divelab/Sys2Bench huggingface dataset:
Question: On a certain farm the ratio of horses to cows is 4:1. If the farm were to sell 15 horses and buy 15 cows, the ratio of horses to cows would then be 13:7. After the transaction, how many more horses than cows would the farm own?
Options:
A)30
B)60
C)75
D)90
E)105
Rationale: Originally, there were 4k horses and k cows.
7(4k-15) = 13(k+15)
28k-13k = 195+105
15k = 300
k = 20
The difference between horses and cows is (4k-15)-(k+15) = 3k-30 = 30
The answer is A.
Answer: A
Question: Length and Breadth of a rectangle is 7 m and 3.5 m respectively. Find the area of circle of maximum radius
Options:
A)9.625
B)9.74
C)9.8
D)9.725
E)9.547
Rationale: Explanation:
area of circle = πb2/4
= 22/7 × 3.52/4
= 9.625sq.m
Answer: Option A
Answer: A
Question: How many integers between 1 and 10^17 are such that the sum of their digits is 2?
Options:
A)133
B)143
C)153
D)163
E)173
Rationale: The integers with a sum of 2 are:
2, 20, 200,...,2*10^16 and there are 17 integers in this list.
Also, these integers have a sum of 2:
11
101, 110
1001, 1010, 1100
etc...
The number of integers in this list is 1 + 2 + ... + 16
Thus, the total number of integers is 1 + 2 + ... + 16 + 17 = 17*18/2 = 153
The answer is C.
Answer: C
Question: If the productivity of a brigade grows by 30% when the number of the workers in the brigade is increased by one, then which of the following is closest to the ratio of the productivity of a 12-person brigade to that of a 10-person brigade?
Options:
A)0.21
B)0.82
C)1.2
D)1.21
E)1.41
Rationale: B = 10-men brigade
p = increase in the productivity = 30%
Solution: B x p = B x 1.3 = 1.3B -------> the productivity of 11 men brigade
1.13B x p = 1.13B x 1.1 = 1.41B -----> the productivity of 12 men brigade
The ratio of the productivity of a 12-men brigade to that of a 10-men brigade = 1.41B/B = 1.41
E
Answer: E
Question: There are 25 doors marked with numbers 1 to 25. And there are 25 individuals marked 1 to 25.
An operation on a door is defined as changing the status of the door from open to closed or vice versa. All doors are closed to start with.
Now one at a time one randomly picked individual goes and operates the doors. The individual however operates only those doors which are a multiple of the number he/she is carrying. For e.g. individual marked with number 5 operates the doors marked with the following numbers: 5, 10, 15,20 and 25.
If every individual in the group get one turn then how many doors are open at the end?
Options:
A)0
B)1
C)2
D)4
E)5
Rationale: Let us start with 1.
When 1 goes, all the doors are open since every number is a multiple of 1.
Also 1 will remain opened since 1 is not a multiple of any number.
Prime numbers can only be operated by people with prime numbers.
So 2,3,5,7,11,13,17,19,23 will be closed when people with respective numbers perform operations on them.
Our numbers left are 4,6,8,9,10,12,14,15,16,18,20,21,22,24,25
From these numbers, only those numbers will remain opened on which even number of operations are performed including the operation performed by number 1.
This is possible only for perfect squares which are 4,9,16 and 25.
So our numbers are 1,4,9,16 and 25.
Answer:- E
Answer: E
Question: On a two-dimensional coordinate plane, the line d = x^2 - x^3 touches the x-axis in how many places?
Options:
A) 0
B) 1
C) 2
D) 3
E) 4
Rationale: Apparently it's d = x^2 - x^3 instead of d = x^2 - d^3.
In this case: the x-intercept is the value(s) of x for d = 0.
0 = x^2 - x^3;
0 = x^2(1 - x);
x = 0 or x = 1.
Answer: C.
Answer: C
Question: Taylor can read m pages in 7 minutes. At this rate, how long will it take him to read n pages?
