divelab/Sys2Bench huggingface dataset:
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 Rs. 9000 ?
Options:
A)11
B)13
C)15
D)18
E)10
Rationale: Required difference = [3 ½ % of Rs.9000] – [3 1/3 % of Rs.9000]
= [(7/20-(10/3)]% of Rs.9000 =1/6 % of Rs.9000
= Rs. [(1/6)8(1/100)*9000] = Rs. 15.
Answer is C.
Answer: C
Question: Solve this logic number sequence puzzle by the correct digit
8080 = 6
1357 = 0
2022 = 1
1999 = 3
6666 = ?
Options:
A)four (4)
B)2
C)5
D)7
E)8
Rationale: A
4
No Of circles in the number.
Answer: A
Question: A fish can go upstream at 35 kmph and downstream at 55 kmph, and then find the speed of the fish in still water?
Options:
A)45
B)55
C)35
D)65
E)70
Rationale: US = 35
DS = 55
M = (35 + 55)/2
= 45
Answer:A
Answer: A
Question: The average age of a committee of 10 members is 30 years. A member aged 60 years retired and his place was taken by another member aged 40 years . The average age of
present committee is;
Options:
A)39 years
B)28 years
C)36 years
D)35 years
E)37 years
Rationale: Total age of the committee = 30*10 = 300,
Total age when a member is retired
and a new one was joined = 300-60 +40, =280
Average age of present committee = 280/10 = 28.
ANSWER:B
Answer: B
Question: The function f is defined for all the positive integers s by the following rule: f(s) is the number of positive integers each of which is less than s and has no positive factor in common with s other than 1 . if p is a prime number then f(p)?
Options:
A)p-1
B)p-2
C)(p+1)/2
D)(p-1)/2
E)2
Rationale: The moment you put a prime number in the function f(s), notice that all the numbers lesser than s have no divisor clashing with divisor of s since s is prime!!.
For instance f(7)= {6, 5, 4, 3, 2, 1}
Thus for f(p) number of integers falling under this set will be p-1
Answer :- A
Answer: A
Question: The average salary of all the workers in a workshop is Rs. 8000. The average salary of 7 technicians is Rs. 14000 and the average salary of the rest is Rs. 6000. The total number of workers in the workshop is:
Options:
A)28
B)19
C)22
D)20
E)21
Rationale: Let the total number of workers be x. Then,
8000x = (14000 * 7) + 6000(x - 7)
= 2000x = 56000
= x = 28.
ANSWER:A
Answer: A
Question: Two teams Arrogant and Overconfident are participating in a cricket tournament. The odds that team Arrogant will be champion is 5 to 3, and the odds that team Overconfident will be the champion is 1 to 4. What are the odds that either Arrogant or team Overconfident will become the champion?
Options:
A)3 to 2
B)5 to 2
C)6 to 1
D)33 to 7
E)3 to 8
Rationale: Explanation :
Odds of winning Arrogant is 5/3, then their probability of winning is 5/ (5+3) i.e 5/8.
Similarly,
Odds of winning Overconfident is 1/4, then their probability of winning is 1/ (1+4) i.e 1/5.
Therefore, the probability of winning of Arrogant or Overconfident is :-
=>(5/8) + (1/5).
=>33/40.
Thus, the required odds will be 33/(40-33) i.e 33/7.
Answer : D
Answer: D
Question: The smallest number which when diminished by 3, is divisible by 12, 16, 18, 21 and 28 is
Options:
A)1008
B)1011
C)1022
D)1032
E)1043
Rationale: Required Number = (L.C.M of 12, 16, 18,21,28)+3
= 1008 + 3
= 1011
Answer: B
Answer: B
Question: Of the 150 people at a party, 70 were women, and 40 women tried the appetizer. If 50 people did not try the appetizer, what is the total number of men who tried the appetizer?
Options:
A)40
B)50
C)60
D)70
E)80
Rationale: Total people at party=150
Women=70
so Men 150-70=80
No. of pple who tried appetizer=150-50 (given info)=100
No of women who tried appetizer=40
So Remaining ppl(men) who tried the appetizer =100-40=60
Correct Option C
Answer: C
Question: A and B together have Sterling 1230. If 4/15 of A's amount is equal to 2/5 of B's amount, how much amount does B have?
