divelab/Sys2Bench huggingface dataset:
Question: Ramesh can finish a piece of work in 16 days. Rohan is twice as efficient as Ramesh.If they work together how many days will they need to finish the same amount of work?
Options:
A)8/3 days
B)9/3 days
C)16/3 days
D)11/3 days
E)7/3 days
Rationale: Ramesh can finish a piece of work in 16 days. Rohan is twice as efficient as Ramesh.
So Rohan can finish a piece of work in 8 days.
days needed to finish the same amount of work = 1/(1/8+1/16)=16/3 days
ANSWER:C
Answer: C
Question: A train of length 110 meter is running at a speed of 60 kmph. In what time, it will pass a man who is running at 6 kmph in the direction opposite to that in which the train is going?
Options:
A)10
B)8
C)6
D)4
E)2
Rationale: Explanation:
Distance = 110 m
Relative speed = 60 + 6 = 66 kmph (Since both the train and the man are in moving in opposite direction)
= m/sec = m/sec
Time taken to pass the man = = 6 s
ANSWER IS C
Answer: C
Question: a,b and c are positive integers less than or equal to 9 and multiple of 3. If a,b and c are assembled into the three-digit number abcabc, which of the following must be a factor of abcabc?
Options:
A)6
B)4
C)7
D)5
E)9
Rationale: as a, b and c are multiple of 3, they can be written as a=3l, b=3m and c=3n. the sum of digits of abc is a+b+c = 3(l+m+n+l+m+n)=6(l+m+n).
Thus, 6 is always a factor.
Answer: A
Answer: A
Question: y =x^2 + bx + 128 cuts the x axis at (h, 0) and (k, 0). If h and k are integers, what is the least value of b?
Options:
A)-129
B)-132
C)32
D)64
E)128
Rationale: As the curve cuts the x-axis at (h,0) and (k,0). Therefore h,k are the roots of the quadratic equation.
For the quadratic equation is in the form of ax^2+bx+c=0,
The product of the roots =c/a= 128/1 = 64 and the sum of the roots =-b/a=-b/1
128 can be expressed as product of two numbers in the following ways:
1 * 128
2 * 64
4 * 32
8 * 16
The sum of the roots is maximum when the roots are 1 and 128 and the maximum sum is 1 + 128 = 129.
The least value possible for b is therefore -129.
a
Answer: A
Question: Last year a certain bond yielded 12 percent of its face value in interest. If that interest was approximately 4 percent of the bonds selling price of $7,500, what is the bonds face value?
Options:
A)$6,000
B)$6,750
C)$7,425
D)$2,500
E)$9,375
Rationale: Interest = 0.12*face value = 0.04*7,500 --> face value = 0.04*7,500/0.12 = 2,500.
Answer: D.
Answer: D
Question: A bakery currently has 5 pies and 6 cakes in its inventory. The bakery’s owner has decided to display 5 of these items in the bakery’s front window. If the items are randomly selected, what is the probability that the display will have exactly 3 pies?
Options:
A)3/11
B)25/77
C)5/11
D)7/11
E)50/77
Rationale: We need the probability that the owner will select PPPCC: 5!/3!∗2!∗(5/11∗4/10∗3/9)∗(6/8∗5/7)=25/77, we are multiplying by 5!/3!∗2! since PPPCC scenario can occur in number of ways: PPPCC, PPCPC, PCPPC, CPPPC, ... Notice that the number of occurrences of PPPCC basically is the number of arrangements of 5 letters PPPCC out of which 3 P's and 2 C's are identical, so it's 5!/3!∗2!
Answer: B.
Answer: B
Question: A train 280 m long, running with a speed of 63 km/hr will pass a tree in?
Options:
A)22 sec
B)16 second
C)77 sec
D)55 sec
E)17 sec
Rationale: Speed = 63 * 5/18 = 35/2 m/sec
Time taken = 280 * 2/35 = 16 sec
Answer:B
Answer: B
Question: You enter a weight loss challenge game and manage to lose 14% of your body weight. For the final weigh in you are forced to wear clothes that add 2% to your weight. What percentage of weight loss is measured at the final weigh in?