Options:
A)(8/m)*n
B)(9/m)*n
C)(10/m)*n
D)(11/m)*n
E)(7/m)*n
Rationale: m page in 7 mins
i.e. 1 page in 7/m mins
i.e. n pages in (7/m)*n
Answer: option E
Answer: E
Question: A candidate scoring 25% in an examination fails by 30 marks , while another candidate scores 50 % mark, gets 20 marks more than the minimum pass marks . Find the minimum pass marks. Find the minimum pass percentage.
Options:
A)26
B)40
C)88
D)27
E)26
Rationale: Let x be the maximum marks,
Then (25% of x)+30 = (50% of x)-20
\inline \Rightarrow \inline \frac{x}{4}+30 = \frac{x}{2}-20
\inline \Rightarrow 2x-x=120+80 \Rightarrow x=200
Hence maximum marks = 200
Minimum pass marks = \inline \frac{200}{4}+30=80
Hence, minimum pass marks = \inline \frac{80}{200}\times 100=40%
Answer: B
Answer: B
Question: A tap can fill a tank in 12 hours. After half the tank is filled, two more similar taps are opened. What is the total time taken to fill the tank completely?
Options:
A)1 hr 20 min
B)4 hr
C)6 hr
D)8 hr 00 min
E)2 hr 50 min
Rationale: Explanation:
1 tap can fill the tank in 12 hours.
Therefore
1 tap can fill half tank in 6 hours.
3 taps can fill the tank in 12/3 hour = 4 hours.
Therefore
3 taps can fill half tank in 4/2 hour = 2 hours.
Total time taken=8 hour 00 minutes
Answer: Option D
Answer: D
Question: Jill is dividing her ten-person class into two teams of equal size for a basketball game. If no one will sit out, how many different match-ups between the two teams are possible?
Options:
A)10
B)25
C)126
D)252
E)630
Rationale: With 10 players, the process of figuring out how many groups of 5 can be formed is pretty straight-forward....
10C5 = 10!/(5!5!) = 256 possible groups of 5
Once forming that first group of 5, the remaining 5 players would all be placed on the second team by default.
The 'twist' is that the two teams of 5 can "show up" in either order:
For example, if we call the two teams of 5 players: A,B,C,D,E and F,G,H,I,J
ABCDE vs. FGHIJ
is the SAME match-up as....
FGHIJ vs. ABCDE
So we are NOT allowed to count that matchup twice. This means we have to divide the 256 by 2.
Final Answer:C
Answer: C
Question: There are three vessels of equal capacity .Vessel A contains Milk and water in the ratio 4:3 ;Vessel B contains Milk and water in the ratio 2:1 and Vessel C contains Milk and water in the ratio 3:2 .If the mixture in all the three vessels is mixed up.What will be the ratio of water to milk ?
Options:
A)9:6
B)3:2
C)118:126
D)122:193
E)201:132
Rationale: 4:3=>4x+3x=7x
2:1=>2y+1y=3y
3:2=>3z+2z=5z
7x=3y=5z
Take LCM of 7,3,5=105
Or simply;
x=3*5=15
y=7*5=35
z=3*7=21
So,
Ratio of Water:Milk= (3x+y+2z)/(4x+2y+3z)=122/193
Ans:D
Answer: D
Question: Two numbers when divided by a divisor leave remainders of 238 and 362 respectively. The remainder obtained when the sum of the numbers is divided by the same divisor is 68. Find the divisor.
Options:
A)276
B)552
C)414
D)1104
E)2202
Rationale: Let x be the divisor.
N1 = xa + 238
N2 = xb + 362
N1 + N2 = x(a+b) + 600 = xc + 68
x(c-a-b) = 532 but we know that x>362, thus (c-a-b) must equal 1.
The answer is B.
Answer: B
Question: The manager of a theater noted that for every 10 admissions tickets sold, the theater sells 3 bags of popcorn at 2.5 $ each, 4 sodas at 1.50 $ each and 2 candy bars at 1.00$ each. To the nearest cent, what is the average (arithmetic mean) amount of these snacks sales per ticket sold?
