divelab/Sys2Bench huggingface dataset:
Question: In how many different ways can the letter of the word 'BOTTLE ' be arranged in such a way that the vowels occupy the odd positions?
Options:
A)63
B)48
C)85
D)52
E)47
Rationale: In the given word there 6 letters in that there are 2 vowels and 4 consonants
no of ways of arranging the vowels=2p2=2
no of ways of arranging the consonants=4p4=24
total number of ways 24*2=48
Answer(B)
Answer: B
Question: Evaluate (51 + 52 + 53 + ... + 100)
Options:
A)3775
B)3665
C)3456
D)3459
E)3569
Rationale: Sn = (1 + 2 + 3 + ... + 50 + 51 + 52 + ... + 100) - (1 + 2 + 3 + ... + 50)
= (50 x 101) - (25 x 51)
= (5050 - 1275)
= 3775.
Option A
Answer: A
Question: The sum of two consecutive integers is 31. Find the numbers.
Options:
A)17, 18
B)7, 8
C)15, 16
D)1, 2
E)8, 9
Rationale: n + (n + 1) = 31
2n + 1 = 31
2n = 30
n = 15
Answer: C
Answer: C
Question: There are two examinations rooms A and B. If 10 students are sent from A to B, then the number of students in each room is the same. If 20 candidates are sent from B to A, then the number of students in A is double the number of students in B. The number of students in room A is:
Options:
A)20
B)80
C)100 students
D)200
E)120
Rationale: Let the number of students in rooms A and B be x and y respectively.
Then, x - 10 = y + 10
x - y = 20 .... (i)
and x + 20 = 2(y - 20)
x - 2y = -60 .... (ii)
Solving (i) and (ii) we get: x = 100 , y = 80.
The required answer A = 100.
ANSWER:C
Answer: C
Question: A number lock on a suitcase has 3 wheels each labelled with 10 digits from 0 to 9. If opening of the lock is a particular sequence of three digits with no repeats, how many such sequences will be possible?
Options:
A)720
B)760
C)680
D)780
E)880
Rationale: On first wheel there can be 10 digits. On the second wheel there will be one of the 9 digits and on the third wheel there will be 8 digits. Therefore, the number of numbers is
10 x 9 x 8 = 720
ANSWER:A
Answer: A
Question: The original price of a camera was displayed as a whole dollar amount. After adding sales tax of 8 percent, the final price was also a whole dollar amount. Which of the following could be the final price of the camera?
Options:
A)$115
B)$101
C)$100
D)$108
E)$109
Rationale: Final price = (1+8/100) * Original Price
= 1.08* Original Price
From options given only 108 is divisible by 1.08 as it is stated OP is whole dollar amount.
Hence D
Answer: D
Question: A candidate who gets 30% of the marks fails by 50 marks. But another candidate who gets 45% marks gets 25 marks more than necessary for passing. Find the number of marks for passing?
Options:
A)276 Marks
B)200 Marks
C)186 Marks
D)187 Marks
E)167 Marks
Rationale: 30% ------------ 50
45% ------------ 25
----------------------
15% ------------- 75
30% -------------- ?
150 + 50 = 200 Marks
Answer: B
Answer: B
Question: In a barrel of juice there is 30 liters; in a barrel of beer there are 50 liters. If the price ratio between barrels of juice to a barrel of beer is 3:4, what is the price ratio between one liter of juice and one liter of beer?
Options:
A)3:2.
B)2:1.
C)3:1.
D)4:3.
E)15:4
Rationale: Price of 30 L juice= 3x
1L= 3x/30
Price of 50 L beer= 4x
1L= 4x/50
Ratio of 1 L price = 3x/30/4x/50= 15:4
E is the answer
Answer: E
Question: If four coins are tossed, the probability of getting two heads and two tails is?
Options:
A)3/8
B)3/9
C)3/7
D)3/56
E)3/1
Rationale: Since four coins are tossed, sample space = 24
Getting two heads and two tails can happen in six ways.
n(E) = six ways
p(E) = 6/24 = 3/8
Answer: A
Answer: A
Question: Barbara has 8 shirts and 10 pants. How many clothing combinations does Barbara have, if she doesn’t wear 2 specific shirts with 3 specific pants?
