divelab/Sys2Bench huggingface dataset:
Question: A small, experimental plane has three engines, one of which is redundant. That is, as long as two of the engines are working, the plane will stay in the air. Over the course of a typical flight, there is a 1/3 chance that engine one will fail. There is a 65% probability that engine two will work. The third engine works only half the time. What is the probability that the plane will crash in any given flight?
Options:
A) 7/12
B) 1/4
C) 1/2
D) 7/24
E) 17/24
Rationale: In probability questions the trap answer is just the multiple of the numbers in the question.
i.e. if you multiply 1/3 * 1/4 * 1/2 = 1/24 is trap answer
The other trap answer could be 2/3 * 3/4 * 1/2 = 6/24 is trap answer
So lets say you have30 secsand you want to guess the answer then B, C are ruled out because they can be traps. You best guess is A, D, E. So you have 33% chances of being correct.
E
Answer: E
Question: Shiwani thought of a two-digit number and divided the number by the sum of the digits of the number. He found that the remainder is 3. Devesh also thought of a two-digit number and divided the number by the sum of the digits of the number. He also found that the remainder is 3. Find the probability that the two digit number thought by Shiwani and Devesh is TRUE?
Options:
A)1/15
B)1/14
C)1/12
D)1/13
E)1/17
Rationale: Explanation :
Let two digit number that Shiwani thought be 'xy', where x and y are single digit number.
Therefore, 10x+y=p(x+y)+3, where p is a natural number
p=10x+y−3x+y.
Also, y+x>3.
Possible values of x and y for which p is a natural number are :-
(x=1,y=5),(x=2,y=3),(x=3,y=1,3,5,9),
(x=4,y=7),(x=5,y=1,2,9),(x=6,y=Null),
(x=7,y=3,5,8),(x=8,y=Null),(x=9,y=4)
There are 14 such two digit numbers that give a remainder of 3 when divided by the sum of the digits.
Probability that Devesh thought of the same number as Shiwani = 1/14
Answer : B
Answer: B
Question: In a certain pond, 90 fish were caught, tagged, and returned to the pond. A few days later, 90 fish were caught again, of which 2 were found to have been tagged. If the percent of tagged fish in the second catch approximates the percent of tagged fish in the pond, what`s the approximate number of fish in the pond?
Options:
A)400
B)625
C)1250
D)2500
E)4091
Rationale: The percent of tagged fish in the second catch is 2/90*100 = 2.22%.
We are told that 2.22% approximates the percent of tagged fish in the pond. Since there are 90 tagged fish, then we have 0.022x = 90 --> x = 4,091.
Answer: E.
Answer: E
Question: How many seconds will a 500 meter 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?
Options:
A)338
B)277
C)500
D)127
E)181
Rationale: Let length of tunnel is x meter
Distance = 800+x meter
Time = 1 minute = 60 seconds
Speed = 78 km/hr = 78*5/18 m/s = 65/3 m/s
Distance = Speed*Time
800+x = (65/3) * 60
800+x = 20 * 65 = 1300
x = 1300 - 800 = 500 meters
Answer:C
Answer: C
Question: In how many of ways can 4 balls be placed in 3 tins if any number of balls can be placed in any tin?
Options:
A) 5C4
B) 5P4
C) 3^4
D) 4^5
E) 5^5
Rationale: Now, each of the 4 different balls has 3 choices (3 tins to go to), so total # of distribution is 3*3*3*3=3^4.
Answer: C.
Answer: C
Question: If the number 653ab is divisible by 90, then (a + b) = ?
Options:
A)2
B)3
C)4
D)6
E)8
Rationale: 90 = 10 x 9
Clearly, 653ab is divisible by 10, so b = 0
Now, 653a0 is divisible by 9.
So, (6 + 5 + 3 + a + 0) = (14 + a) is divisible by 9. So, a = 4.
Hence, (a + b) = (4 + 0) = 4.
