divelab/Sys2Bench huggingface dataset:
Question: If a and b are both prime numbers greater than 10, which of the following CANNOT be true?
I. ab is an even number.
II. The difference between a and b equals 117.
III. The sum of a and b is even.
Options:
A)I only
B)I and II only
C)I and III only
D)II and III only
E)I, II and III
Rationale: CONCEPT: Prime Numbers greater than 10 will all be ODD
I. ab is an even number - Can't be True because both a and b are ODD
II. The difference between a and b equals 117 - Can't be True because both a and b are ODD and Difference of two Odd No. must be EVEN
III. The sum of a and b is even - This will be True because both a and b are ODD and Sum of two Odd No. must be EVEN
ANSWER:B
Answer: B
Question: Two trains, one from P to Q and the other from Q to P, start simultaneously. After they meet, the trains reach their destinations after 9 hours and 16 hours respectively. The ratio of their speeds is
Options:
A)4:1
B)4:2
C)4:5
D)4:3
E)4:6
Rationale: Ratio of their speeds = Speed of first train : Speed of second train
= 16−−√9√
= 4:3
Answer is D.
Answer: D
Question: It is given that 2^32 + 1 is exactly divisible by a certain number. Which one of the following is also divisible by the same number B?
Options:
A)a. 2^96 + 1
B)b. 2^16 - 1
C)c. 2^16 + 1
D)d. 7 * 2^33
E)e. 2^64 + 1
Rationale: a³ + b³ =(a+b)(a² -ab +b²)
Now, let (2^32 + 1) be (a+b)
a³ + b³ = (2^96 + 1)
Now, as mentioned in formula above,
a³ + b³ is always divisible by (a+b)
So any factor of B= (a+b) is a factor of (a³ + b³)
Henca A
Answer: A
Question: If two numbers, a and b, are to be chosen from a set of 4 consecutive integers starting with 1 and a set of three consecutive even integers starting with 6, respectively, what is the probability that b/a will not be an integer?
Options:
A)1/6
B)1/4
C)1/3
D)1/2
E)2/3
Rationale: a is from the following set {1,2,3,4}
b is from the following set {6,8,10}
The total number of ways of choosing 2 integers, one from each set is 4*3 = 12 ways.
The possibilities where b/a is not an integer is for the following outcomes:
{b,a} = {6,4},{8,3},{10,3},{10,4} = 4 ways
Thus the probability is 4/12 = 1/3
The answer is C.
Answer: C
Question: If |x| = 7x - 5, then x = ?
Options:
A)1
B)1/2
C)1 and 1/2
D)2
E)-1
Rationale: Answer: A
Approach:
Substituted option A i.e x=1. Inequality satisfied.
D
Answer: D
Question: The maximum number of students among them 1048 pens and 828 pencils can be distributed in such a way that each student gets the same number of pens and same number of pencils is:
Options:
A)4
B)8
C)16
D)1911
E)None of these
Rationale: Explanation:
Required number of students = H.C.F of 1048 and 828 = 4. Answer: A
Answer: A
Question: An art gallery owner is hanging paintings for a new show. Of the eight paintings she has to choose from, she can only hang two on the main wall of the gallery. Assuming that she hangs as many as possible on that wall, in how many ways can she arrange the paintings?
Options:
A)18
B)30
C)56
D)120
E)216
Rationale: Arrangment means permutations questions..
8P2 = 8!/2! = 56.
IMO option C is correct answer..
Answer: C
Question: A watch passes through three hands and each person gains 25%. If the third person sells it for $125, what did the first person pay for it?
Options:
A)$54
B)$60
C)$64
D)$72
E)$80
Rationale: 1.25*1.25*1.25 * original price = 125
(5/4)^3 * original price = 125
original price = 64*125 / 125 = $64
The answer is C.
Answer: C
Question: The distance between Delhi and Mathura is 140 kms. A starts from Delhi with a speed of 20 kmph at 7 a.m. for Mathura and B starts from Mathura with a speed of 25 kmph at 8 p.m. from Delhi. When will they meet?