Options:
A)1.48$
B)1.55$
C)1.60$
D)1.64$
E)1.70$
Rationale: For every 10 tickets amount of snacks sold is 3*2.5+4*1.5+2*1=$15.5, hence amount of the snacks sales per ticket is $15.5/10=~$1.55.
Answer: B.
Answer: B
Question: A batsman in his 17th innings makes a score of 85 and their by increasing his average by 3. What is his average after the 17th innings ?
Options:
A)25
B)32
C)37
D)42
E)50
Rationale: 16x + 85 = 17(x + 3)
x = 34 + 3 = 37
Answer C
Answer: C
Question: A man can row upstream at 25 kmph and downstream at 35 kmph, and then find the speed of the man in still water?
Options:
A)33
B)88
C)30
D)99
E)71
Rationale: US = 25
DS = 35
M = (35 + 25)/2 = 30
Answer: C
Answer: C
Question: Two numbers are in respectively 10% and 40% more than a third number. The ratio of the two numbers is?
Options:
A)11:14
B)7:9
C)17:25
D)15:26
E)2:3
Rationale: Let the 3rd number be x
Then, first number = 110% of x = 110x/100 = 11x/10
second number = 140% of x = 140x/100 = 7x/5
Ratio of first two numbers = 11x/10 : 7x/5 = 11:14
Answer is A
Answer: A
Question: A box contains 2 black, 3 orange and 4 pink ribbons. If two ribbons are drawn at random. What is the probability that both are orange?
Options:
A)5/12
B)1/13
C)1/14
D)1/12
E)1/24
Rationale: Total number of ribbons = 2 + 3 + 4 = 9
Let S be the sample space.
n(S) = Total number of ways of drawing 2 ribbons out of 9 = 9C2
Let E = Event of drawing 2 orange ribbons.
n(E) = Number of ways of drawing 2 orange ribbons= 3C2
P(E)=n(E)/n(S)=3C2/9C2 =(3*2/2) / (9*8/2) =3/36 =1/12
ANSWER:D
Answer: D
Question: Integers 3n+2 and 8n+9 are divisible by an integer p. If p is not equal to 1, then p equals to?
Options:
A)2
B)3
C)5
D)7
E)11
Rationale: If p divides 3n+2, then p divides 24n+16.
If p divides 8n+9, then p divides 24n+27.
Then p must equal 11.
The answer is E.
Answer: E
Question: 617 + 6.017 + 0.617 + 6.0017 = ?
Options:
A)629.3657
B)629.7563
C)629.6357
D)629.5637
E)629.6753
Rationale: 617.00
6.017
0.617
+ 6.0017
--------
629.6357
---------
Answer is C.
Answer: C
Question: Five years ago, the average age of A, B, C and D was 45 years. With E Joining them now, the average of all the five is 52 years. The age of E is?
Options:
A)45
B)60
C)48
D)49
E)46
Rationale: Solution
5 years ago average age of A,B,C,D = 45 years
=> 5 years ago total age of A, B, C, D = 45 x 4 = 180 years
=> Total present age of A, B, C, D = 180 + 5x4 = 200 years
If E's present age is x years = 200+x/5= 52
x=60 years. Answer B
Answer: B
Question: In a game of billiards, A can give B 20 points in 60 and he can give C 30 points in 60. How many points can B give C in a game of 120?
Options:
A)15
B)77
C)45
D)18
E)12
Rationale: A scores 60 while B score 40 and C scores 30.
The number of points that C scores when B scores 100 = (100 * 30)/40 = 25 * 3 = 75.
In a game of 100 points, B gives (120 - 75) = 45 points to C.
Answer:C
Answer: C
Question: A WORKS TWICE AS FAST AS B. IF B CAN COMPLETE A WORK IN 4 DAYS INDEPENDENTLY, THE NUMBER OF DAYS IN WHICH A AND B CAN TOGETHER FINISH THE WORK IS:
Options:
A)1/2 DAYS
B)3/4 DAYS
C)1/4 DAYS
D)4/3 DAYS
E)NONE OF THESE
Rationale: RATIO OF RATES OF WORKING OF A AND B = 2:1. SO, RATIO OF TIME TAKEN = 1:2
A'S 1 DAY'S WORK = 1/2, B'S 1 DAY'S WORK = 1/4
(A+B)'S 1 DAY'S WORK = (1/2+1/4)=3/4=4/3
SO, A AND B TOGETHER CAN FINISH THE WORK IN 4/3 DAYS.