ANSWER:C
Answer: C
Question: For all positive integers x, f(x)=f(x+1). If f(3)=15, then what is f(7)?
Options:
A)8
B)12
C)15
D)21
E)35
Rationale: Here we go---
f(x) = f(x+1) ---(1)
f(3) = 15 ----(2)
Now
f(7) = f(6+1)-----> f(6) = f(5+1)-------> f(5) = f(4+1) ------> f(4) = F(3+1)---> f(3) = 15
Now backtrack
f(4) = 15-----> f(5) = 15 ------> f(6) = 15 ----> f(7) = 15
Though I picked option C
I am still not 100% sure of the answer(don't know why)
My bets on C.
Answer: C
Question: A shopkeeper sold an article for 720 after giving 10% discount on the labelled price and made 20% profit on the cost price. What would have been the percentage profit,had he not given the discount’?
Options:
A)25%
B)30%
C)23%
D)28%
E)None of these
Rationale: Cost price = 720×100/120= 600
S.P. at no discount = 720×100/90 = 800
∴ % profit = 200×100/600 = 33 1⁄3 %
Answer E
Answer: E
Question: I bought two books; for Rs.480. I sold one at a loss of 15% and other at a gain of 19% and then I found each book was sold at the same price. Find the cost of the book sold at a loss?
Options:
A)337
B)280
C)299
D)266
E)299
Rationale: x*(85/100) = (480 - x)119/100
x = 280
Answer: B
Answer: B
Question: In the new budget the price of milk rose by 20%. By how much percent must a person reduce his consumption so that his expenditure on it does not increase?
Options:
A)7.5%
B)9.1%
C)10.9%
D)16.67%
E)15%
Rationale: Reduce in consumption = R/(100+R) *100% = 20/120 *100 = 16.67%
Answer is D
Answer: D
Question: A car is running at a speed of 90 kmph. What distance will it cover in 15 second?
Options:
A)375 m
B)395 m
C)373 m
D)372 m
E)371 m
Rationale: Explanation:
Given : Speed = 108 kmph = (90 x (5/18)) m/sec = 25 m/sec
Distance covered in 15 second = (25 x 15) m = 375 m.
ANSWER: A
Answer: A
Question: A motor car starts with the speed of 70km/hr with its speed increasing every two hours by 10kmph. In how many hours will it cover 345 kms
Options:
A)4 hrs
B)5 hrs
C)6 hrs
D)4 ½ hrs
E)5 hrs
Rationale: Explanation:
Distance covered in first 2 hours = 70×2 =140km
Distance covered in next 2 hours = 80×2 =160km
Remaining distance = 345 -140-160 =45km
Speed of the fifth hour =90km/hr
Time taken to cover 45km = 45/90 = ½ hr
Total time taken = 2+2+ ½ = 4 ½ hrs
Answer: Option D
Answer: D
Question: A military commander has to choose 2 soldiers out of a company of 4 for guarding the headquarters. How many different group combinations of 2 does he have to choose from?
Options:
A)4
B)10
C)12
D)15
E)35
Rationale: A military commander has to choose 2 soldiers out of a company of 5.
different group combinations of 2
He can do this in 5C2 ways
5*4/2*1= 10 ways
ANSWER:B
Answer: B
Question: In a group of 140 people, 90 have an age of more 30 years, and the others have an age of less than 20 years. If a person is selected at random from this group, what is the probability the person's age is less than 20?
Options:
A)0.35
B)0.55
C)0.65
D)0.75
E)0.85
Rationale: Number of people whose age is less than 20 is given by
140 - 90 = 50
Probability P that a person selected at random from the group is less than 20 is given by
50 / 140 = 0.35
correct answer A
Answer: A
Question: In a apartment, 30% of the people speak English, 20% speak Hindi and 10% speak both. If a people is selected at random, what is the probability that he has speak English or Hindi?