Options:
A)10.50 a.m.
B)10.40 a.m.
C)10.30 a.m.
D)11.40 a.m.
E)1.40 a.m.
Rationale: D = 140 – 20 = 120
RS = 20 + 25 = 45
T = 120/45 = 2 2/3 hours
8 a.m. + 2 hrs 40 min = 10.40 a.m.
ANSWER:B
Answer: B
Question: A number when multiplied by 3 and then subtracted by 2 becomes the reverse of itself. Can you find out which smallest number is that?
Options:
A)33
B)28
C)55
D)71
E)23
Rationale: B
28 is the required number.
28 * 3 - 2 = 82.
Answer: B
Question: A batsman scored 100 runs which included 3 boundaries and 8 sixes. What percent of his total score did he make by running between the wickets?
Options:
A)50%
B)40%
C)60%
D)70%
E)80%
Rationale: Number of runs made by running = 100 - (3 x 4 + 8 x 6)
= 100 - (60)
= 40
Now, we need to calculate 40 is what percent of 100.
=> 40/100 x 100 = 40 %
ANSWER:B
Answer: B
Question: There are 10000 families, having 4 children for each family. In how many families 2 daughters are probable.
Options:
A)625
B)529
C)425
D)354
E)725
Rationale: Probability to have 2 daughter = 1/2^4 = 1/16
so answer = 10000*1/16 = 625
ANSWER:A
Answer: A
Question: If the average marks of three batches of 55, 60 and 45 students respectively is 40, 62, 58, then the average marks of all the students is
Options:
A)54.48
B)53.31
C)54.6
D)54.58
E)None of these
Rationale: Explanation:
(55Ã—40)+(60Ã—62)+(45Ã—58) / 55+60+45
8530 / 160=53.3
Option B
Answer: B
Question: How many odd three-digit integers greater than 600 are there such that all their digits are different?
Options:
A)40
B)56
C)72
D)81
E)120
Rationale: 3 (hundred's digit) * 9 (ten's digit) * 8 (unit's digit) = 216
Now take numbers in the range 600 - 900.
Total numbers where all digits are different = 216 (as before)
[highlight]Number of odd numbers = 3 * 8 * 5 = 120[/highlight] (now there are 5 possibilities for the unit's digit)
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)167
B)266
C)150
D)776
E)122
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: Let Y be the smallest positive integer such that 12 and 8 are factors of 20*Y, So the value of Y is:
Options:
A)7
B)9
C)11
D)13
E)15
Rationale: You can calculate the LCM(12,8) (Least commom multiple of 12 and 8) = 36
and calculate the LCM(36,20) = 180
And making 180/20 we obtain 9.
So, the Answer is B.
Answer: B
Question: If the sales tax reduced from 3 1/2 % to 3 1/3%, then what difference does it make to a person who purchases an article with market price of $ 8400 ?
Options:
A)14
B)24
C)34
D)12
E)13
Rationale: Required difference = [3 1/2 % of $8400] – [3 1/3 % of $8400]
= [(7/20)-(10/3)]% of $8400 =1/6 % of $8400
= $ [(1/6)*(1/100)*8400] = $ 14.
Answer A.
Answer: A
Question: A number, x is chosen at random from the set of positive integers less than 20. What is the probability that (18/x) > x?
Options:
A) 1/5
B) 2/9
C) 3/19
D) 4/19
E) 7/9
Rationale: Number x has to be chosen from numbers 1-19
(18/x) > x
=> 18 > x^2
=>x^2 - 18 < 0
x can have 2 values only 1 , 2 , 3 , 4
Therefore , probability = 4 / 19
Answer D
Answer: D
Question: If a committee of 3 people is to be selected from among 8 married couples so that the committee does not include two people who are married to each other, how many such committees are possible?
Options:
A)120
B)240
C)250
D)380
E)448
Rationale: You now have your Committee of 3 people. But you've selected them in an order, when order doesn't matter.