CORRECT OPTION: D
Answer: D
Question: You hold some gold in a vault as an investment. Over the past year the price of gold increases by 50%. In order to keep your gold in the vault, you must pay 8% of the total value of the gold per year. What percentage has the value of your holdings changed by over the past year.
Options:
A)35%
B)36%
C)37%
D)38%
E)40%
Rationale: (100%+50%)*(100%-8%) = 150*0.92 = 138% an increase of 38%
Your gold holdings have increased in value by 38%.
The Answer is D
Answer: D
Question: A and B entered into a partnership investing Rs.25000 and Rs.30000 respectively. After 4 months C also joined the business with an investment of Rs.35000. What is the share of C in an annual profit of Rs.47000?
Options:
A)Rs.18000
B)Rs.15000
C)Rs.17000
D)Rs.14000
E)Rs.16000
Rationale: Explanation:
25*12: 30*12: 35*8
15:18:14
14/47 * 47000 = 14000
ANSWER IS D
Answer: D
Question: If a choir consists of 2 boys and 7 girls, in how many ways can the singers be arranged in a row, so that all the boys are together? Do not differentiate between arrangements that are obtained by swapping two boys or two girls.
Options:
A)120
B)30
C)24
D)8
E)17
Rationale: There are 8 possibilities:
bbggggggg
gbbgggggg
ggbbggggg
gggbbgggg
ggggbbggg
gggggbbgg
ggggggbbg
gggggggbb
Think of all 2 boys as a single unit. Together with 7 girls it makes a total of 8 units. The difference between the arrangements is the position of the boys (as a single unit). So the problem reduces to finding the number of unique patterns generated by changing the position of the boys who can occupy 1 of 8 available positions. If the number of available unique positions is 8, then the number of unique patterns equals 8 as well.
Answer: D.
Answer: D
Question: What is the cost of leveling the field in the form of parallelogram at the rate of Rs.60/10 sq.metre, whose base & perpendicular distance from the other side being 34m & 34m respectively?
Options:
A)s.1156
B)s. 1300
C)s. 1400
D)s. 2480
E)s. 3600
Rationale: Area of the parallelogram = Length of the base * Perpendicular height
= 34 * 34 = 1156
Total cost of levelling = Rs. 1156
A
Answer: A
Question: The product of all the prime number less than or equal to 11 is
Options:
A)10^1
B)10^2
C)10^3
D)10^4
E)10^5
Rationale: D)
Answer: D
Question: In store A there are 10 pairs of pants for every 100 store B has. The price ratio between the pants in store B and the pants in store A is 3:4. If all the pants were sold in both places until the stock ran out, what is the ratio between the total amount stores A earned to the total amount store B earned?
Options:
A)3:16.
B)2:3.
C)1:3.
D)3:4.
E)2:15.
Rationale: 1st statement : ratio of pants
Store A : Store B
10x : 100x
X:10X
Price :
4y:3y
Total revenue
4xy : 30xy
2:15
Answer is E
Answer: E
Question: In how many ways can 10 Frenchmen, 10 Spanish be seated along a circle so that they are alternate?
Options:
A)8!*7!
B)10!*9!
C)5!*9!
D)10!*5!
E)11!9!
Rationale: Required number is = 10!*9!
Answer is B
Answer: B
Question: Find the H.C.F. of 2^3 X 3^2 X 5 X 7^4, 2^2 X 3^5 X 5^2 X 7^3,2^3 X 5^3 X 7^2
Options:
A)980
B)990
C)970
D)950
E)960
Rationale: The prime numbers common to given numbers are 2,5 and 7.
H.C.F. = 2^2 x 5 x7^2 = 980.
Answer is A.
Answer: A
Question: 0.003 x 0.2 = ?