Options:
A)1/3
B)2/7
C)2/5
D)3/7
E)3/11
Rationale: P (E) = 30 / 100 = 3 / 10 , P (H) = 20 / 100 = 1 / 5 and P (E ∩ H) = 10 / 100 = 1 / 10
P (E or H) = P (E U H)
= P (E) + P (H) - P (E ∩ H)
= (3 / 10) + (1 / 5) - (1 / 10) = 4 / 10 = 2/5
C
Answer: C
Question: If a fraction is multiplied by itself and then divided by the reciprocal of the same fraction, the result is 18 26/27. Find the fraction.
Options:
A)8/27
B)1 1/3
C)2 2/3
D)3 /3
E)None of these
Rationale: Answer
If the required fraction be P
According to the question
(P x P) / (1/P) = 1826/27
⇒ P3 = 512/27
∴ P = 8/3 = 2 2/3
Correct Option: C
Answer: C
Question: If 6 spiders make 3 webs in 7 days, then how many days are needed for 1 spider to make 1 web?
Options:
A)10
B)12
C)14
D)15
E)16
Rationale: Explanation:
Let, 1 spider make 1 web in x days.
More spiders, Less days (Indirect proportion)
More webs, more days (Direct proportion)
Hence we can write as
(spiders)6:1
(webs) 1:7}::x:3
â‡’6Ã—1Ã—7=1Ã—3 Ã— x
â‡’x=14
Answer: Option C
Answer: C
Question: Company A has 13 employees, 8 of whom belong to the union. If 5 people work any one shift, and the union contract specifies that at least 4 union members work each shift, then how many different combinations of employees might work any given shift?
Options:
A)56
B)231
C)336
D)350
E)406
Rationale: There are total of 13 employees, 8 of whom belong to the union and 5 doesn't. Out of 5 people working a shift at least 4 must belong to the union.
Now, at lest 4 out of 5 means that 4 or all 5 employees must belong to the union:
Out of 5 people working a shift 4 employees belong to the union and 1 doesn't: C48∗C15=3500;
Out of 5 people working a shift all 5 employees belong to the union: C58=56
Total # of ways: 350+56=406
Answer: E.
Answer: E
Question: 3 Years ago, the average age of a family of 5 members was 20 years. A baby having been born, the average age of the family is the same today. The present age of the baby is
Options:
A)1 year.
B)1.5 Years.
C)2 Years.
D)3 Years.
E)5 Years.
Rationale: We're told that 3 YEARS AGO, the average age of a family of 5 members was 20 years.
This means that the SUM of their ages was (5)(20) = 100 years.
A baby was born (meaning that there are now 6 family members). We're told that the PRESENT average age of the family members is the SAME.
This means that the sum of the ages is (6)(20) = 120 years.
We're asked for the PRESENT age of the baby.
Since each of the original 5 family members has aged 3 years since the initial average was calculated, the sum of their PRESENT ages is...
100 + (5)(3) = 115.
120-115 =5
E
Answer: E
Question: The salary of a worker is first increased by 30% and afterwards reduced by 30%. What is net change in his salary?
Options:
A)910% increase
B)10% increase
C)9% decrease
D)12% decrease
E)15% increase
Rationale: (30 * 30)/100 = 9% decrease
ANSWER C
Answer: C
Question: Set A consists of integers -9, 8, 3, 10, and J; Set B consists of integers -2, 5, 0, 7, -6, and Q. If R is the median of Set A and W is the mode of set B, and R^W is a factor of 34, what is the value of Q if J is negative?
Options:
A)-2
B)Q=0
C)1
D)2
E)5
Rationale: since j is negative, therefore median of the set will be 3. which is an odd number. also, we know that odd^n will always be odd. now since 34 is even, therefore 3^w will have only one factor with 34 for w=0.
mode of the set is a number which occurs maximum number of time in the set. now, since Q is the mode of the set. therefore Q=0. hence answer is B
Answer: B
Question: To asphalt 1km road, 30 men spent 12 days working 8 hours per day. How many days, 20 men will spend to asphalt a road of 2km working 14 hours a day?