Options:
A)13%
B)9.22%
C)9%
D)14%
E)12.28%
Rationale: (100%-14%)*(100%+2%) = 0.86*1.02 = 12.28%
The weigh in records your weight loss at 12.28%!
The Answer is E
Answer: E
Question: Find the invalid no.from the following series 3, 7, 15, 27, 63, 127, 255
Options:
A)3
B)7
C)27
D)127
E)255
Rationale: Go on multiplying the number by 2 and adding 1 to it to get the next number.So, 27 is wrong.
C
Answer: C
Question: Two trains are running in opposite directions with the same speed. If the length of each train is 240 m and they cross each other in 12 sec, then the speed of each train is?
Options:
A)22
B)77
C)72
D)88
E)21
Rationale: Let the speed of each train be x m/sec.
Then, relative speed of the two trains = 2x m/sec.
So, 2x = (240 + 240)/12 => x = 20
Speed of each train = 20 m/sec.
= 20 * 18/5 =- 72 km/hr.Answer: C
Answer: C
Question: 300 gm of sugar solution has 40% sugar. How much sugar should be added to make it 50% in the solution?
Options:
A)80 gm
B)20 gm
C)60 gm
D)67 gm
E)63 gm
Rationale: Explanation:
No explanation is available for this question!
ANSWER:C
Answer: C
Question: If taxi fares were $1.00 for the first 1/5 mile and $0.40 for each 1/5 mile there after, then the taxi fare for a 3-mile ride was
Options:
A)$1.56
B)$2.40
C)$3.80
D)$4.20
E)$6.60
Rationale: In 3 miles , initial 1/5 mile charge is $1
rest of the distance = 3 - (1/5) = 14/5
rest of the distance charge = 14(0.4) = $5.6 (as the charge is 0.4 for every 1/5 mile)
=> total charge for 3 miles = 1+5.6 = 6.6
Answer is E.
Answer: E
Question: Set R consists of integers {3, -8, Y, 19, -6} and set B consists of integers {k, -3, 0, 16, -5, 9}. Number L represents the median of set R, number M represents mode of set B and number Z = L^M. If Y is an integer greater than 21, for what value of k will Z be a divisor of 26?
Options:
A)-2
B)-1
C)0
D)1
E)2
Rationale: R = {3,-8,Y,19,-6}
B = {k,-3,0,16,-5,9}
Y > 21
So L = Median of R = 3
M = Mode of Set B
Z = (3)^M
If Z is a divisor of 26, (3)^M = 1 because 26 does not have 3 as a factor
=> M = 0
Hence k = 0, as M is mode and 0 will be the most frequently occuring number in set B.
Answer - C
Answer: C
Question: A shop owner sells 30mtr of cloth and gains SP of 10 metres. Find the gain %?
Options:
A)30%
B)40%
C)50%
D)56%
E)78%
Rationale: Here, selling price of 10 m cloth is obtained as profit.
Profit of 10 m cloth = (S.P. of 30 m cloth) – (C.P. of 30 m cloth)
Selling price of 20 m cloth = Selling Price of 30 m of cloth
Let cost of each metre be Rs. 100.
Therefore, cost price of 20 m cloth = Rs. 2000 and S.P. of 20 m cloth = Rs. Rs. 3000
Profit% =	10	× 100 = 50%
20
Profit of 50 % was made by the merchant.
C
Answer: C
Question: An aeroplane covers a certain distance at a speed of 240 kmph in 4 hours. To cover the same distance in 1 2/3 hours, it must travel at a speed of:
Options:
A)520
B)620
C)576
D)740
E)720
Rationale: Distance = (240 x 4) = 960 km.
