loom contributes equally to sales and manufacturing expenses.
But the monthly charges are fixed at Rs 75,000.
If one loan breaks down sales and expenses will decrease.
New profit :-
=>500000Ã—(55/56)âˆ’150000Ã—(55/56)âˆ’75000.
=>Rs 2,68,750
Decrease in profit
=>2,75,000âˆ’2,68,750
=>Rs. 6,250
Answer : B
Answer: (B) 6250
Question: Which of the following is closer to (3!+2!)-(3!-2!)?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
Rationale: 3!+2!)-(3!-2!)=6+2-6+2
= 4
Answer: E
Answer: (E) 4
Question: A is twice as good a work man as B and together they finish a piece of work in 14 days.The number of days taken by A alone to finish the work is :
(A) 11
(B) 21
(C) 28
(D) 42
(E) None of these
Rationale: Solution
(A’s 1 day’s work): (B’s 1 day’s work)= 2 : 1.
(A + B)'s 1 day’s work = 1/14
Divide 1/14 in the ratio 2 : 1.
∴ A’s 1 day’s work = (1/14 x2/3)= 1/21
Hence,A alone can finish the work in 21 days.
Answer B
Answer: (B) 21
Question: A certain machine produces 550 units of product P per hour. Working continuously at this constant rate, this machine will produce how many units of product P in 5 days?
(A) 7,000
(B) 24,000
(C) 66,000
(D) 100,000
(E) 168,000
Rationale: Since 5 days consist of 24*5 hours the total is 120 hours.
Since every hour the machine produces 550 units of product P the total product during 120 hours is 120*550=66,000.
Correct Option : C
Answer: (C) 66,000
Question: If a certain number X is divided by 82, the reminder is 5. what is the reminder when X+13 is divided by 41?
(A) 3
(B) 18
(C) 6
(D) 16
(E) 5
Rationale: X can be written as 82K + 5 or X = 5,87,169,etc.
X + 13 = 82K + 5+13= 82K +18 or X + 13 = 18,100, 182 etc.
When divided by 41, we will get the remainder 18.
B
Answer: (B) 18
Question: If the simple interest on a sum of money for 2 years at 5% per annum is Rs.50, what is the compound interest on the same at the same rate and for the same time?
(A) Rs. 52
(B) Rs. 51.25
(C) Rs. 54.25
(D) Rs. 60
(E) Rs. 70
Rationale: Simple interest for 2 years = Rs.50 ie. For 1 years Rs. 25. . In the first year the S.I and C.I are
same ie.Rs. 25. So in the 2nd year in C.I calculated for 1 years interest also. So in second years for
Rs.25 interest is 25*5/100 = 1.25 . So total C.P = 51.25.
ANSWER:B
Answer: (B) Rs. 51.25
Question: If x^2 – 2y^2 = 2xy, then (x + y)^2 =
(A) x^2
(B) 2x^2-y^2
(C) 4xy
(D) 2y^2
(E) – y^2
Rationale: (x+y)^2 = x^2 + y^2 + 2xy = x^2 + y^2+ x^2-2y^2 = 2x^2-y^2
Correct option : B
Answer: (B) 2x^2-y^2
Question: Stalin gets on the elevator at the 11th floor of a building and rides up at a rate of 57 floors per minute. At the same time Jose gets on an elevator on the 51st floor of the same building and rides down at a rate of 63 floors per minute. If they continue traveling at these rates, at which floor will their paths cross?
(A) 19
(B) 28
(C) 34
(D) 32
(E) 30
Rationale: Steve gets on the elevator at the 11th floor of a building and rides up at a rate of 57 floors per minute. At the same time Joyce gets on an elevator on the 51st floor of the same building and rides down at a rate of 63 floors per minute. If they continue traveling at these rates, at which floor will their paths cross?
40 floors/120 floors per minute=1/3 minutes
11+57/3=30
51-63/3=30
Answer : E
Answer: (E) 30
Question: A contractor hires 100 men to finish a job in 50 days. After 40 days, n men leave. After some more days, the contractor hires 2n more men to complete the job on time. For how many days did these 2n men work?