Options:
A)24
B)23
C)24
D)20.57
E)22
Rationale: Man-hours required to asphalt 1 km road=30*12*8=2880
Man-hours required to asphalt 2 km road=2880*2=5760
Man-hours available per day=20*14=280
Therefore number of days=5760/280=20.57 days
Ans=D
Answer: D
Question: The average age of a committee of 10 members is 25 years. A member aged 55 years retired and his place was taken by another member aged 35 years . The average age of
present committee is;
Options:
A)23 years
B)38 years
C)36 years
D)35 years
E)37 years
Rationale: Total age of the committee = 25*10 = 250,
Total age when a member is retired
and a new one was joined = 250-55 +35, =230
Average age of present committee = 230/10 = 23.
ANSWER:A
Answer: A
Question: A board 6ft. 9 inches long is divided into 3 equal parts . What is the length of each part?
Options:
A)5ft. 7 inches
B)3ft. 7 inches
C)2ft. 3 inches
D)2ft. 7 inches
E)1ft. 7 inches
Rationale: Length of board=6ft. 9 inches=(6*12+9)inches=81 inches.
Therefore, Length of each part = (81/3) inches = 27 inches = 2ft. 3 inches
Answer is C.
Answer: C
Question: A company pays 18.5% dividend to its investors. If an investor buys Rs.50 shares and gets 25% on investment, at what price did the investor buy the shares?
Options:
A)25
B)66
C)18
D)37
E)01
Rationale: Explanation:
Dividend on 1 share = (18.5 * 50)/100 = Rs.9.25
Rs.25 is income on an investment of Rs.100
Rs.9.25 is income on an investment of Rs. (9.25 * 100)/25 = Rs.37
ANSWER: D
Answer: D
Question: A man saves 30% of his monthly salary. If an account of dearness of things he is to increase his monthly expenses by 30%, he is only able to save Rs. 300 per month. What is his monthly salary?
Options:
A)Rs. 4000
B)Rs. 3750
C)Rs. 5000
D)Rs. 5500
E)Rs. 6500
Rationale: Income = Rs. 100
Expenditure = Rs. 70
Savings = Rs. 30
Present Expenditure 70+70*(30/100) = Rs. 91
Present Savings = 100 – 91 =Rs. 8
If savings is Rs. 8, salary = Rs. 100
If savings is Rs.300, salary = 100/8*300 = 3750
Answer : B
Answer: B
Question: What least number should be subtracted from 3,381 so that the remainder when divided by 9, 11, and 17 will leave in each case the same remainder 8 ?
Options:
A)6
B)7
C)8
D)12
E)15
Rationale: The LCM of 9, 11 and 17 is 1,683. The next multiple is 2*1,683 = 3,366.
3,366 + {remainder} = 3,366 + 8 = 3,374, which is 7 less than 3,381.
Answer: B.
Answer: B
Question: Company X provides bottled water to its employees in 10 liter bottles, $2 each. At least how many 10L bottles must Company X buy monthly, so that new contract with $50 fixed monthly rate and $1 for 50L bottle each paid off? (Assume that no other costs apply)
Options:
A) 28
B) 29
C) 30
D) 31
E) 32
Rationale: let the no. of 10 liter bottles be x, so the no. of 50l bottles will be x/5 (to equate the vol.) since the total cost will be equal , 2x= 50+x/5 so x= 27.77 or 28. Answer is (A).
Answer: A
Question: X completes a work in 120 days and Y complete the same work in 30 days. If both of them work together, then the number of days required to complete the work will be?
Options:
A)24 days.
B)22days.
C)34 days.
D)40 days.
E)45 days.
Rationale: If X can complete a work in x days and Y can complete the same work in y days, then, both
of them together can complete the work in x y/ x+ y days
Therefore, here, the required number of days = 120Ã— 30/ 150 = 24 days.
A)
Answer: A
Question: There are 11 women and 9 men in a certain club. If the club is to select a committee of 2 women and 2 men, how many different such committees are possible?