Options:
A)Sterling 460
B)Sterling 484
C)Sterling 550
D)Sterling 492
E)None
Rationale: Explanation: 4/15A = 2/5B
A = (2/5 x 15/4)B
A = 3/2 B
A/B = 3/2
A : B = 3 : 2.
B's share = Sterling (1230 x 2/5) = Sterling 492.
Answer: Option D
Answer: D
Question: Tom opened a shop investing Rs.20000. Jose joined him 8 months later, investing Rs.35000.What will be Tom's and Jose's share of profit ratio after two years?
Options:
A)4:9
B)6:7
C)7:6
D)5:8
E)8:5
Rationale: SoL = ~s- So Tom's and Jose's share of profit ratio= 20*24:35*16 = 6:7
Answer: B
Answer: B
Question: In how many ways, a committee of 7 members can be selected from 6 men and 5 ladies, consisting of 4 men and 3 ladies?
Options:
A)180
B)150
C)200
D)310
E)250
Rationale: (4 men out 6) and (3 ladies out of 5) are to be chosen
Required number of ways = 6C4*5C3 = 150
Answer is B
Answer: B
Question: If each of 3 digit code is formed of integers from 1 to 20, inclusively, and each of the digits are different, how many possible codes are there?
Options:
A)6,040
B)6,840
C)6,240
D)6,340
E)8,440
Rationale: Code consists of 3 digits and no digit is repeated.
First digit of the code can have 20 possibilities
Second digit can have 19 possibilities
Third digit can have 18 possibilities
Total number of possible codes = 20*19*18 = 6840
Answer: B
Answer: B
Question: The sum of the first 60 positive even integers is 3,660. What is the sum of the first 60 odd integers?
Options:
A)3600
B)3400
C)3300
D)3200
E)3100
Rationale: Sum of first n even numbers = n(n+1) =3660
Sum of first n odd numbers = n^2 = 60*60 = 3600 (here n=60)
Answer : A
Answer: A
Question: A trolley which travels at a constant speed and can cover the platform of length 300m in two minute. How long it will take a train of length 200m and having a speed 60kph to pass the trolley?
Options:
A)11.21
B)14.11
C)16.32
D)18.35
E)20.45
Rationale: Speed of the trolley= 300/120= 2.5m/s
Speed of the train = 60kph = 16.67m/s
Relative speed of train with respect to trolley=16.67-2.5 = 14.17m/s
Time taken by the train to pass the trolley= 200/14.17=14.11s
Answer: B
Answer: B
Question: The sector of a circle has radius of 21 cm and central angle 270o. Find its perimeter?
Options:
A)91.5
B)92
C)93
D)141
E)95
Rationale: Perimeter of the sector = length of the arc + 2(radius)
= (270/360 * 2 * 22/7 * 21) + 2(21)
= 141 cm
Answer: Option D
Answer: D
Question: A sum of Rs.100 is lent at simple interest of 3% p.a. for the first month, 9% p.a. for the second month, 27% p.a. for the third month and so on. What is the total amount of interest earned at the end of the year approximately
Options:
A)Rs.797160
B)Rs.791160
C)Rs.65930
D)Rs.66430
E)Rs.67430
Rationale: Total amount of Interest is
I = P/100 * 1[3/12 + 9/12 +27/12…. 312/12
Where P = 100; I = 1/12 (3+9+…..312)
I = 1/12(3(312-1))/3-1
= 531440* 3/12*2 =Rs.66430
ANSWER:D
Answer: D
Question: A bill is discounted at 10% per annum. If banker's discount is allowed, at what rate percent should the proceeds be invested so that nothing will be lost?