Speed = Distance/Time
Speed = 960/(5/3) km/hr. [We can write 1 2/3 hours as 5/3 hours]
Required speed = (960 x 3/5) km/hr = 576 km/hr
Answer C) 576 Km/hr
Answer: C
Question: Two pipes A and B can fill a cistern in 37 minutes and 45 minutes respectively. Both pipes are opened. The cistern will be filled in just half an hour, if the B is turned off after?
Options:
A)7
B)9
C)11
D)13
E)15
Rationale: Let B be turned off after x minutes. Then,
Part filled by (A + B) in x min. + Part filled by A in (30 -x) min. = 1.
x 2	+	1 + (30 - x).	2	= 1
75	45	75
11x	+	(60 -2x)	= 1
225	75
11x + 180 - 6x = 225.
x = 9.
B)
Answer: B
Question: The lengths of the legs of a right triangle are x and y, while the length of the hypotenuse is
x + y- 4. What is the maximum radius of a circle inscribed in this triangle?
Options:
A)1
B)2
C)4
D)22
E)cannot be determined from the information given
Rationale: Length of hypotenuse: x + y-4 = a + b. Hence x + y = a + b + 4.
Sum of lengths of legs: x + y = a + b + 2r.
Therefore 2r = 4, so r = 2.
correct answer B
Answer: B
Question: The ratio between the school ages of Neelam and Shaan is 5:6 respectively. If the ratio between the one-third age of Neelam and half of Shaan's age of 5:9, then what is the school age of Shaan?
Options:
A)19
B)27
C)16
D)15
E)17
Rationale: Let the school ages of Neelam and Shaan be 5x and 6x years respectively.
Then, (1/3 * 5x)/(1/2 * 6x) = 5/9
15 = 15
Thus, Shaan's age cannot be determined.Answer: D
Answer: D
Question: In a clothing store, there are six different colored neckties (red, orange, yellow, green, blue, and indigo) and six different colored shirts (red, orange, yellow, green, blue, and indigo) that must be packed into boxes for gifts. If each box can only fit one necktie and one shirt, what is the probability that all of the boxes will contain a necktie and a shirt of the same color
Options:
A)719/720
B)1/120
C)2/233
D)3/543
E)1/720
Rationale: 6 ties and 6 shirts...
red tie can take any of 6 shirts..
orange can take any of the remaining 5 shirts
yellow any of remaining 4..
and so on till last indigo chooses the 1 remaining..
Total ways= 6*5*4*3*2*1= 720
out of this 720, ONLY 1 way will have same colour tie and shirt..
prob = 719/720
A
Answer: A
Question: The denominator of a fraction is 1 less than twice the numerator. If the numerator and denominator are both increased by 1, the fraction becomes 3/5. Find the fraction?
Options:
A)5/7
B)5/1
C)5/9.
D)5/2
E)5/8
Rationale: Let the numerator and denominator of the fraction be 'n' and 'd' respectively.
d = 2n - 1
(n + 1)/(d + 1) = 3/5
5n + 5 = 3d + 3
5n + 5 = 3(2n - 1) + 3 => n = 5
d = 2n - 1 => d = 9
Hence the fraction is : 5/9.
Answer: C
Answer: C
Question: Find the amount on Rs.8000 in 9 months at 20% per annum, if the interest being compounded quarterly?
Options:
A)2277
B)9261
C)686
D)1268
E)2612
Rationale: A = 8000(21/20)3 = 9261
Answer: OB
Answer: B
Question: 1+2=10
2+3=26
3+4=50 then
4+5=?
Options:
A)80
B)81
C)82
D)83
E)84
Rationale: 1+2=10..... (1+2)^2+1 =10
2+3=26....... (2+3)^2+1=26
3+4=50 then...(3+4)^2+1=50
4+5=82........ (4+5)^2+1=82
ANSWER:C
Answer: C
Question: Six computers, each working at the same constant rate, together can process a certain amount of data in 9 days. How many additional computers, each working at the same constant rate, will be needed to process the same amount of data in 6 days?