(A) 20
(B) 18
(C) 16
(D) 12
(E) 5
Rationale: Step1: Find Each day what % of work is finished ; it requires 50 days to complete which means each day 1/50= 2% work will be completed.
Step 2 : After 40 Days = 40* 2= 80% of work is finished. remaining is 20% ( which means if same 100 men were about to complete the job they would have required 10 more days)
Step3: Let us assume all people have left job. therefore contractor hires 2n people. initially it was taking 10 days to compete for n people. at present 2n people are present to finish job. hence 5 more days.
E
Answer: (E) 5
Question: Each Machine of type A has 2 steel parts and 3 chrome parts. Each machine of type B has 3 steel parts and 5 chrome parts. If a certain group of type A and type B machines has a total of 40 steel parts and 32 chrome parts, how many machines are in the group
(A) 12
(B) 13
(C) 14
(D) 15
(E) 16
Rationale: Look at the below representation of the problem:
Steel Chrome total
A 2 3 40 >>no. of type A machines=40/5=8
B 3 5 32 >>no. of type B machines=32/8=4
So the answer is 12 i.e A.
Hope its clear .
Answer: (A) 12
Question: A and B started business in partnership investing Rs. 20,000 and Rs. 15,000 respectively. After six months, C joined them with Rs. 20,000. What will be B's share in the total profit of Rs. 25,000 earned at the end of 2 years from the starting of the business?
(A) 7500
(B) 2878
(C) 2662
(D) 2992
(E) 2772
Rationale: A:B:C = (20000 * 24) : (15000 * 24) : (20000 * 18) = 4:3:3
B's share = 25000 * 3/10 = Rs. 7500.
Answer: A
Answer: (A) 7500
Question: A salesmanâ€™s terms were changed from a flat commission of 5% on all his sales to a fixed salary of Rs.1000 plus 2.5% commission on all sales exceeding Rs. 4,000. If his remuneration as per new scheme was Rs. 600 more than that by the previous schema, his sales were worth?
(A) Rs. 14,000
(B) Rs. 12,000
(C) Rs. 30,000
(D) Rs. 40,000
(E) Rs. 45,000
Rationale: Explanation:
[1000 + (X-4000) * (2.5/100)] - X * (5/100) = 600
X = 12000
ANSWER IS B
Answer: (B) Rs. 12,000
Question: A man buys s cycle for $100 and sells it at a loss of 40%. What is the selling price of the cycle?
(A) $50
(B) $60
(C) $70
(D) $80
(E) $90
Rationale: S.P. = 60% of the $100 = 60/100 * 100 = $60
Answer is B
Answer: (B) $60
Question: The variables m and n are positive integers. When m is divided by 18, there is a remainder of 12, and when n is divided by 24, there is a remainder of 14. Which of the following are possible values of m + n?
I. 50
II. 68
III. 90
(A) I only
(B) III only
(C) I and II
(D) I only III
(E) II and III
Rationale: m = 18k + 12 --> Values are 12, 30, 48, 66, 84
n = 24k + 14 --> Values are 14, 38, 62, 86
I. 50 --> 12 + 38 --> Possible
II. 68 --> 30 + 38--> Possible
III. 92 --> Not possible
Answer: C
Answer: (C) I and II
Question: A shop sells two variants of chocolates - one that costs $3 and the other that costs $5. If the shop sold $151 chocolates on a given day, how many different combinations of (number of $3 sold, number of $5 sold) exist?
(A) 8
(B) 10
(C) 12
(D) 14
(E) 16
Rationale: $151 = 29*$5 + 2*$3
We can find other combinations by reducing the $5 chocolates by 3 (which is -$15)and increasing the $3 chocolates by 5 (which is +$15).
The number of $5 chocolates can be 29, 26, 23, 20,...,2 for a total of 10 combinations.
The answer is B.
Answer: (B) 10
Question: In a graduating class of 234 students, 144 took geometry and 119 took biology. What is the difference between the greatest possible number and the smallest possible number of students that could have taken both geometry and biology?