Options:
A)91/9%
B)100/9%
C)11
D)92/9%
E)None of these
Rationale: Explanation :
Let the amount = Rs.100
Then BD = Rs.10 (∵ banker's discount, BD is the simple Interest on the face value of the bill for unexpired time and bill is discounted at 10% per annum)
Proceeds = Rs.100 – Rs.10 = Rs.90
Hence we should get Rs.10 as the interest of Rs.90 for 1 year so that nothing will be lost
⇒ 10 = (90 × 1 × R)/100
⇒ R = (10 × 100)/90 = 100/9 Answer : Option B
Answer: B
Question: If 1/a^2 + a^2 represents the diameter of circle O and 1/a + 4a = 3, which of the following best approximates the circumference of circle O?
Options:
A)28
B)22
C)20
D)16
E)12
Rationale: Given that (1/a)+a =3
Square both sides of the equation:
We get,
[(1/a)^2 + a^2 + 2*(1/a)*a] = 9
=> (1/a)^2 + a^2 + 2 = 9
=> (1/a)^2 + a^2 = 7 ----------------- (1)
Diameter D = (1/a)^2 + a^2
= 7 (From (1))
So Radius = D/2 = 7/2
Circumference = 2*Pi*r
= 2*(22/7)*(7/2)
=12
So the answer should be E.
Answer: E
Question: A man invested Rs. 1552 in a stock at 97 to obtain an income of Rs. 300. The dividend from the stock is :
Options:
A)7.5 %
B)18.75 %
C)9.75 %
D)None of these
E)Cannot be determined
Rationale: Solution
By investing Rs. 1552,income = Rs. 128.
By investing Rs. 97, income = Rs. (300/1552x97)= Rs 18.75
âˆ´ Dividend =1 8.75%.
Answer B
Answer: B
Question: A person travelled from his house to office at 10km/hr and office to house at 90km/hr. Then find the average speed?
Options:
A)15km/hr
B)18km/hr
C)25km/hr
D)28km/hr
E)33km/hr
Rationale: Average speed = (2*10*90)/(10+90)= 18km/hrAnswer is B
Answer: B
Question: Peter can cover a certain distance in 1 hr. 24 min. by covering two-third of the distance at 4 kmph and the
rest at 5 kmph. Find the total distance.
Options:
A)4 km
B)5 km
C)6 km
D)7 km
E)8 km
Rationale: time=distance/speed
let total distance travelled be x in 84/60 hrs
2/3 rd of x travelled in 4 km/hr
1/3 rd of distance travelled in 5 km/hr
2x/(3*4)+x/(3*5)=84/60
x=6 km
ANSWER:C
Answer: C
Question: A goods train runs at the speed of 72 kmph and crosses a 270 m long platform in 26 seconds. What is the length of the goods train?
Options:
A)230 m
B)250m
C)643m
D)832m
E)270m
Rationale: Speed =	(72 x	5/18)m/sec	= 20 m/sec.
Time = 26 sec.
Let the length of the train be x metres.
Then,	x + 270/26	= 20
x + 270 = 520
x = 250.
Answer:B
Answer: B
Question: A straight line in the xy- plane has y-intercept of 10 . On this line the x-coordinate of the point is 100 and y-coordinate is 1000 then what is the slope of the line?
Options:
A)2
B)5.5
C)6.5
D)3.2
E)9.9
Rationale: Eq of line = Y = MX +C
C= 10
X=100
Y=100M + 10,
Substitute Y by 1000 as given in question.
1000=100M+10 , M =9.9.
correct option is E
Answer: E
Question: Two trains start from A & B and travel towards each other at
speed of 50kmph and 60kmph resp. At the time of the meeting the
second train has traveled 120km more than the first.the distance
between them.
Options:
A)1300 km
B)1310 km
C)1320 km
D)1330 km
E)1340 km
Rationale: Let the distance traveled by the first train be x km
then distance covered by the second train is x + 120km
x/50 = x+120 / 60
x= 600
so the distance between A & B is x + x + 120 = 1320 km
Answer is C.
Answer: C
Question: The pilot of a small aircraft with a 40-gallon fuel tank wants to fly to Cleveland, which is 480 miles away. The pilot recognizes that the current engine, which can fly only 8 miles per gallon, will not get him there. By how many miles per gallon must the aircraft’s fuel efficiency be improved to make the flight to Cleveland possible?
Options:
A)2
B)4
C)12
D)40
E)160
Rationale: Actual miles/gallon is = 480/4 = 12 miles/gallon.