Options:
A)41
B)66
C)36
D)70
E)84
Rationale: 8 shirts
9 pants
we can combine 2 shirts with (10-3) pants
2*7=14
we can combine the other shirts (6) with any pants (9)
7*10=70
Thus total :70+14=84	ANS:E
Answer: E
Question: A tour group of 25 people paid a total of $630 for entrance to a museum. If this price included a 5% sales tax, and all the tickets cost the same amount, what was the face value of each ticket price without the sales tax?
Choices
Options:
A)$22
B)$23.94
C)$24
D)$25.20
E)$30
Rationale: Soln:-
630/25=x+0.05x
630/25=1.05x
x=(630*100)/(25*105)
=63*10*4/21*5=24
ANSWER:C
Answer: C
Question: After getting 2 successive discounts, a shirt with a list price of Rs 150 is available at Rs 105. If the second discount is 12.55,find the first discount
Options:
A)38%
B)15%
C)20%
D)12%
E)36%
Rationale: Let the first discount be x%
Then,87.5% of (100-x)% of 150= 105
87.5/100*(100-x)/100*450=150=>105=>100-x=(105*100*100)/(150*87.5)=80
x=(100-80)=20
first discount = 20%
Ans: C
Answer: C
Question: A father can do a certain job in x hours. His son takes twice as long to do the job. Working together, they can do the job in 6 hours. How many hours does the father take to do the job?
Options:
A)9
B)18
C)12
D)20
E)16
Rationale: Explanatory Answers
The father completes the job in x hours.
So, the son will take 2x hours to complete the same job.
In an hour, the father will complete 1/x of the total job.
In an hour, the son will complete 1/2x of the total job.
So, if the father and son work together, in an hour they will complete 1/x + 1/2x of the job.
i.e., in an hour they will complete 3/2x of the job.
The question states that they complete the entire task in 6 hours if they work together.
i.e., they complete 1/6<sup>th</sup> of the task in an hour.
Equating the two information, we get 3/2x = 1/6
Cross multiplying and solving for x we get 2x = 18 or x = 9.
The father takes 9 hours to complete the job.
Answer A
Answer: A
Question: A 2-year certificate of deposit is purchased for Q dollars. If the certificate earns interest at a n annual rate of 6 percent compound quarterly, which of the following represents the value, in dollars, of the certificate at the end of 2 years?
Options:
A)k(1.06)^2
B)k(1.06)^8
C)k(1.015)^2
D)Q(1.015)^8
E)k(1.03)^4
Rationale: Annual Rate of interest= 6%
Quaterly rate of interest= 6/4% = 1.5%
Now, periods of compounding in 2 years= 8 (8 quarters)
Thus Q(1.015)^8
Answer: D
Answer: D
Question: Walking 6/5 of his usual rate, a boy reaches his school 4 min early. Find his usual time to reach the school?
Options:
A)22
B)99
C)27
D)24
E)20
Rationale: Speed Ratio = 1:6/5 = 5:6
Time Ratio = 6:5
1 -------- 6
4 --------- ? 24 m.Answer:D
Answer: D
Question: 12 persons can complete the work in 18 days. after working for 6 days, 4 more persons added to complete the work fast. in how many more days they will complete the work?
Options:
A)10 days
B)9 days
C)8 days
D)7 days
E)6 days
Rationale: total work 12*18=216 units
after 6 days work finished 6*12=72 units
remaining work 216-72=144 units
remaing days =144(12+4)=9 days
ANSWER:B
Answer: B
Question: An investor invests in a new fund. The fund averages 20% growth annually for the first three years, but it loses 25% of its value in the fourth year. At the end of four years, the value of the fund is approximately what percent of the original amount?
Options:
A)135.7%
B)129.6%
C)123.5%
D)117.4%
E)112.6%
Rationale: 0.75*1.2^3 = 1.296
The answer is B.