Options:
A)0.0006
B)0.006
C)0.06
D)0.6
E)6.0
Rationale: 3 x 2 = 6.
Sum of decimal places = 4
0.003 x 0.2 = 0.0006
Answer: Option A
Answer: A
Question: If a, b, and c are consecutive odd positive integers and a < b < c, which of the following could be equal to c - b - a+1 ?
Options:
A)-2
B)2
C)-5
D)-3
E)-4
Rationale: let we put values. a=1, b=3, c=5
5-3-1=1
1+1 =2
Answer :B
Answer: B
Question: How many integers are between 8 and 122/7, inclusive?
Options:
A)8
B)10
C)12
D)15
E)16
Rationale: 122/7 = 17.xx
We are not concerned about the exact value of 122/7 as we just need the integers.
The different integers between 8 and 122/7 would be 8, 9, 10, 11, 12,13,14,15,16,17
Total number of integers = 10
Option B
Answer: B
Question: A bus takes 6 hours to cover a distance of 540 Km. how much should the speed in Kmph be maintained to cover the same direction in 3/2th of the previous time?
Options:
A)50 Kmph
B)60 Kmph
C)63 Kmph
D)65 Kmph
E)70 Kmph
Rationale: Time = 6
Distance = 540
3/2 of 6 hours = 6 * 3/2 = 9 Hours
Required speed = 540/9 = 60 Kmph
B
Answer: B
Question: The cost of 14 packets of sugar, each weighing 900 grams is Rs. 28. What will be the cost of 27 packets, if each packet weighs 1 kg?
Options:
A)Rs 52.50
B)Rs 56
C)Rs 58.50
D)Rs 60
E)None of these
Rationale: Explanation :
Let the required cost be Rs. x. Then,
More packets, More cost (Direct Proportion)
More weight, More cost (Direct Proportion)
Packets 14 : 27
Weight 900 : 1000 :: 28 : x
(14 x 900 x x) = (27 x 1000 x 28)
x = (27 x 1000 x 28) /14 x 900
=60
Answer D
Answer: D
Question: Let C be defined as the sum of all prime numbers between 0 and 32. What is C/3
Options:
A)155
B)129
C)61
D)47
E)53.3
Rationale: Prime numbers between 0 and 30 - 2 , 3 , 5 , 7, 11 , 13 , 17 , 19 , 23 , 29, 31
Sum,C = 160
C/3 = 53,3
Answer E
Answer: E
Question: Twelve contestants at the county fair have entered their cakes to be judged in the cake decorating competition. A purple ribbon, blue ribbon, red ribbon, and white ribbon will be given to the first, second, third, and fourth place competitors, respectively. How many different ways are there to award the four ribbons to the contestants?
Options:
A)8!(4!*4!)
B)12!(8!*4!)
C)8!/4!
D)12!/8!
E)12!/4!
Rationale: The mistake you are doing is that you are neglecting the 4! ways in you can arrange 4 contestants for the 4 prizes.
Number of ways you can select 4 people out of 12 = 12C4
Once you select the 4 people, you have the following arrangement, PBRW (PBRW being the 4 prizes) but the same group of people can also be chosen against BRWP etc. Thus you get 4! ways of arranging 4 prizes.
Thus total possible ways = 12C4*4! = 12!/8!. D is the correct answer.
Answer: D
Question: A man can hit the target once in four shots. If he fires three shots in succession, what is the probability that he will hit the target?
Options:
A)1
B)1/64
C)81/64
D)37/64
E)185/256
Rationale: In three shots he can hit once,twice,thrice,all hit
the probability of hitting the target is p(1hit out of 4)+P(2hit out of 4)++p(All hit)
it is total probability-probability of not hitting the target
=>1-(3/4*3/4*3/4)
=>37/64
ANSWER:D
Answer: D
Question: A rectangular lawn of dimensions 80 m * 40 m has two roads each 10 m wide running in the middle of the lawn, one parallel to the length and the other parallel to the breadth. What is the cost of traveling the two roads at Rs.3 per sq m?