Current engine miles/gallon is 8 miles/gallon.
Additional 4 miles/gallon is required to match the actual mileage.
ANSWER:B
Answer: B
Question: A person's present age is two-fifth of the age of his mother. After 8 years, he will be one-half of the age of his mother. How old is the mother at present
Options:
A)33
B)37
C)39
D)40
E)82
Rationale: Explanation:
Let the mother's present age be x years.
Then, the person's present age = years.
2(2x + 40) = 5(x + 8)
x = 40
Answer: D) 40
Answer: D
Question: A number consists of two digits. If the digits interchange places and the new number is added to the original number, then the resulting number will be divisible by:
Options:
A)3
B)5
C)9
D)11
E)13
Rationale: Let the ten's digit be x and unit's digit be y.
Then, number 10x + y.
Number obtained by interchanging the digits = 10y + x.
(10x + y) + (10y + x) = 11(x + y)
which is divisible by 1
ANSWER:D
Answer: D
Question: {150, 260, 250, n}
Which of the following could be the median of the 4 integers listed above?
I. 175
II. 215
III. 235
Options:
A)I only
B)II only
C)I and II only
D)II and III only
E)I, II, and III
Rationale: If 175 is the median, (n+250) / 2 = 175. Then n = 100. But n < 150, so 175 can not be the median.
If 215 is the median, (n+250) / 2 = 215. Then n = 180. Thus 215 can be the median.
If 235 is the median, (n+250) / 2 = 235. Then n = 220. Thus 235 can be the median.
The answer is D.
Answer: D
Question: A boat can move upstream at 15 kmph and downstream at 35 kmph, then the speed of the current is?
Options:
A)5
B)6
C)10
D)8
E)9
Rationale: US = 15
DS = 35
M = (35 - 15)/2 = 10
Answer: C
Answer: C
Question: What number should replace the question mark? 10, 30, 14, 25, 18, 20, ---?
Options:
A)19
B)21
C)25
D)22
E)20
Rationale: Answer: D
10, 30, 14, 25, 18, 20, 22?
There are two alternate sequences: +4 and -5.
Answer: D
Question: 3 men or 6 women can do a piece of work in 20 days. In how many days will 12 men and 8 women do the same work?
Options:
A)12/9 days
B)15/4 days
C)82/8 days
D)22/76 days
E)22/2 days
Rationale: 3M = 6W ---- 20 days
12M + 8W -----?
24W + 8 W = 32W ---?
6W ---- 20 32 -----?
6 * 20 = 32 * x => x = 15/4 days
Answer:B
Answer: B
Question: A man purchases 8 pens for Rs.9 and sells 9 pens for Rs.8, how much profit or loss does he make?
Options:
A)40.98% loss
B)20.98% loss
C)60.98% loss
D)50.98% loss
E)10.98% loss
Rationale: Explanation:
81 ---- 17
100 ----- ? Ã¨ 20.98%loss
Answer:B
Answer: B
Question: Mother,her daughter and her grand child weighs 110 kg. daughter and her daughter(child) weighs 60 kg. child is 1/5th of her grand mother. What is the age of the daughter?
Options:
A)46
B)47
C)48
D)49
E)50
Rationale: mother + daughter + child = 110kg
daughter + child = 60kg
mother = 110 - 60 = 50kg
child = 1/5th of mother = (1/5)*50 = 10kg
So now daughter = 110 -(mother + child) = 110 - (50+10) = 50kg
ANSWER:E
Answer: E
Question: If m is an integer, which of the following must be an even integer?
Options:
A)m^2-m-1
B)m^2-4m+6
C)m^2-5m+5
D)m^2+3m+8
E)m^2+2m+10
Rationale: Check the options by plugging in some values ( Preferably smaller integers like 1 and 2 )
A: m^2-m-1 = -1 { If m = 1 }
B: m^2-4m+6 = 3 { If m = 1 }
C: m^2-5m+5 = 1 { If m = 1 }
D: m^2+3m+8 = 12 { If m = 1 }m^2+3m+8 = 18 { If m = 2 }
E: m^2+2m+10 = 13 { If m = 1 ]
Thus the only possible answer is (D)
Answer: D
Question: The ratio of 2 numbers is 2:8 and their H.C.F. is 40. Their L.C.M. is ?