(A) 144
(B) 115
(C) 113
(D) 88
(E) 31
Rationale: Greatest Possible Number taken both should be 144 (As it is maximum for One)
Smallest Possible Number taken both should be given by
Total - Neither = A + B - Both
Both = A+B+Neither - Total (Neither must be 0 to minimize the both)
So 144 + 119 + 0 - 234 = 29
Greatest - Smallest is 144-29 = 115
So answer must be B. 115
Answer: (B) 115
Question: John drove for 3 hours at a rate of 50 miles per hour and for 2 hours at 60 miles per hour. What was his average speed for the whole journey?
(A) The average speed is 54 miles per hour.
(B) The average speed is 32 miles per hour.
(C) The average speed is 44 miles per hour.
(D) The average speed is 60 miles per hour.
(E) The average speed is 72 miles per hour.
Rationale: Step 1: The formula for distance is
Distance = Rate × Time
Total distance = 50 × 3 + 60 × 2 = 270
Step 2: Total time = 3 + 2 = 5
Step 3: Using the formula
average speed formula
270/5 = 54
Answer(A)
Answer: (A) The average speed is 54 miles per hour.
Question: If 18 bindres bind 900 books in 10 days , How many binders will be required to bind 660 books in 12 days?
(A) 71
(B) 12
(C) 18
(D) 11
(E) 29
Rationale: Explanation:
Let the required no of binders be X.
Less books , Less binders (Direct Proportion)
More days, Less binders (Indirect proportion)
\inline \fn_jvn \left.\begin{matrix} Books\: 900:600\\ Days\: \: 12:10 \end{matrix}\right\}::18:x
\inline \fn_jvn \therefore \inline \fn_jvn (900\times 12\times x)=(600\times 10\times 18) \inline \fn_jvn \Leftrightarrow x= \inline \fn_jvn \frac{600\times 10\times 18}{900\times 12} = 11
Answer: D
Answer: (D) 11
Question: In a class, there are 20 boys whose average age is decreased by 2 months, when one boy aged 21 years replaced by a new boy. The age of the new boy is?
(A) 14 years 8 months
(B) 15 years
(C) 16 years 4 months
(D) 17 years 8 months
(E) 17 years
Rationale: Total decrease = (20 x 2) months
= 3 years 4 months
Age of the new boy
= 21 years - 3 years 4 months.
= 17 years 8 months.
ANSWER:D
Answer: (D) 17 years 8 months
Question: If 100 cats kill 100 mice in 100 days, then 4 cats would kill 4 mice in how many days ?
(A) 1 day
(B) 4 days
(C) 40 days
(D) 100 days
(E) 50 days
Rationale: as
100 cats kill 100 mice in 100 days
1 cats kill 1 mouse in 100 days
then
4 cats kill 4 mice in 100 days
ANSWER:D
Answer: (D) 100 days
Question: A cistern has a leak which would empty the cistern in 20 minutes. A tap is turned on which admits 4 liters a minute into the cistern, and it is emptied in 24 minutes. How many liters does the cistern hold?
(A) 480
(B) 456
(C) 345
(D) 356
(E) 368
Rationale: 1/x - 1/20 = -1/24
x = 120
120 * 4 = 480
Answer: A
Answer: (A) 480
Question: Reduce
803876
to the lowest terms
(A) 1112
(B) 2324
(C) 2627
(D) 47
(E) None of these
Rationale: Explanation:
HCF of 803 and 876 is 73, Divide both by 73, We get the answer 11/12
Answer: Option A
Answer: (A) 1112
Question: A 25 cm wide path is to be made around a circular garden having a diameter of 4 meters. Approximate area of the path is square meters is?
(A) 3.34
(B) 3.32
(C) 3.2
(D) 3.08
(E) 3.17
Rationale: Area of the path = Area of the outer circle - Area of the inner circle
= ∏{4/2 + 25/100}2 - ∏[4/2]2
= ∏[2.252 - 22] = ∏(0.25)(4.25) { (a2 - b2 = (a - b)(a + b) }
= (3.14)(1/4)(17/4) = 53.38/16
= 3.34 sq m
Answer: A
Answer: (A) 3.34
Question: Two tailors X and Y are paid a total of Rs. 550 per week by their employer. If X is paid 120 percent of the sum paid to Y, how much is Y paid per week?
(A) Rs. 200
(B) Rs. 250
(C) Rs. 300
(D) Rs. 350
(E) None
Rationale: Solution
Let the sum paid to Y per week be Rs. z.