Options:
A)120
B)720
C)1,060
D)1,520
E)1,980
Rationale: these are two independent events. meaning picking men from a group of men has no effect on picking women from group of women. so you have to multiply here.
11c2*9c2 =1980
Answer is E.
Answer: E
Question: The LCM of two numbers is 2310 and HCF is 30. If one of the numbers is 210. Then what is the other number ?
Options:
A)715
B)825
C)330
D)582
E)465
Rationale: First number * Second Number = LCM * HCF
Other number = 2310 * 30 / 210 = 11*30 = 330
ANSWER :C
Answer: C
Question: Between 100 and 200, how many numbers are there in which one digit is the average of the other two?
Options:
A)11
B)12
C)10
D)8
E)9
Rationale: Answer is 11 :A
Let's list the numbers between 100 and 200 that have digits in which one of them is average of the other 2.
(One rule before listing, it should always start with 1XX)
{102, 111, 123, 135, 147, 159 } in these five, except 111, the others has 2 ways of rearranging, i.e., 123 can also be written as 132, and so is for 135 as 153.
Therefore 1 + 2 * 5 numbers = 11
Answer: A
Question: mixture contains alcohol and water in the ratio 4 : 3. If 8 liters of water is added to the mixture, the ratio becomes 4: 5. Find the quantity of alcohol in the given mixture.
Options:
A)10
B)99
C)27
D)4
E)29
Rationale: Let the quantity of alcohol and water be 4x litres and 3x litres respectively
32x = 4(3x+5)
20x = 20
x = 1
Quantity of alcohol = (4 x 1) litres = 4 litres.
Answer: D
Answer: D
Question: A is 20 percent more efficient than B. If the two person can complete a piece of work in 60 days.in how many days. A working alone can complete the work
Options:
A)110
B)277
C)287
D)279
E)2781
Rationale: As A is 20% more efficient than B, If B's per day work is 100 units then A's 120.
Both persons together completes (100 + 120) units = 220 units a day.
They took 60 days to complete the work. So total work = 60 x 220
If A alone set to complete the work, he takes = 60×220120=11060×220120=110 days
Answer:A
Answer: A
Question: Sam’s car was fined when he gave Joe and Peter a ride, so they decided to help Sam pay the fine. Joe paid $6 more than 1/4 of the fine and Peter paid $6 less than 1/3 of the fine, leaving pay $10 less than 1/2 the fine to complete the payment. What fraction of the fine did Sam pay?
Options:
A)$50
B)$40
C)$35
D)$44
E)$45
Rationale: Call the fine F. Joe paid (1/4)F + 4 and Peter paid (1/3)F – 4, leaving (1/2)F – 5 left. If we add those three up, they should add up to F.
F = [(1/4)F + 6] + [(1/3)F – 6] + [(1/2)F – 10]
F = (1/4)F + (1/3)F + (1/2)F – 10
Multiply all terms by 12 to clear the fractions.
12F = 3F + 4F + 6F – 120
12F = 13 F – 120
–F = – 120
F = 120
Well, if the fine cost $120, then Sam paid the part not covered by Joe or Peter. Half the fine is $60, and Sam paid $10 less than this: $50.
Answer = A
Answer: A
Question: A and B invests Rs.8000 and Rs.9000 in a business. After 4 months, A withdraws half of his capital and 2 months later, B withdraws one-third of his capital. In what ratio should they share the profits at the end of the year?
Options:
A)32 : 48
B)32 : 42
C)32 : 45
D)32 : 41
E)42 : 45
Rationale: Explanation:
A : B
(8000*4)+(4000*8) : (9000*6)+(6000*6)
64000 : 90000
32 : 45
Answer:C
Answer: C
Question: 65 + 5 * 12 / (180/3) = ?