Options:
A)400
B)120
C)80
D)320
E)40
Rationale: Let the numbers be 2x and 8x
Their H.C.F. = 40
so the numbers are 2*40 , 8*40 = 80, 320
L.C.M. = 320
Answer is D
Answer: D
Question: The diagonals of a rhombus are 10 cm and 15 cm. Find its area?
Options:
A)75
B)129
C)150
D)123
E)117
Rationale: 1/2 * 10 * 15 = 75
Answer:A
Answer: A
Question: A board of length L feet is cut into two pieces such that the length of piece A is 2 feet less than three times the length of piece B. Which of the following is the length, in feet, of piece A?
Options:
A)(L - 2)/4
B)(3L - 2)/4
C)(L + 2)/3
D)(3L + 2)/3
E)(2L - 1)/4
Rationale: A+B = L so we know that B = L - A.
A = 3B-2
A = 3(L-A) - 2
4A = 3L - 2
A = (3L-2) / 4
The answer is B.
Answer: B
Question: When 50% of one number is added to a second number,the second number increases to its four-thirds. What is the ratio between the first number and the second number?
Options:
A)3 : 2
B)3 : 4
C)2 : 3
D)Data inadequate
E)None of these
Rationale: Let the numbers be y and x respectively
x + 50% of y = 4x⁄3 or, y⁄2 = 4x⁄3 - x
or, y⁄2 = x⁄3
or, y⁄x = 2⁄3
Answer C
Answer: C
Question: Equal amount of water were poured into two empty jars of different capacities, which made one jar 1/8 full and other jar 1/6 full. If the water in the jar with lesser capacity is then poured into the jar with greater capacity, what fraction of the larger jar will be filled with water?
Options:
A)1/7
B)2/7
C)1/2
D)7/12
E)1/4
Rationale: Same amount of water made bigger jar 1/8 full, then the same amount of water(stored for a while in smaller jar) were added to bigger jar, so bigger jar is 1/8+1/8=1/4 full.
Answer: E.
Answer: E
Question: If a/x = 2/3 and a/y =1/ 2, then (x + y) =
Options:
A)A)2a
B)B)7a/2
C)C)6a
D)D)7a
E)E)9a
Rationale: Ratio 1:
3a = 2x
Ratio 2:
4a = 2y
x+y = 7a/2
Answer is B
Answer: B
Question: A train running at 1/5 of its own speed reached a place in 20 hours. How much time could be saved if the train would have run at its own speed?
Options:
A)8hrs
B)10hrs
C)12hrs
D)16 hrs
E)6hrs
Rationale: time taken if run its own speed = 1/5*20 = 4 hrs
Time saved = 20 - 4 = 16 hrs
Answer : D
Answer: D
Question: " I am eight times as old as you were when I was as old as you are " , said a man to his son. Find out their present ages if the sum of the their ages is 75 years.
Options:
A)23
B)24
C)25
D)26
E)27
Rationale: present age of boy x and previous age of boy y
so present age of dad : 8y and previous age is x
so the gap between duration must be same
so 8y-x=x-y --> x=9y/2
and x+8y = 75 (given) --> 9y/2 + y=75 so y=6 and and x=27
therefore fathers age is 8y = 8*6 = 48
and child's age = x=27
ANSWER:E
Answer: E
Question: Merry has only pennies, dimes, and nickels in a jar. The jar has at least 1 but no more than 4 pennies. If the jar has at least 1 nickel and 1 dime, which of the following could NOT be the total amount of money in the jar?
Options:
A)55
B)56
C)57
D)58
E)59
Rationale: Let there be a pennies , b nickels and c dimes
so total amount can be 1+5b+10c cents to 4+5b+10c
as you can see the equation of total whenever divided by 5 would leave a remainder from 1 to 4 ( as pennies can only be from 1 to 4 and hence a is limited to values from 1 to 4)
So the total can never be divisible by 5 and hence only 55 that is c is the option which is divisible by 5.
so answer is A
Answer: A
Question: an article with cost price of 320 is sold at 18% profit. what is the selling price?