Selection #1 = Jack
Selection #2 = Susan
Selection #3 = Mary
Assume this is a good committee where Jack is not married to Susan or Mary and Susan and Mary are not married. The above committee will be the same as the following committee:
Selection #1 = Susan
Selection #2 = Mary
Selection #3 = Jack
To account for the fact that the order does not matter, we must divide out the number of ways a single committee can be the same members but in different order. 3 places = 3!, 3*2*1 = 6.
16*14*12 / 6 = 448. Answer E.
Answer: E
Question: A certain restaurant offers 8 kinds of cheese and 2 kinds of fruit for its dessert platter. If each dessert platter contains an equal number of kinds of cheese and kinds of fruit, how many different dessert platters could the restaurant offer?
Options:
A)8
B)12
C)15
D)21
E)44
Rationale: As dessert platter should contain equal number of kinds of cheese and fruits, desert can contain:
A. 2 kinds of cheese and 2 kinds of fruits --> 8C2*2C2=28*1=28
B. 1 kind of cheese and 1 kind of fruit --> 8C1*2C1=8*2=16
A+B=28+16=44
Answer: E.
Answer: E
Question: Braun invested a certain sum of money at 8% p.a. simple interest for 'n' years. At the end of 'n' years, Braun got back 4 times his original investment. What is the value of n?
Options:
A)50 years
B)25 years
C)12 years 6 months
D)37 years 6 months
E)40 years
Rationale: Explanatory Answer
Let us say Braun invested $100.
Then, at the end of 'n' years he would have got back $400.
Therefore, the Simple Interest earned = 400 - 100 = $300.
We know that Simple Interest = (Principal * number of years * rate of interest) / 100
Substituting the values in the above equation we get 300 = (100 * n * 8) / 100
Or 8n = 300
Or n = 37.5 years.
choice is (D)
Answer: D
Question: A train covers a distance of 12 km in 10 min. If it takes 3 sec to pass a telegraph post, then the length of the train is?
Options:
A)60 m
B)188 m
C)120 m
D)80 m
E)189 m
Rationale: Speed = (12/10 * 60) km/hr = (72 * 5/18) m/sec
= 20 m/sec.
Length of the train = 20 * 3
= 60 m.
Answer:A
Answer: A
Question: A lady bought five books namely A,B,C,D,E to distribute her 3 child. How many ways she can distribute books?
Options:
A)3^3
B)3^4
C)3^5
D)3^6
E)3^2
Rationale: 3*3*3*3*3
3^5
ANSWER:C
Answer: C
Question: A man invested Rs. 1552 in a stock at 97 to obtain an income of Rs. 128. The dividend from the stock is:
Options:
A)8%
B)6%
C)7%
D)9%
E)10%
Rationale: By investing 1552 income = 128
by investing rs 97 income = (128/1552 * 97) = rs 8
=>8%
ANSWER A
Answer: A
Question: What is the value of the following expression?
(1/ (2^2 – 1)) + (1/ (4^2 – 1)) + (1/ (6^2 – 1)) + .... + (1/ (16^2 – 1))
Options:
A)a. 9/19
B)b. 10/19
C)c. 10/21
D)d. 11/21
E)e. 8/17
Rationale: it can be written into
1/3+1/15+ 1/35.....1/256
i.e
1/3+1/2*(1/3-1/5)+1/2*(1/5-1/7).... til last term - 1/2*(1/17)
all terms from 1/5 .. to second last term get cancelled
left with
1/3+1/6-1/34=1/2-1/34=16/34=8/17
E
Answer: E
Question: In final exam of class IX there are 50 students 10 % students failed. How many students passed to class X?
Options:
A)33
B)378
C)37
D)39
E)45
Rationale: Percentage of students passed to class X = 100 % - 10 % = 90 %
90 % of 50
= 90/100 × 50
= 4500/100
= 45
Therefore, 45 students passed to class X.