Options:
A)3
B)5
C)6
D)9
E)12
Rationale: Explanation: If six computers require 9 days to process the data, thats
a total of 54 computer-days the product of 6 and 9. If you change the number
of computers or the number of days, 54 will have to remain the product, whether
that means 54 days of one computer or one day with 54 computers.
In 6 days, the number of computers is:
6c = 54
c = 9
9 computers is 3 more than the 6 that it took to do the job in 9 days, so
the correct choice is (A).
Answer: A
Question: A cube is divided into 125 identical cubelets. Each cut is made parallel to some surface of the cube. But before doing that, the cube is painted with green on one set of opposite faces, red on another set of opposite faces, and blue on the third set of opposite faces. How many cubelets are painted with exactly one colour?
Options:
A)36
B)42
C)48
D)54
E)60
Rationale: Each side of the cube has 5 x 5 = 25 cubelets.
Only the interior cubelets are painted one colour.
On each side, 3 x 3 = 9 cubelets are painted one colour.
Since the cube has six sides, the number of cubes with one colour is 6*9 = 54
The answer is D.
Answer: D
Question: If x/4 – (x – 3)/5 = 1, then find the value of x.
Options:
A)9
B)7
C)6
D)8
E)5
Rationale: Explanation:
x/4 – (x - 3)/5 = 1
(5x – 4(x – 3))/20 = 1
5x - 4x + 12 = 20
x = 8
ANSWER:A
Answer: A
Question: You walk one mile to school every day. You leave home at the same time each
day, walk at a steady speed of 3 miles per hour, and arrive just as school begins. Today you
were distracted by the pleasant weather and walked the rst half mile at a speed of only 2
miles per hour. At how many miles per hour must you run the last half mile in order to arrive
just as school begins today?
Options:
A)4 miles per hour
B)6 miles per hour
C)8 miles per hour
D)10 miles per hour
E)12miles per hour
Rationale: Recall the formula s = v t, where in this case, s is distance (in miles) traveled at a
constant speed of v (miles per hour), for a time of t hours. The rst statement indicates that
it usually takes you only 20 minutes to go to school (solve for t in 1 = 3 t and change units)
Today, it took you 15 minutes to cover the rst half mile (solve for t in 1=2 = 2 t and
change units). You only have 5 more minutes to arrive (that is 1/12th of an hour), and need
to cover another half mile. Solve for v in the equation 1=2 = (1=12) v.
correct answer B
Answer: B
Question: A train 560 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 140 m long?
Options:
A)40
B)56
C)41
D)42
E)34
Rationale: Speed = 45 * 5/18 = 25/2 m/sec
Total distance covered = 560 + 140 = 700 m
Required time = 700 * 2/25 = 40 sec
Answer: Option B
Answer: B
Question: If {b} denote the remainder when 3b is divided by 2 then which of the following is equal to 1 for all positive integers b?
I. {2b+1}
II. {2b}+1
III. 2{b+1}
Options:
A)I only
B)II only
C)I and II
D)III only
E)II and III
Rationale: C - I and II
3b/2 = 0 or 1
I just substituted 1 in the equations and solved.
Answer: C
Question: Kim can do a work in 3 days while David can do the same work in 2 days. Both of them finish the work together and get Rs. 150. What is the share of Kim?
Options:
A)22
B)60
C)88
D)66
E)12
Rationale: Kim's wages : David's wages = Kim's 1 day work : David's 1 day work = 1/3 : 1/2 = 2:3
Kim's share = 2/5 * 150 = Rs. 60
Answer: B
Answer: B
Question: A 5-digit code consists of one number digit chosen from 1, 2, 3 and four letters chosen from A, B, C, D, E. If the first and last digit must be a letter digit and each digit can appear more than once in a code, how many different codes are possible?