Options:
A)2288
B)2779
C)3300
D)3900
E)2781
Rationale: Area = (l + b â€“ d) d
(80 + 40 â€“ 10)10 => 1100 m2
1100 * 3 = Rs.3300
Answer:C
Answer: C
Question: The radius of the two circular fields is in the ratio 3: 5 the area of the first field is what percent less than the area of the second?
Options:
A)54%
B)74%
C)53%
D)64%
E)24%
Rationale: r = 3 πr2 = 9
r = 5 πr2 = 25
25 π – 16 π
100 ---- ? => 64%
Answer:D
Answer: D
Question: A survey of a village showed that 1 / 10 of the total population speak neither Hindi nor English. 1 / 5 of them cannot speak English and 3 / 7 of them cannot speak Hindi. What percentages of people know only one language?
Options:
A)100/7
B)200/7
C)300/7
D)400/7
E)500/7
Rationale: persons who can speak English = 1 - (1/5) = 4/5
persons who can speak Hindi = 1 - (3/7) = 4/7
persons who can speak any or both = 1 - 1/10 = 9/10
so total persons speak both = 4/5 + 4/7 - 9/10 = 33/70
persons speak any = 1 - 33/70 - 1/10 = 3/7
% = 300/7
ANSWER:B
Answer: B
Question: An engineer designed a ball so that when it was dropped, it rose with each bounce exactly one-half as high as it had fallen. The engineer dropped the ball from a 32-meter platform and caught it after it had traveled 46.5 meters. How many times did the ball bounce?
Options:
A)4
B)6
C)7
D)8
E)9
Rationale: Going down = 32 m
Going Up = 16 --> Total = 48
Going down = 16 --> Total = 64
Going Up = 8 --> Total = 72
Going down = 8 --> Total = 80
Going up = 4 --> Total = 84
Going down = 4 --> Total = 86
Going up = 2 --> Total = 88 (Caught)
No of bounces = 4
Answer : A
Answer: A
Question: Tom opened a shop investing Rs.30000. Jose joined him 2 months later, investing Rs.45000. They earned a profit of Rs.63000 after completion of one year. What will be Jose's share of profit?
Options:
A)20000
B)10000
C)25000
D)35000
E)30000
Rationale: SoL = ~s- So Anju’s share = [5/9] x 63000 = 35000
D
Answer: D
Question: If py + z = p(y + z), which of the following must be true?
Options:
A) x = 0 and z = 0
B) p = 1 and y = 1
C) p = 1 and z = 0
D) p = 1 or y = 0
E) p = 1 or z = 0
Rationale: py + z = py + pz
z = pz
case 1: z not= 0, p = z/z = 1
case 2: z = 0, 0 = p0 = 0
Combining 2 cases: p = 1 or z =0
E. is the answer.
Answer: E
Question: In a regular week, there are 5 working days and for each day, the working hours are 8. A man gets Rs. 2.40 per hour for regular work and Rs. 3.20 per hours for overtime. If he earns Rs. 432 in 4 weeks, then how many hours does he work for ?
Options:
A)160
B)170
C)175
D)195
E)180
Rationale: Suppose the man works overtime for x hours.
Now, working hours in 4 weeks = (5 x 8 x 4) = 160.
160 x 2.40 + x x 3.20 = 432
3.20x = 432 - 384 = 48
x = 15.
Hence, total hours of work = (160 + 15) = 175.
ANSWER :C
Answer: C
Question: During school lunch, 60% of the children packed fruit in their lunches. Of those children, 25% have an apple. The remaining children eat from the cafeteria where they are given an apple. What percentage of children have an apple with their lunch?
Options:
A)15% of the children have an apple.
B)45% of the children have an apple.
C)55% of the children have an apple.
D)85% of the children have an apple.
E)None of these.
Rationale: Explanation:Let total number of children be 100,Then, number of children who packed fruit = 60.Number of those children with apples = 25% of 60 = 15.Number of children eating at the cafeteria = 40.Total number with an apple = 40 + 15 = 55.Thus, 55% of the children have an apple.Answer: Option C
Answer: C
Question: A merchant sells an item at a 20% discount, but still makes a gross profit of 20 percent of the cost. What percent E of the cost would the gross profit on the item have been if it had been sold without the discount?