Answer:E
Answer: E
Question: 16 men can complete a piece of work in 25 days. In how many days can 20 men complete that piece of work?
Options:
A)55 days
B)77 days
C)20 days
D)88 days
E)44 days
Rationale: 16 * 25 = 20 * x => x
= 20 days
Answer: C
Answer: C
Question: Find the principal which yields a simple interest of Rs. 20 and compound interest of Rs. 22 in two years, at the same percent rate per annum?
Options:
A)s. 520
B)s. 480
C)s. 420
D)s. 100
E)s. 200
Rationale: Explanation:
SI in 2 years = Rs. 20, SI in 1 year = Rs. 10
CI in 2 years = Rs. 22
% rate per annum = [(CI – SI) / (SI in 1 year)] *100
= [(22 – 20) / 20] * 100
= 10 % p.a.
Let the principal be Rs. X
Time = T = 2 years
% rate = 10% p.a.
SI = (PRT/100)
20 = (X*10*2) / 100
X = Rs. 100
ANSWER: D
Answer: D
Question: When positive integer N is divided by positive integer J, the remainder is 25. If N/J = 204.05, what is value of J?
Options:
A)600
B)500
C)800
D)200
E)900
Rationale: When a number is divided by another number, we can represent it as : Dividend = Quotient * Divisor + Remainder
So, Dividend/Divisor = Quotient + Remainder/Divisor
Given that N/J = 204.05
Here 204 is the quotient.
Given that Remainder = 25
So, 204.05= 204 + 25/J
So, J = 500
Answer: B
Answer: B
Question: Anu can do a work in 6 days and Binu alone in 9 days. Anu and Binu undertook to do it for Rs.5400. With help of Minu, they completed the work in 3 days. How much is to be paid to Minu and Anu?
Options:
A)s.750, Rs.2250
B)s.2000, Rs.750
C)s.750, Rs.2000
D)s.800, Rs.1250
E)s.900, Rs.2700
Rationale: Minuâ€™s one dayâ€™s work = 1/3 - 1/6 + 1/9= 1/3 - 5/18 = 1/18
Anuâ€™s wages: Binuâ€™s wages: Minuâ€™s wages = 1/6 : 1/9 : 1/18 = 6: 4: 2
Minuâ€™s share = Rs.5400* 2/12 = Rs.900
Anuâ€™s share = Rs.5400* 6 /12 = Rs.2700
ANSWER:E
Answer: E
Question: If money is invested at r percent interest, compounded annually, the amount of the investment will double in approximately 50/r years. If Luke's parents invested $15,500 in a long term bond that pays 12 percent interest compounded annually, what will be the approximate total amount of the investment 12 years later, when Luke is ready for college?
Options:
A)62,000
B)85,500
C)95,500
D)100,500
E)120,000
Rationale: Answer equals E in 48 years. I thought by 50th year it would reach 120,000. Options should have been separated more widely for clarity.
Answer: E
Question: If log72 = m, then log4928 is equal to
Options:
A)2(1 + 2m)
B)(1 + 2m)/2
C)2/(1 + 2m)
D)1 + m
E)1 + 2m
Rationale: log4928 = 1/2log7(7x4) = 1/2(1 + log74)
= 1/2 + (1/2). 2log72
= 1/2 + log72
= 1/2 + m = (1 + 2m)/2.
ANSWER:B
Answer: B
Question: The simple interest accrued on an amount of ₹ 84000 at the end of 3 yr is ₹ 30240. What would be the compound interest accrued on the same amount at the same rate in the same period?
Options:
A)22
B)77
C)66
D)88
E)61
Rationale: Answer:D
Answer: D
Question: Rs.2500 is divided into two parts such that if one part be put out at 5% simple interest and the other at 6%, the yearly annual income may be Rs.140. How much was lent at 5%?