Answer: B
Question: If 0 < a < b and k = (2a + 6b)/b , which of the following must be true?
Options:
A)k < 2
B)k < 7
C)k < 8
D)k > 9
E)k > 11
Rationale: Here's another approach:
k = (2a + 6b)/b
= 2a/b + 6b/b
= 2(a/b) + 6
Since 0 < a < b, we know that a/b is less than 1, which means that 2(a/b) is some number less than 2.
So, we get k = (some number less than 2) + 6
From here, we can see that k must be less than 8
Answer: C
Answer: C
Question: A man buys an article and sells it at a profit of 20%. If he had bought it at 20% less and sold it for Rs.78 less, he could have gained 25%. What is the cost price?
Options:
A)s.370
B)s.375
C)s.375
D)s.390
E)s.300
Rationale: CP1 = 100 SP1 = 120
CP2 = 80 SP2 = 80 * (125/100) = 100
20 ----- 100
78 ----- ? => 390
ANSWER:D
Answer: D
Question: If 25% of a number exceeds 8% of it by 11.9, then find the number?
Options:
A)76
B)70
C)55
D)65
E)22
Rationale: Use the elimination method to find the correct option.
Of all the options only 70 fits
25% of 70 = 17.5
8% of 70 = 5.6
17.5 - 5.6 = 11.9
Required number is 70.
ANSWER:B
Answer: B
Question: A CAR MOVES AT THE SPEED OF 80KM/HR. WHAT IS THE SPEED OF THE CAR IN METRES PER SECOND?
Options:
A)8 m/sec
B)20 1/9 m/sec
C)22 2/0 m/sec
D)Cannot be determined
E)None of these
Rationale: SPEED = (80*5/18)M/SEC=200/9 M/SEC = 22 2/9 M/SEC.
CORRECT OPTION: C
Answer: C
Question: Three 6 faced dice are thrown together. The probability that no two dice show the same number on them is ?
Options:
A)5/8
B)5/9
C)5/1
D)5/3
E)5/2
Rationale: No two dice show same number would mean all the three faces should show different numbers. The first can fall in any one of the six ways. The second die can show a different number in five ways. The third should show a number that is different from the first and second. This can happen in four ways.
Thus 6 * 5 * 4 = 120 favourable cases.
The total cases are 6 * 6 * 6 = 216.
The probability = 120/216
=5/9.
Answer:B
Answer: B
Question: 6 2/3 * 9 3/5 * 2 1/3 + 1 1/3 = ?
Options:
A)150 1/3
B)150 2/3
C)149 2/3
D)149 1/3
E)None of these
Rationale: Explanation:
6 2/3 * 9 3/5 * 2 1/3 + 1 1/3 = 20/3 * 48/5 * 7/3 + 4/3
= 448/3 + 4/3 = 452/3 = 150 2/3
ANSWER IS B
Answer: B
Question: Parameshwaran invested an amount of 12,000 at the simple interest rate of 10 pcpa and another amount at the simple interest rate of 20 pcpa. The total interest earned at the end of one year on the total amount invested became 14 pcpa. Find the total amount invested
Options:
A)22,000
B)25,000
C)20,000
D)24,000
E)None of these
Rationale: Let the amount invested at 20% rate be x. According to the question,
12000 × 10⁄100 + x × 20⁄100 = (12000 + x) × 14⁄100
or, 1200 + x⁄5 = 1680 + 7⁄50x
or, x⁄5 - 7⁄50x = 480
or, 3⁄50x = 480
\ x = 8000
\ Total amount invested = (12000 + 8000)= 20000
Answer C
Answer: C
Question: P can do a work in 60 days. Q can do the same work in 9 days and R can do the same in 12 days. Q and R start the work and leave after 3 days. P finishes the remaining work in --- days.