Options:
A)20%
B)40%
C)50%
D)60%
E)75%
Rationale: Let the Market Price of the product is MP.
Let the Original Cost Price of the product is CP.
Selling Price (Discounted Price) = 100%of MP - 20%MP
= 80% of MP. ---------------- (1)
Profit made by selling at discounted price = 20% of CP -------------- (2)
Apply the formula:
Profit E= Selling Price - Original Cost Price
=> 20% of CP = 80% of MP - 100% CP
=> MP = 120CP/80 = 3/2 (CP)
Now if Product is sold without any discount, then,
Profit = Selling Price (without discount) - Original Cost Price
= Market Price - Original Cost Price
= MP - CP
= 3/2 CP - CP
= 1/2 CP
=50%of CP
Thus, Answer should beC.
Answer: C
Question: How many 4-letter word with or without meaning can be formed out of the letters of the word 'LOGARITHMS' if repetition of letters is not allowed.
Options:
A)2450
B)1230
C)5040
D)1042
E)2116
Rationale: 'LOGARITHMS' contains 10 different letters
Required number of words
= Number of arrangements of 100 letters taking
4 at a time
= 10P4
= 10 * 9 * 8 * 7
= 5040
Ans: C
Answer: C
Question: What is the 16th digit to the right of the decimal point in the decimal expansion of 1/37?
Options:
A) 0
B) 2
C) 4
D) 7
E) 9
Rationale: 1/37=0.027027... So, we have a repeating cycle of 027. Every third digit (2nd, 4th, 6th, ...) to the right of the decimal point is alternating by 2, 0, 7 thus 16th digit is 0.
Answer: A.
Answer: A
Question: If a clock takes seven seconds to strike seven, how long will it take to strike ten ?
Options:
A)7 seconds
B)9 seconds
C)10 seconds
D)15 seconds
E)None of these
Rationale: Explanation:
Clearly, seven strikes of a clock have 6 intervals while 10 strikes have 9 intervals.
Therefore, Required time=[7/6*9]seconds = 10 1/2 seconds.
Answer: E
Answer: E
Question: A restaurant meal cost $34.50 and there was no tax. If the tip was more than 10 percent but less than 15 percent of the cost of the meal, then the total amount paid must have been between
Options:
A) $40 and $42
B) $39 and $41
C) $38 and $40
D) $37 and $39
E) $36 and $37
Rationale: The total amount for the meal was between 34.5*1.1=37.95 and 34.5*1.15=39.675. Only option which covers all possible values of the meal is C.
Answer: C.
Answer: C
Question: If {y} denote the remainder when 3y is divided by 2 then which of the following is equal to 1 for all positive integers y?
I. {2y+1}
II. {2y}+1
III. 2{y+1}
Options:
A)I only
B)II only
C)I and II
D)III only
E)II and III
Rationale: C - I and II
3y/2 = 0 or 1
I just substituted 1 in the equations and solved.
Answer: C
Question: 30 men can do a work in 40 days. When should 10 men leave the work so that the entire work is completed in 40 days after they leave the work?
Options:
A)87 days
B)10 days
C)55 days
D)44 days
E)20 days
Rationale: Total work to be done = 30 * 40 = 1200
Let 10 men leave the work after 'P' days, so that the remaining work is completed in 40 days after they leave the work.
40P + (10 * 40) = 1200
40P = 800 => P = 20 days
Answer:E
Answer: E
Question: Joshua and Jose work at an auto repair center with 1 other workers. For a survey on health care insurance, 2 of the 6 workers will be randomly chosen to be interviewed. What is the probability that Joshua and Jose will both be chosen?
Options:
A)1/15
B)1/12
C)1/9
D)1/6
E)1/3
Rationale: Two Methods
1) Probability of chosing Josh first = 1/3
Probability of chosing Jose second = 1/2
total = 1/6
Probability of chosing Jose first = 1/3
Probability of chosing Josh second = 1/2
Total = 1/6
Final = 1/6 + 1/6 = 1/3
E
Answer: E