Options:
A)22
B)77
C)29
D)66
E)21
Rationale: 65 + 5 * 12 / (180/3) = 65 + 5 * 12 / (60)
= 65 + (5 * 12)/60 = 65 + 1 = 66.Answer:D
Answer: D
Question: Mother is aged 3times more than her daughter Rose. After 8 years, she would be two and a 1/2times of Rose's age. After further 8 years, how many times would he be of Rose's age?
Options:
A)1
B)2
C)3
D)5
E)6
Rationale: Let Ronit's present age be x years. Then, father's present age =(x + 3x) years = 4x years.
(4x + 8) = 5 (x + 8)
2
8x + 16 = 5x + 40
3x = 24
x = 8.
Hence, required ratio = (4x + 16)/(x + 16) = 48/24= 2.
B
Answer: B
Question: What approximate value should come in place of the question mark (?) in the following equation ?
2⁄7 of 1596 + 3015 = ? – 2150
Options:
A)7200
B)48000
C)5610
D)58000
E)6300
Rationale: ? ≈ 2 × 230 + 3000 + 2150
= 460 + 3000 + 2150 = 5610
Answer C
Answer: C
Question: If (1 – 1.25)N = 3, then N =
Options:
A) −400
B) −140
C) −4
D) 4
E) -12
Rationale: (1 – 1.25)N = 3
Simplify to get: -0.25N = 3
Rewrite as (-1/4)N = 3
Multiply both sides by -4 to get: N = -12
Answer: E
Answer: E
Question: If a and b are positive integers, which of the following cannot be odd?
Options:
A)(2+4a)/(4+4b)
B)(4a)/(b)
C)a/b
D)(4+a)/(2+4b)
E)(4+a)/(1+4b)
Rationale: A. (2+4a)/(4+4b) - Under any condition this can't be odd. Answer
B. (4a)/(b) = 4.1/4 = 1 = Odd
C. a/b = 4/4 = Odd
D.(4+a)/(2+4b) = (4+2)/(2+4.1) = 1 = Odd
E.(4+a)/(1+4b) = (4+1)/(1+4.1) = 1 = Odd
ANSWER:A
Answer: A
Question: The telephone bill of a certain establishment is party fixed and partly varies as the number of calls consumed. When in a certain month 540 calls made the bill is Rs.1800. In another month 620 calls are consumed then the bill becomes Rs.2040. In another month 500 units are consumed due to more holidays. The bill for that month would be :
Options:
A)Rs.1560
B)Rs.1680
C)Rs.1840
D)Rs.1950
E)Rs.1850
Rationale: Let the fixed amount be Rs. X and the cost of each unit be Rs. Y.
Then, 540y + x = 1800 …. And 620y + x = 2040
On subtracting (i) from (ii), we get 80y = 240 -> y = 3
Putting y = 3 in (i) we get :
540 * 3 + x = 1800 x = (1800-1620) = 180
. : Fixed charges = Rs.180, Charge per unit = Rs.3.
Total charges for consuming 500 units = 180 +(500*3) = Rs.1680
ANSWER:B
Answer: B
Question: Three people each took 4 tests. If the ranges of their scores in the 4 practice tests were 17, 28 and 35, what is the minimum possible range in scores of the three test-takers?
Options:
A)a 17
B)b) 28
C)c) 35
D)d) 45
E)e) 80
Rationale: It is finding the minimum range between all their scores, if all test taker scores are between 0 and maximum range we will have:
A- 0 and 17
B- 0 and 28
therefore the minimum range is 28, it cant be any lower however you play with the numbers.
B
Answer: B
Question: Mary rolls a die 5 times. What is the probability that she gets a one on the last one of the five rolls?
Options:
A)100/1000
B)7775/7776
C)none
D)1
E)888/881
Rationale: the die has 6 sides and it was rolle 5 times, then 6*6*6*6*6=7776
the number of ways to get 1 is 1
then 1/7776
the probability would be
1-1/7776=7775/7776
Answer B
Answer: B
Question: Sakshi can do a piece of work in 20 days. Tanya is 25% more efficient than Sakshi. The number of days taken by Tanya to do the same piece of work is?