Options:
A)7
B)8
C)9
D)15
E)25
Rationale: Work done by P in 1 day = 1/60
Work done by Q in 1 day = 1/9
Work done by R in 1 day = 1/12
Work done by Q and R in 1 day = 1/9 + 1/12 = 7/36
Work done by Q and R in 3 days = 3Ã—7/36 = 7/12
Remaining work = 1 â€“ 7/12 = 5/12
Number of days in which P can finish the remaining work = (5/12) / (1/60) = 25
Option E
Answer: E
Question: If the price of 25 toys is 500, then what will the price of 10toys ?
Options:
A)144
B)361
C)117
D)287
E)200
Rationale: One toy price = 500/25 = 20
10 toy price = 10 * 20 = 200
Answer : E
Answer: E
Question: There are 10 members from that a total of 6 men & 4 ladies a committee of 3 is to be formed. If Mrs. A is not willing to join the committee in which Mr. B is a member, whereas Mr.B is willing to join the committee only if Mrs C is included, how many such committee are possible?
Options:
A)43
B)54
C)65
D)91
E)99
Rationale: We first count the number of committee in which
(i). Mr. Y is a member
(ii). the ones in which he is not
case (i): As Mr. Y agrees to be in committee only where Mrs. Z is a member.
Now we are left with (6-1) men and (4-2) ladies (Mrs. X is not willing to join).
We can choose 1 more in5+\inline {\color{Blue} 2C_{1}}=7 ways.
case (ii): If Mr. Y is not a member then we left with (6+4-1) people.
we can select 3 from 9 in \inline {\color{Blue} 9C_{3}}=84 ways.
Thus, total number of ways is 7+84= 91 ways.
D
Answer: D
Question: The average of five integers is 71, and none of these integers is greater than 100. If the average of three of the integers is 76, what is the least possible value of one of the other two integers?
Options:
A)5
B)15
C)20
D)21
E)27
Rationale: When it comes to averages, we know thataverage value = (sum of n values)/n
We can rewrite this into a useful formula:sum of n values = (average value)(n)
The average of five integers is 71
So, the sum of ALL 5 integers = (71)(5) =355
The average of three of the integers is 65
So, the sum of the 3 integers = (76)(3) =228
So, the sum of the 2 REMAINING integers =355-228=127
If the sum of the 2 REMAINING integers =127, and we want to minimize one value, we must MAXIMIZE the other value.
100 is the maximum value so let 1 integer = 100, which means the other must equal 27
Answer: E
Answer: E
Question: There are 8 books on a shelf that consist of 3 paperback books and 5 hardback books. If 4 books are selected at random without replacement, how many different combinations are there that at least one paperback book is selected?
Options:
A)35
B)45
C)50
D)55
E)65
Rationale: The total number of ways to select 4 books is 8C4 = 70
The number of ways which do not include any paperbacks is 5C4 = 5
The number of combinations with at least one paperback is 70-5 = 65
The answer is E.
Answer: E
Question: In a flight of 600 km, an aircraft was slowed down due to bad weather. Its average speed for the trip was reduced by 200 km/hr and the time of flight increased by 30 minutes. The duration of the flight is?
Options:
A)1 hr
B)3 hr
C)2 hr
D)6 hr
E)8 hr
Rationale: A
1 hr
Let the duration of the flight be x hours. Then,
600/x - 600/(x + 1/2) = 200
x(2x + 1) = 3 2x2 + x - 3 = 0
(2x + 3)(x - 1) = 0
x = 1 hr
Answer: A
Question: The price of a cycle is reduced by 25 per cent. The new price is reduced by a further 40 per cent. The two reductions together are equal to a single reduction of
Options:
A)45%
B)55%
C)35%
D)32.5%
E)30%
Rationale: Price = p
initially price reduced by 25% which means new price is 3/4P
Now on this new price further 40percent is reduced which means the new price is merely 60percent of 3/4P
==> (3/4)x(3/5)P = 9/20P is the new price after both deduction which is 45percent of the original value P. This implies this entire series of deduction is worth having discounted 55% of P. So answer is B = 55%
Answer: B
Question: One pump drains one-half of a pond in 8 hours, and then a second pump starts draining the pond. The two pumps working together finish emptying the pond in one-half hour. How long would it take the second pump to drain the pond if it had to do the job alone?