Options:
A)198
B)200
C)204
D)378
E)347
Rationale: sp=1.18*320=378
ANSWER:D
Answer: D
Question: The area of a rectangular plot is 460460 square metres. If the length is 15%15% more than the breadth, what is the breadth of the plot?
Options:
A)14 metres
B)20 metres
C)18 metres
D)12metres
E)16 metres
Rationale: Explanation:
length 115% of breadth.
length×breadth =460 m2
⇒ 115% of breadth×breadth =460 m2
⇒ 115/100×breadth×breadth =460 m2
⇒ breadth×breadth =400 m2
⇒ breadth =20 m
Answer: Option B
Answer: B
Question: A reading list for a certain course consists of 10 books, of which 7 are poems and the rest are novels. Each student is required to read a selection of 4 books from the list, including at most 2 novels. How many selections of 4 books satisfy the requirements?
Options:
A)90
B)115
C)130
D)144
E)175
Rationale: Ans: B
Solution: Selection requires at most 2 novels, means=
0N4P + 1N3P + 2N2P
7c1*3c3+ 7c2*3c2 + 7c3*3c1
= 7+ 63 + 105
= 175
Ans: E
Answer: E
Question: In a survey conducted to find out the readership of three Newspapers A,B and C, it was found that the number of newspaper A is at least 20 and at most 40. The number of people who read newspaper B is at least 50 and at most 70. The number of people who read newspaper C is at least 70 and at most 83. It was also found that 4 people read all three newspapers. Find the minimum number of people who read both A and B but not C.
Options:
A)A)1
B)B)2
C)C)3
D)D)0
E)E)5
Rationale: I wish I could draw a diagram to show you but by giving you number A and B, it might help a little.
A and B and C is 4 - that means A and B is at least 4. This seems trivial given the value intervals of A and B but definitely helps to think through how to minimize A and B but not C
A and B but not C = |A|-|B| - 4
So i would pick A=20 and B =50 to minimize the value to a 2. (ANS B)
Answer: B
Question: Ramesh can finish a work in 20 days and Sushil in 25 days. They both work together for 5 days and then Sushil goes away. In how many days will Ramesh complete the remaining work?
Options:
A)22 days
B)68 days
C)77 days
D)eleven days
E)88 days
Rationale: (5 + x)/20 + 5 / 25 = 1 => x = 11 days
Answer: D
Answer: D
Question: Analysis of the various vehicle prices in a car dealership shop revealed that :
I) trucks cost 12% less than SUVs
II) Minivans cost 20% less than trucks
III) sedans cost 8% less than minivans
what percent of SUV's cost is a sedan?
Options:
A)88.9%
B)90%
C)66.24%
D)70.3%
E)78.8%
Rationale: Let the cost of suv be $100
I) trucks cost 10% less than SUVs--100-10=90
II) Minivans cost 20% less than trucks--90-18=72
III) sedans cost 8% less than minivans--72-5.76=66.24
what percent of SUV's cost is a sedan=66.24*100/100
Answer is C
Answer: C
Question: The expression mn+m is odd when the m and n are integers. Which of the following expressions must be even?
Options:
A)m
B)n
C)m + n
D)mn - m
E)m + n^2
Rationale: mn+m is odd
m and n are integers
If m were even mn+m would be even despite any value of n.
n can't be odd, so n must be even.
Ans : B
Answer: B
Question: A train passes a man standing on the platform. If the train is 70 meters long and its speed is 72 kmph, how much time it took in doing so?
Options:
A)6 ½ sec
B)4 ½ sec
C)3 ½ sec
D)8 ½ sec
E)2 ½ sec
Rationale: D = 70
S = 72 * 5/18 = 20 mps
T = 70/20 = 3 ½ sec
Answer: C
Answer: C
Question: What is the least number of digits (including repetitions) needed to express 10^500 in decimal notation?
Options:
A)a) 4
B)b) 100
C)c) 101
D)d) 501
E)e) 1001
Rationale: 10^n is a decimal number with a 1 followed by n zeros.