Options:
A)2333
B)2777
C)2688
D)1000
E)2871
Rationale: (x*5*1)/100 + [(2500 - x)*6*1]/100 = 140
X = 1000
Answer: D
Answer: D
Question: ACME’s manufacturing costs for sets of horseshoes include a $11,450 initial outlay, and $19.75 per set. They can sell the sets for $52.50. If profit is revenue from sales minus manufacturing costs, and the company produces and sells 987 sets of horseshoes, what was their profit?
Options:
A)$20,874.25
B)$30,943.25
C)$41,308.50
D)$51,817.50
E)$53,624.25
Rationale: The numbers are ugly, and the answer choices are widely spread out. This problem is absolutely screaming for estimation!
So here’s some more fast and furious estimation. Initial manufacturing outlay: round that from $11450 to $10000. Cost per set: round to $20. Sales revenue per set: $50. Number produced & sold: 1000. OK, now we’re in business.
Cost equals 10000 + 20*1000 = 10000 + 20000 = $30000. Sales revenue = 50*1000 = $50000. Profit = (Sales Revenue) – (Cost) =$50000 – $30000 = $20000. Answer choice (A) is the only answer even close to that. Single digit calculations all the way, and it was enough to get the answer!
Answer A
Answer: A
Question: A person purchased a TV set for Rs. 13000 and a DVD player for Rs. 5000. He sold both the items together for Rs. 21600. What percentage of profit did he make?
Options:
A)48%
B)70%
C)40%
D)45%
E)20%
Rationale: The total CP = Rs. 13000 + Rs. 5000
= Rs. 18000 and SP
= Rs. 21600
Profit(%)
= (21600 - 18000)/18000 * 100
= 20%
Answer: E
Answer: E
Question: a man owns 2/3 of market reserch beauro buzness,and sells 3/4 of his shares for 45000rs,what is the value of buzness?
Options:
A)150000
B)90000
C)85000
D)190000
E)250000
Rationale: If value of business=x
Total sell (2x/3)(3/4)=45000
->x=150000
ANSWER:B
Answer: B
Question: here's an easy question of averages, but let's try to see innovative ways of solving this.
A class has 12 boys and x girls. Average score of boys and girls is 84 and 92 respectively. the average of the whole class is 86, what is the value of x?
Options:
A)a) 6
B)b) 4
C)c) 8
D)d) 10
E)e) 12
Rationale: 12(84)+92x/12+x=86
1008+92x/12+x=86
1008+92x=86(12+x)
1008+92x=1032+86x
X's one side, numbers one side we get,
92x - 86x=1032-1008
6x=24
hence, x=4
Answer B
Answer: B
Question: In the quadratic equation ax2 - 11x + 40 = 0, if the sum of two roots is 1.1, what is the product of the two roots?
Options:
A)7
B)6
C)5
D)4
E)3
Rationale: Explanation:
The sum of the roots of the quadratic equation ax2 - bx + c = 0 are (-b/a) and the product of the roots are (c/a).
Thus, in the equation ax2 - 11x + 40 = 0, where a = a, b = - 11 and c = 40.
we get, sum of the roots = - (- 11) / a = 1.1
a = 11 / 1.1 = 10
Product of the roots = 40 / 10 = 4
ANSWER: D
Answer: D
Question: How many different positive integers exist between 106 and 107, the sum of whose digits is equal to 2?
Options:
A)6
B)7
C)5
D)8
E)18
Rationale: Explanatory Answer
Find the number of such integers existing for a lower power of 10 and extrapolate the results.
Between 10 and 100, that is 101 and 102, we have 2 numbers, 11 and 20.
Similarly, between 100 and 1000, that is 102 and 103, we have 3 numbers, 101, 110 and 200.
Therefore, between 106 and 107, one will have 7 integers whose sum will be equal to 2.
Alternative approach
All numbers between 106 and 107 will be 7 digit numbers.
There are two possibilities if the sum of the digits has to be '2'.
Possibility 1: Two of the 7 digits are 1s and the remaining 5 are 0s.
The left most digit has to be one of the 1s. That leaves us with 6 places where the second 1 can appear.
So, a total of six 7-digit numbers comprising two 1s exist, sum of whose digits is '2'.