Options:
A)1 hour
B)1.1 hour
C)3 hours
D)5 hours
E)6 hours
Rationale: First pump drains 1/2 of the tank in 8 hours
so 16 hours it will take to drain the full tank.
Let, 2nd pump drains the full tank in a hours
so both together can drain (1/16+1/a) part in 1 hour
son in 1/2 hour they drain 1/2*(1/16+1/a) part of the tank
given that in 1/2 hour they drain 1/2 of the tank
hence we can say
1/2*(1/16+1/a) = 1/2
solving u get a = 16/15=1.1
Hence answer is B
Answer: B
Question: At what rate of compound interest per annum will a sum of $1200 becomes 1348.32 in 2 years?
Options:
A)5%
B)6%
C)7%
D)8%
E)10%
Rationale: Let the rate be R% p.a.
1200*(1+R/100)^2 = 1348.32
(1+R/100)^2 = 134832/120000 = 11236/10000
(1+R/100)^2 = (106/100)^2
1+R/100 = 106/100
R = 6%
Answer is B
Answer: B
Question: The credit card and a global payment processing companies have been suffering losses for some time now. A well known company recently announced its quarterly results. According to the results, the revenue fell to $48.0 billion from $72.0 billion, a year ago. By what percent did the revenue fall?
Options:
A)20.8
B)30.4
C)31.8
D)32.5
E)33.3
Rationale: $72-$48=24$
(24/72)*100=33.33%
ANSWER:E
Answer: E
Question: If two numbers are in the ratio 5:2. If 20 is subtracted from both of the numbers then the ratio becomes 4:2 then find the smallest number?
Options:
A)30
B)20
C)40
D)50
E)12
Rationale: 5:2
5x - 20 : 3x - 20 = 4 : 2
2[5x - 20] = 4[3x - 20]
10x - 40 = 12x - 80
12x - 10x = 80 - 40
x = 20
Then smallest number is = 2x
2x = 40
C
Answer: C
Question: A train 150 m long passes a man,running at 6 kmph in the direction opposite to that of the train,in 6 seconds.The speed of the train is
Options:
A)54 kmph
B)60 kmph
C)66 kmph
D)72 kmph
E)84 kmph
Rationale: speed of train relative to man: 150/6 * 18/5 km/hr
= 90 km/hr
let speed of train= x
therefore x+6 = 90
x= 90-6
x=84 km/hr
ANSWER:E
Answer: E
Question: In his pocket, a boy has 3 red marbles, 5 blue marbles, and 5 green marbles. How many will he have to take out of his pocket to ensure that he has taken out at least one of each color?
Options:
A)9
B)10
C)11
D)12
E)13
Rationale: The worst case scenario would be that he has taken 5 blue and 5 green, a total of 10 marbles, and still doesn't have 3 distinct colors. But the next draw, marble number 11, will surely be red as only the red marbles are left in his pocket.
The answer is C.
Answer: C
Question: Of 800 surveyed students, 20% of those who read book A also read book B and 25% of those who read book B also read book A. If each student read at least one of the books, what is the difference between the number of students who read only book A and the number of students who read only book B?
Options:
A)20
B)25
C)30
D)55
E)100
Rationale: Say the number of students who read book A is A and the number of students who read book B is B.
Given that 20% of those who read book A also read book B and 25% of those who read book B also read book A, so the number of students who read both books is 0.2A=0.25B --> A=1.25B.
Since each student read at least one of the books then {total}={A}+{B}-{Both} --> 800=1.25B+B-0.25B --> B=400, A=1.25B=500 and {Both}=0.25B=100.
The number of students who read only book A is {A}-{Both}=500-100=400;
The number of students who read only book B is {B}-{Both}=400-100=300;
The difference is 400-300 = 100.
Answer: E.
Answer: E
Question: What is the ratio W of the surface area of a cube to the surface area of a rectangular solid identical to the cube in all ways except that its length has been doubled?