Options:
A)375
B)625
C)1,875
D)3,750
E)5,625
Rationale: Choose one number from 3 numbers in 3C1 = 3 ways
Choose one position from the middle three for the number in 3C1 = 3 ways
The other four positions can be filled by the 5 letters in 5^4 ways.
Therefore total number of codes possible = 3*3*(5^4) = 5,625
ANSWER:E
Answer: E
Question: A cyclist covers a distance of 750 meter in 2 minutes 50 seconds. What is the speed in km/hr of cyclist
Options:
A)16 km/hr
B)17 km/hr
C)15.84 km/hr
D)19 km/hr
E)20 km/hr
Rationale: Explanation:
Speed=Distance/Time
Distance=750meter
Time=2 min 50sec=170sec
Speed=750/170=4.4m/sec
=>4.4âˆ—18/5km/hr=15.84km/hr
Option C
Answer: C
Question: A goods train runs at the speed of 72 km/hr and crosses a 250 m long platform in 26 sec. What is the length of the goods train?
Options:
A)288
B)277
C)274
D)270
E)281
Rationale: Speed = 72 * 5/18 = 20 m/sec.
Time = 26 sec.
Let the length of the train be x meters.
Then, (x + 250)/26 = 20
x = 270 m.
Answer: D
Answer: D
Question: A man purchased 1 blankets @ Rs.100 each, 5 blankets @ Rs.150 each and two blankets at a certain rate which is now slipped off from his memory. But he remembers that the average price of the blankets was Rs.150. Find the unknown rate of two blankets?
Options:
A)278
B)277
C)278
D)450
E)650
Rationale: 10 * 150 = 1500
1 * 100 + 5 * 150 = 850
1500 – 850= 650
Answer:E
Answer: E
Question: A board 7ft. 9 inches long is divided into 3 equal parts . What is the length of each part?
Options:
A)2ft. 7 inches
B)4ft. 7 inches
C)1ft. 7 inches
D)3ft. 7 inches
E)None of them
Rationale: Length of board=7ft. 9 inches=(7*12+9)inches=93 inches.
Therefore, Length of each part = (93/3) inches = 31 inches = 2ft. 7 inches
Answer is A.
Answer: A
Question: Renu can do a piece of work in 6 days, but with the help of her friend Suma , she can do it in 5 days. In what time Suma can do it alone?
Options:
A)10
B)12
C)14
D)15
E)30
Rationale: Renuâ€™s one dayâ€™s work = 1/6
Sumaâ€™s one dayâ€™s work = 1/5 - 1/6 = 1/30
Suma can do it alone in 30 days.
ANSWER:E
Answer: E
Question: Roycee's club with a total membership of 30 has formed 3 committees, M, S and R which have 8,12, and 5 members respectively. If no member of committee M is on either of the other 2 committees, what is the greatest possible number of members in the club who are on none of the committees.
Options:
A)5
B)7
C)8
D)10
E)12
Rationale: Roycee's club with a total membership of 30 has formed 3 committees, M, S and R which have 8,12, and 5 members respectively.Given no member of committee M is on either of the other 2 committees -- hence (M n R) and (M n S) and (M n R n S) is zero.
Hence only M is 8. Now we need to consider only S, (S n R) and R.
(M U R U S) = M + R + S - (M n R) - (M n S) - (R n S) + (M n R n S) + Neither.
30 = 8 + (12 - x) + (5 - x) + 0 + 0 + x + 0 + Neither.
22 = (12-x) + (5-x) + x + Neither.
Now the max value of x could be 5 and the min value of x could be 0.
When x is 5 (max), Neither is 10.
When x is 0 (min), Neither is 5. We need maximum no of people who do not belong to any group. Hence max value of neither is 10.
Answer 10 (D).
Answer: D
Question: A cycle is bought for Rs.900 and sold for Rs.1080, find the gain percent?