Possibility 2: One digit is 2 and the remaining are 0s.
The only possibility is 2000000.
Total count is the sum of the counts from these two possibilities = 6 + 1 = 7
Choice B is the correct answer.
Answer: B
Question: Rashmi walks to her bus stop at 5 kmph and reaches there late by 10 minutes. On the next day,she increases her speed to 6 kmph and reaches the bus stop 10 minutes early.How far is the bus stop ?
Options:
A)13
B)12
C)11
D)10
E)9
Rationale: Let the distance to the bus stop is "d"km
Time taken by her(at 5kmph)=d/5hour, and
Time taken by her(at 6kmph)=d/6 hour
As per given condition,
d/5 - d/6 = 20/60
d= 10 kms
ANSWER:D
Answer: D
Question: Two angles of a triangle have ratio 5:3, and the third angle is the difference of the other two. Find the smallest angle of such a triangle in degrees.
Options:
A)16
B)18
C)20
D)24
E)36
Rationale: The angles are 5x, 3x, and (5x-3x) = 2x [note that 2x is the smallest angle]
the angles of a triangle add up to 180, so
5x+3x+2x=180
10x = 180
x = 18
2x is the smallest angle, so 2*18 = 36 is the smallest angle
E
Answer: E
Question: There are two sticks of which the longer one is 10 cm longer than the short stick. Find the length of the shorter stick if the total length of both the sticks is 24 cm?
Options:
A)6
B)7
C)8
D)12
E)14
Rationale: Since, 24 is the total length. Shorter is any one from answers.
Try Back solving from first answer, i.e. 6. 6+(6+10) = 22<24
Hence, Select next greater no. : 7 +(7+10) =24. So, 7 is the answer
Answer: B
Question: At a florist shop on a certain day, all corsages sold for either $20 or $30. If 10 of the corsages that sold for $30 had instead sold for $20, then the store's revenue from corsages that day would have been reduced by 20 percent. What was the store's actual revenue from corsages that day?
Options:
A)$200
B)$400
C)$500
D)$800
E)$1000
Rationale: Let, No. of corsages @ $20 = x, no. of corsages @ $30 = y and revenue= r
so, 20x+30y=r.........(1)
Now,
Given the situation, 20(x+10) + 30(y-10)= r-.2r
=> 20x+200+30y-300 = .8r
=> 20x+30y = .8r+100............(2)
so, r = .8r+100
=> r = 500
The answer is C.
Answer: C
Question: If a rod is sold for Rs.34.80, there is a loss of 25%. Find out the CP of the rod?
Options:
A)45
B)46
C)46.4
D)47.23
E)47.34
Rationale: SP=34.80Loss=25%CP=100(100−Loss%)×SP=100(100−25)×34.80=10075×34.80=4×34.803=4×11.60=46.40
C
Answer: C
Question: In the city of San Durango, 60 people own cats, dogs, or rabbits. If 30 people owned cats, 40 owned dogs, 18 owned rabbits, and 12 owned exactly two of the three types of pet, how many people owned all three?
Options:
A)2
B)4
C)8
D)12
E)32
Rationale: You are considering a case when cat dogs and rabbit are not exactly equal to 12 .
The solution shall be 60=30+40+18-12-2x
and hence x shall be 8.
Answer C
Answer: C
Question: Which is greater than 4?
Options:
A)5
B)-5
C)-1/2
D)-25
E)1/2
Rationale: 5 greater than 4.
Answer: A
Answer: A
Question: A shopkeeper sold an article offering a discount of 5% and earned a profit of 23.5%. What would have been the percentage of profit earned if no discount was offered?
Options:
A)24
B)28
C)30
D)32
E)34
Rationale: Let C.P. be Rs. 100.
Then, S.P. = Rs. 123.50
Let marked price be Rs. x. Then, 95/100 x = 123.50
x = 12350/95 = Rs. 130
Now, S.P. = Rs. 130, C.P. = Rs. 100
Profit % = 30%.