Options:
A)1/4
B)3/8
C)1/2
D)3/5
E)2
Rationale: Let X be the side of the cube. Therefore X^2*6= surface area.
the rectangle is the same other than length is 2X. The width and height are the same as the cube. 2*W*H+2*W*L+2*H*L= 2X^2+4X^2+4X^2= 10X^2.
6X^2/10X^2 = 3/5 = W.
Answer = D
Answer: D
Question: A fruit seller had some apples. He sells 40% apples and still he has 420. Originally he had how many apples?
Options:
A)400
B)500
C)700
D)450
E)650
Rationale: Suppose originally he had x apples
then (100-40)% of x = 420
60x/100 = 420
x= 700
Answer is C
Answer: C
Question: If two girls starting from same point, walking in the opposite directions with 5km/hr and 10km/hr as average speeds respectively. Then the distance between them after 5 hours is?
Options:
A)45
B)55
C)65
D)75
E)85
Rationale: Explanation:
Total distance = Distance traveled by person A+ Distance traveled by person B
= (5Ã— 5) + (10Ã— 5)
= 25+ 50
= 75 Km
Answer:D
Answer: D
Question: Exactly 10% of the reporters for a certain wire service cover local politics in Country X. If 30% of the reporters who cover politics for the wire service do not cover local politics in Country X, what percent of the reporters for the wire service do not cover politics?
Options:
A) 20%
B) 42%
C) 44%
D) 85%
E) 84%
Rationale: You are correct. People who cover local politics are a subset of people who cover politics.
30% of reporters who cover politics do not cover local politics so 70% DO cover local politics.
Reporters covering local politics= 70% of reporters covering politics= 10% of all reporters
Reporters covering politics/All Reporters = 10/70 = 1/7
Reporters not covering politics/All Reporters = 6/7 = 85%=D
Answer: D
Question: Mary sold boxes of butter cookies. Ann sold 5 times as much as she did. 18 boxes of cookies were sold that day, how many boxes did Mary sell?
Options:
A)3
B)5
C)6
D)10
E)18
Rationale: # of boxes of cookies Mary sold = x
Ann sold 5 times more = 5x
x + 5x = 18
6x = 18
x = 18/6 = 3
ANSWER: A
Answer: A
Question: The numbers of pizza slices that are sold in Joey's Pizza are only in quantities of 2 and 4 slices per customer. How many slices cannot be bought?
Options:
A)42.
B)38.
C)33.
D)22.
E)20.
Rationale: Let X pizzas of 2 slices and Y pizzas of 4 slices.
2X + 4Y.
Lets check options wise.
A. 42 => 2(15) + 4(3)
B. 38 => 2(15) + 4(2)
C. 33 = we can't write anything with 5 and 8 series..Lets try 2(15) + 4(3) = 32 , 2(16) + 4(3) = 34 , nothing works out.
D. 22 => 2(10) + 4(3)
E. 20 => 2(6) + 4(2)
Answer: correct option is C
Answer: C
Question: What will come in place of the x in the following Number series? 46080, 3840, 384, 48, ?, 2, 1
Options:
A)1
B)3
C)5
D)8
E)9
Rationale: 46080 /12 = 3840
3840 /10 = 384
384 /8 = 48
48 /6 = 8
8/4 = 2
2 /2 = 1
D
Answer: D
Question: In a function they are distributing noble prize. In how many ways can 3 prizes be distributed among 3 boys when a boy gets any no. of prizes?
Options:
A)55
B)58
C)64
D)65
E)27
Rationale: Ans.(E)
Sol. In this case, repetitions are allowed, so all the three prizes can be given in 4 ways, i.e. (3 x 3 x 3) ways = 33 ways = 27 ways Or nr ways = 33 ways = 27 ways
Answer: E
Question: In a jar there are 3 golf balls and 2 ping pong balls. What is the probability of drawing at least one golf ball when drawing two consecutive balls randomly?
Options:
A)1/4
B)1/2
C)3/5
D)9/10
E)16/20
Rationale: P(at least one gold ball) = 1 - P(no golf ball, so 2 ping pong balls) = 1- 2/5*1/4 = 9/10.
Answer: D.