Options:
A)15
B)16
C)18
D)25
E)20
Rationale: Explanation:
Ratio of times taken by Sakshi and Tanys = 125:100 = 5:4
Suppose Tanya takes x days to do the work.
5:4 :: 20:x => x= 16 days.
Hence, Tanya takes 16 days to complete the work.
ANSWER IS B
Answer: B
Question: Three grades of milk are 1 percent,4 percent and 3 percent fat by volume. If x gallons of the 1 percent grade, y gallons of the 2 percent grade, and z gallons of the 3 percent grade are mixed to give x+y+z gallons of a 1.5 percent grade, what is x in terms of y and z?
Options:
A)y + 3z
B)(y +z) / 4
C)2y + 3z
D)3y + z
E)4y + 3z
Rationale: Soln:
The resulting equation is
=> (.01x + .04y + .03z)/(x+y+z) = 1.5/100
=> x + 4y + 3z = 1.5x + 1.5y + 1.5z
taking x to one side and y and z to other side we get
=> x = 4y + 3z
Ans is E
Answer: E
Question: Peter bought an item at 20% discount on its original price. He sold it with 40% increase on the price he bought it. The sale price is by what percent more than the original price?
Options:
A)7.2
B)7.5
C)10
D)12
E)None
Rationale: Sol.
Let the original price be Rs. 100. Then, C.P. = Rs. 80.
S.P. = 140% of Rs. 80 = Rs. [112-100%] = 12%.
Answer D
Answer: D
Question: The area of a rectangular plot is 24 times its breadth. If the difference between the length and the breadth is 10 metres, what is its breadth?
Options:
A)14 metres
B)5 metres
C)7.5 metres
D)Data inadequate
E)None of these
Rationale: L × B = 24 × B
∴ L = 24 m
and L – B = 10
∴ B = 24 – 10 = 14 m
Answer A
Answer: A
Question: If p and q are positive integers, how many integers are larger than pq and smaller than p(q + 5)?
Options:
A)3
B)P + 2
C)p – 2
D)2p – 1
E)5p - 1
Rationale: The number of integers between x and y, where x>y is (x-y)-1. For example, the number of integers between 1 and 5 is (5-1)-1=3: 2, 3, and 4.
Thus, the number of integers between pq and p(q+5)=pq+5p is (pq+5p-pq)-1=5p-1.
Answer: E.
Answer: E
Question: A, B and C have Rs.500 between them, A and C together have Rs.200 and B and C Rs.350. How much does C have?
Options:
A)50
B)49
C)87
D)76
E)66
Rationale: A+B+C = 500
A+C = 200
B+C = 350
--------------
A+B+2C = 550
A+B+C = 500
----------------
C = 50
Answer:A
Answer: A
Question: A man sells a horse for Rs.200 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?
Options:
A)227
B)299
C)277
D)860
E)460
Rationale: CP = SP + 1CP = SP - g
200 + x = 980 - 2x
3x = 780 => x = 260
CP = 200 + 260= 460
Answer: E
Answer: E
Question: A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?
Options:
A)388
B)378
C)240
D)388
E)771
Rationale: Speed = [54 * 5/18] m/sec = 15 m/sec.
Length of the train = (15 * 20) m = 300 m.
Let the length of the platform be x meters.
Then, x + 300 / 36 = 15
x + 300 = 540
x = 240 m.
Answer: C
Answer: C
Question: The average age of applicants for a new job is 32, with a standard deviation of 8. The hiring manager is only willing to accept applicants whose age is within one standard deviation of the average age. Assuming that all applicants' ages are integers and that the endpoints of the range are included, what is the maximum number of different ages of the applicants?
Options:
A)8
B)77
C)7
D)18
E)34
Rationale: Minimum age = Average - 1 Standard deviation = 32 - 8 = 24
Maximum age = average + 1 Standard deviation = 32+ 8 = 40
Maximum number of different ages of the applicants = 30 - 24 + 1 = 7
Answer C
Answer: C