ANSWER:C
Answer: C
Question: A man complete a journey in 10 hours. He travels first half of the journey at the rate of 21 km/hr and second half at the rate of 24 km/hr. Find the total journey in km
Options:
A)200 Km
B)222 Km
C)224 Km
D)248 Km
E)None of these
Rationale: Explanation:
Let time taken to travel the first half = x hr
Then time taken to travel the second half = (10 - x) hr
Distance covered in the the first half = 21x [because, distance = time*speed]
Distance covered in the the second half = 24(10 - x)
Distance covered in the the first half = Distance covered in the the second half
So,
21x = 24(10 - x)
=> 45x = 240
=> x = 16/3
Total Distance = 2*21(16/3) = 224 Km [multiplied by 2 as 21x was distance of half way]
Option C
Answer: C
Question: Ravi bought 5 pencil and 10 eraser for Rs 4 . Sheetal bought 3 pencil and 9 eraser for Rs 3 then what would be the cost of pencil and eraser.
Options:
A).15p, .30p
B).50p,.27p
C).40p,.20p
D).20p,.40p
E).50p,.40p
Rationale: Let pencil be x and eraser be y so
5x+10y=4
3x+9y=3
By solving the above two equations we get x=.40p and y=.20p correct ans is C
Answer: C
Question: A coin is tossed live times. What is the probability that there is at the least one tail?
Options:
A)31/32
B)31/17
C)31/19
D)31/12
E)31/13
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
Question: The average of a batsman for 40 innings is 50 runs. His highest score exceeds his lowest score by 172 runs. If these two innings are excluded, his average drops by 2 runs. Find his highest score.
Options:
A)172
B)173
C)174
D)175
E)176
Rationale: Total runs = 40 × 50 = 2000
Let his highest score be = x
Then his lowest score = x – 172
Now 200−x−(x−172) /38=48
⇒ 2x = 2172 – 1824
⇒ x = 174
Answer C
Answer: C
Question: The product of the digits of the four-digit number T is 36. No two digits of are identical. How many different numbers are possible values of T ?
Options:
A)6
B)12
C)24
D)36
E)48
Rationale: The main question here is how can you arrange 4 different digits T. We don't even need to find the number. from the question itself we know that there are 4 different digits and none of them is 0 as the product is non-zero.
Therefore no of ways to arrange 4 diff. digits is 4! which is 24
hence C
Answer: C
Question: Set A of 8 positive integers may have the same element and have 37. And set B of 8 positive integers must have different elements and have 37. When m and n are the greatest possible differences between 37 and other elements’ sums in set A and set B, respectively, m-n=?
Options:
A)21
B)22
C)23
D)25
E)26
Rationale: This is maximum-minimum. Hence, 37-(1+1+1+1+1+1+1)=30 and 37-(1+2+3+4+5+6+7)=9. So, 30-9=21. The correct answer is B.
Answer: B
Question: A man swims downstream 72 km and upstream 45 km taking 9 hours each time; what is the speed of the current?
Options:
A)1.6
B)1.5
C)1.9
D)1.2
E)1.7
Rationale: 72 --- 9 DS = 8
? ---- 1
45 ---- 9 US = 5
? ---- 1 S = ?
S = (8 - 5)/2 = 1.5
Answer: B
Answer: B
Question: A boats man can row in still water at speed of 7 km/hr. It takes 6 hours more to travel the same distance in upstream than in downstream if the speed of the river is 3 km/hr. what is the distance between the two destinations?
Options:
A)40
B)87
C)126
D)18
E)91
Rationale: Explanation:
x = 7 km/hr ; y = 3 km/hr
Ds = 10 km/hr ; Us = 4 km/hr
Distance (d) is same. Therefore, if time taken for downstream is t hours, the time for upstream is (t + 6) hours.
10*t = 4*(t + 6)
6t = 24 ; t = 4 hours
d = 10*4 = 40 km
ANSWER: A
Answer: A