So 10^500 will include 500 0's + 1 digit for 1 = 501
So the answer is D.
Answer: D
Question: A shopkeeper sells two articles at Rs.1000 each, making a profit of 20% on the first article and a loss of 20% on the second article. Find the net profit or loss that he makes?
Options:
A)99%
B)3%
C)2%
D)4%
E)8%
Rationale: SP of first article = 1000
Profit = 20%
CP = (SP)*[100/(100+P)] = 5000/6 = 2500/3
SP of second article = 1000
Loss = 20%
CP = (SP)*[100/(100-L)] = 5000/4 = 1250
Total SP = 2000
Total CP = 2500/3 + 1250 = 6250/3
CP is more than SP, he makes a loss.
Loss = CP-SP = (6250/3)- 2000 = 250/3
Loss Percent = [(250/3)/(6250/3)]*100
=0.04 * 100
= 4%
Answer:D
Answer: D
Question: Set X consists of the integers from 1 to 12, inclusive, while set Y consists of the integers from 0 to 20, inclusive. How many distinct integers do belong to the both sets at the same time?
Options:
A)12
B)15
C)10
D)20
E)8
Rationale: X= {1,2,3,4, 5,6, 7, 8, 9, 10, 11, 12}
Y = {0,1,2,3,4,5,6, 7, 8, 9, 10,11,12,13,14,15,16,17,18,19,20}
Common elements = {1,2,3,4,5,6,7,8,9,10,11,12} = 12 elements
Answer: Option A.
Answer: A
Question: A man can row at 5 kmph in still water. If the velocity of the current is 1 kmph and it takes him 1 hour to row to a place and come back. how far is that place.
Options:
A).4 km
B)1.4 km
C)2.4 km
D)3.4 km
E)None of these
Rationale: Explanation:
Let the distance is x km
Rate downstream = 5 + 1 = 6 kmph
Rate upstream = 5 - 1 = 4 kmph
then
x/6 + x/4 = 1 [because distance/speed = time]
=> 2x + 3x = 12
=> x = 12/5 = 2.4 km
Option C
Answer: C
Question: An article is bought for Rs.600 and sold for Rs.500, find the loss percent?
Options:
A)16 2/7%
B)16 2/2%
C)16 3/3%
D)16 2/3%
E)13 2/3%
Rationale: 600 ---- 100
100 ---- ? =>
16 2/3%
Answer:D
Answer: D
Question: Bruno and Sacha are running in the same direction around a stadium. Sacha runs at a constant speed of 10 meters per second, and Bruno runs at a constant speed of 5 meters per second. At a certain point Sacha overtakes Bruno. If one minute afterward, Sacha stops and waits for Bruno to reach him, then how many seconds does he have to wait?
Options:
A)12
B)24
C)36
D)60
E)72
Rationale: the difference of the speed is 5m per second so in one minute Sacha will be 300 m ahead of Bruno..
Bruno will cover this in 300/5=60 secs..
D
Answer: D
Question: A student worked for 20 days. For each of the amounts shown in the first row of the table, the second row gives the number of days that the student earned that amount. What is the amount of money that the student earned per day for the 20th day?
Amounts earned per day : $96 $84 $80 $70 $48
Number of days : 4 7 4 3 2
Options:
A)(1) $96
B)(2) $84
C)(3) $80
D)(4) $70
E)(5) $48
Rationale: 4+7+4+3+2 = 20
The series is as follows. Arrange the terms in increasing order of amounts earned and cumulatively add up the number of days of each amount.
1st to 2nd term = 48 (2 days)
3rd to 5th term = 70 (3 days)
6th to 9th term = 80 (4 days)
10th to 16th term = 84 (7 days)
17th to 20th term = 96 (4 days)
Pick A
Answer: A
Question: Joan and Karl each bought a stove and the sum of their purchases was $700. If twice of what Joan paid was $80 more than what Karl paid, what did Joan pay for her stove?
Options:
A)$240
B)$260
C)$280
D)$300
E)$320
Rationale: J+K=700 so K=700-J
2J=K+80
2J=(700-J)+80
3J=780
J=260
The answer is B.
Answer: B