Answer: D
Question: A train 360 m long runs with a speed of 45 km/hr. What time will it take to pass a platform of 150 m long?
Options:
A)38 sec
B)35 sec
C)44 sec
D)40.8 sec
E)none of these
Rationale: Speed = 45 km/hr = 45 Ã— (5/18) m/s
= 150/12 = 50/4 = 25/2 m/s
Total distance = length of the train + length of the platform
= 360 + 150 = 510 meter
Time taken to cross the platform = 510/(25/2) = 510 Ã— 2/25 = 40.8 seconds
ANSWER:D
Answer: D
Question: If x + y = 3 and x – y = 3, then x^2 - y^2 =
Options:
A)-4
B)4
C)10
D)9
E)40
Rationale: The fastest approach has already been shown. Here's one more option.
Given:
x + y = 3
x – y = 3
Add the two equations to get: 2x = 6, which means x = 3
If x = 3, we can plug that value into either equation, to conclude that y = 0
If x = 3 and y = 0, then x² - y² = 9
Answer: D
Answer: D
Question: The average weight of 8 person's increases by 2.5 kg when a new person comes in place of one of them weighing 65 kg. What might be the weight of the new person?
Options:
A)76 kg
B)76.5 kg
C)85 kg
D)Data inadequate
E)None of these
Rationale: Total weight increased = (8 x 2.5) kg = 20 kg.
Weight of new person = (65 + 20) kg = 85 kg.
Answer: Option C
Answer: C
Question: A certain country had a total annual expenditure of $2.4 x 10^11 last year. If the population of the country was 240 million last year, what was the per capita expenditure?
Options:
A) $ 500
B) $1,000
C) $2,000
D) $3,000
E) $5,000
Rationale: Total expenditure / Population = per capita expenditure
Hence, (2,4 x 10^11) / 240 000 000 = (2,4 x 10^11) / (2,4 x 10^8) = 1 x 10^(11-8) =
1 x 10^3 = 1000.
Answer is B.
Answer: B
Question: A, B, C together started a business. A invested Rs.5000 for 5 months B invested Rs.3000 for 6 months and C Rs.7000 for 3 months. If they get a total profit of Rs.7600. Find the share of A?
Options:
A)2999
B)2500
C)2777
D)2999
E)17212
Rationale: 5*5:3*6:7*3
25 : 30 : 21
25/76 * 7600 = 2500
Answer:B
Answer: B
Question: A cycle is bought for Rs.900 and sold for Rs.1260, find the gain percent?
Options:
A)40%
B)20%
C)80%
D)30%
E)24%
Rationale: 900 ---- 360
100 ---- ? => 40%
Answer: A
Answer: A
Question: The sum of two numbers is 45. Sum of their quotient and reciprocal is 2.05, Find the product of the numbers.
Options:
A)339
B)500
C)288
D)277
E)112
Rationale: Sol: Let a, b be the numbers.
a + b = 45
ab+baab+ba = 2.05
⇒a2+b2ab⇒a2+b2ab = 2.05
⇒(a+b)2−2abab=2.05⇒(a+b)2−2abab=2.05
⇒(a+b)2⇒(a+b)2 = 2.05ab + 2ab = 4.05ab
⇒⇒ ab = 4524.054524.05 = 500
Answer:B
Answer: B
Question: For positive integers m and n, which of the following can be written as n^2?
Options:
A)m+2
B)m+3
C)m+1
D)m+4
E)m-2
Rationale: Plug values: if m=8, then m+1=9
The question asks which of the following CAN be written as y^2. If m=8, then m+1 CAN be written as 3^2.
Answer: D
Answer: D
Question: A and B can together finish a work in 40days. They worked together for 10days and then B left. After another 6 days, A finished the remaining work. In how many days A alone can finish the job?
Options:
A)10
B)25
C)60
D)8
E)20
Rationale: A+B 10days work = 10*1/40 = 1/4
Remaining work = 1-1/4 = 3/4
3/4 work is done by A in 6 days
whole work will be done by A in 6 *4/3 = 8days
Answer is D
Answer: D