Then, z + 120% of z = 550.
‹=›z + 120 / 100 z = 550
‹=› 11 / 5 z = 550
‹=›z = [550 x 5 / 11] = 250.
Answer B
Answer: (B) Rs. 250
Question: here are 6 periods in each working day of a school. In how many ways can one organize 5 subjects such that each subject is allowed at least one period?
(A) 2120
(B) 4123
(C) 3621
(D) 1800
(E) 1450
Rationale: 5 subjects can be arranged in 6 periods in 6P5 ways.
Any of the 5 subjects can be organized in the remaining period (5C1 ways).
Two subjects are alike in each of the arrangement. So we need to divide by 2! to avoid overcounting.
Total number of arrangements
= 6P5× 5C1 /2!=1800
Ans: D
Answer: (D) 1800
Question: If (18^a) * 9^(3a – 1)= (2^5)(3^b) and a and b are positive integers, what is the value of a?
(A) 22
(B) 11
(C) 9
(D) 6
(E) 5
Rationale: (18^a) * 9^(3a – 1)= (2^5)(3^b)
= 2^a . 9^a . 9^(3a – 1) = (2^5)(3^b)
Just compare powers of 2 from both sides
Answer = 5 = E
Answer: (E) 5
Question: A dishonest dealer professes to sell his goods at Cost Price but still gets 35% profit by using a false weight. What weight does he substitute for a kilogram?
(A) 740 1/7 grams
(B) 740 20/27 grams
(C) 740 8/3 grams
(D) 740 1/3 grams
(E) 740 1/27 grams
Rationale: If the cost price is Rs.100, then to get a profit of 35%, the selling price should be Rs.135.
If 135kg are to be sold, and the dealer gives only 100kg, to get a profit of 35%.
How many grams he has to give instead of one kilogram(1000 gm).
135 gm ------ 100 gm
1000 gm ------ ?
(1000 * 100)/135 = 740 20/27 grams.
Answer:B
Answer: (B) 740 20/27 grams
Question: If the probability of rain on any given day in Chicago during the summer is 20%, independent of what happens on any other day, what is the probability of having exactly 3 rainy days from July 4 through July 7 inclusive?
(A) 2/25
(B) 3/125
(C) 7/125
(D) 12/625
(E) 16/625
Rationale: One possible case is: rainy-rainy-rainy-not rainy.
The probability of this case is 1/5*1/5*1/5*4/5 = 4/625
The number of possible cases is 4C3 = 4.
P(exactly 3 rainy days) = 4*4/625 = 16/625
The answer is E.
Answer: (E) 16/625
Question: Vishal invested 10% more than Trishul. Trishul invested 10% less than Raghu. If the total sum of their investments is Rs. 5780, how much amount did Raghu invest ?
(A) 1287
(B) 2887
(C) 2000
(D) 1129
(E) 1192
Rationale: Let money invested by Raghu = Rs. x
Money invested by Trishul = 9/10 x = 0.9x
Money invested by Vishal = 9/10x * 110/100 = 0.99x
Also, x+0.9x+0.99x = 5780
= x= 5780/2.89 = 2000
Therefore, amount invested by Raghu is Rs. 2000.
Answer: C
Answer: (C) 2000
Question: P beats Q by 125 meter in a kilometer race. Find Q's speed if P's speed is 32 meter/sec.
(A) 21 meter/sec
(B) 7 meter/sec
(C) 14 meter/sec
(D) 18 meter/sec
(E) 28 meter/sec
Rationale: P's speed = 32 m/s
P's distance = 1000m (as it is a km race)
t = 1000/32 = 31.25 sec
Q's distance = 1000-125= 875m
Q's time to complete this distance is also 62.5 sec.
Q's speed = dist/time = 875/31.25 = 28 m/s
Hence E is the answer.
Answer: (E) 28 meter/sec
Question: Pipes A and B can fill a cistern in 8 and 24 minutes respectively. They are opened an alternate minutes. Find how many minutes, the cistern shall be full?
(A) 11
(B) 12
(C) 99
(D) 75
(E) 72
Rationale: 1/8 + 1/24 = 1/6
6 * 2 = 12
Answer: B
Answer: (B) 12