Options:
A)20%
B)30%
C)15%
D)10%
E)35%
Rationale: 900---- 180
100---- 20%
ANSWER A
Answer: A
Question: Two musicians, Maria and Perry, work at independent constant rates to tune a warehouse full of instruments. If both musicians start at the same time and work at their normal rates, they will complete the job in 45 minutes. However, if Perry were to work at four Maria’s rate, they would take only 30 minutes. How long would it take Perry, working alone at his normal rate, to tune the warehouse full of instruments?
Options:
A)1 hr 20 min
B)1 hr 45 min
C)1 hr
D)2 hr 20 min
E)3 hr
Rationale: Sol:
Lets Perry Rate be P and Rate of Maria be M
(rate)*(time)= Work or rate = work/time
first equation=> P+M = 1/45
converting it to hrs P+M= 1/(45/60) => 1/(3/4) =>4/3
second equation => M+4M =>1/30
converting it to hrs 5M=1/(30/60) =>1/(1/2) =>2
therefore M= 2/5 and P=14/15
Rate of Perry = 14/15
time= work/rate (work = 1 job)
Time ~ 1 hrs
Answer : C
Answer: C
Question: A person took some amount with some interest for 2 years, but increase the interest for 1%, he paid Rs.110/- extra, then how much amount he took?
Options:
A)s.5500/-
B)s.6000/-
C)s.4000/-
D)s.7000/-
E)s.8000/-
Rationale: Explanation:
2 years = Rs.110/-
year = 110/2
Rate of Interest = 1%
100/1% × 110/2 = Rs.5500/-
P = Rs.5500/-
Answer: Option A
Answer: A
Question: The cross-section of a water channel is a trapezium in shape. If the channel is 12 meters wide at the top and 8 meters wide at the bottom and the area of cross-section is 700 square meters, what is the depth of the channel (in meters)?
Options:
A)50
B)60
C)70
D)80
E)90
Rationale: 1/2 * d * (12 + 8) = 700
d = 70
The answer is C.
Answer: C
Question: A salesman’s terms were changed from a flat commission of 5% on all his sales to a fixed salary of Rs.1000 plus 2.5% commission on all sales exceeding Rs. 4,000. If his remuneration as per new scheme was Rs. 600 more than that by the previous schema, his sales were worth?
Options:
A)12003
B)12000
C)12002
D)12022
E)12023
Rationale: [1000 + (X-4000) * (2.5/100)] - X * (5/100) = 600
X = 12000
Answer:B
Answer: B
Question: Find the surface area of a cuboid 12 m long, 14 m broad and 7 m high
Options:
A)868 sq.cm
B)600 sq.cm
C)700 sq.cm
D)900 sq.cm
E)None of these
Rationale: Explanation:
Surface area = [2 (12 x 14 + 14 x 7 + 12 x 7)] cm2 = (2 x 350)cm2 = 700 cm2.
Answer: C
Answer: C
Question: The list price of an article is Rs.65. A customer pays Rs.56.16 for it. He was given two successive discounts, one of them being 10%. The other discount is?
Options:
A)9%
B)4%
C)6%
D)3%
E)5%
Rationale: 65*(90/100)*((100-x)/100)
= 56.16
x = 4%
Answer:B
Answer: B
Question: The least number which should be added to 2497, so that the sum is exactly divisible by 5, 6, 4 and 3, is
Options:
A)3
B)13
C)23
D)33
E)43
Rationale: LCM of 5, 6, 4 and 3 = 60
On dividing 2497 by 60, the remainder is 37.
Number to be added = 60 - 37 = 23
Answer : C
Answer: C
Question: After MM students took a test, there was a total of 64% of correct answers. If the test contains 50 questions, what is the least number of questions that the next student have to get right to bring the total of correct answers to 70% ?
Options:
A)+ 20
B)+ 35
C)+ 15
D)+ 20
E)+ 45
Rationale: Denote xx as the required number of correct answers. xx must satisfy the equation 0.64∗M∗50+x/50M+50=7/10 or 350M+350=320M+10x or x=3M+35
Answer: B
Answer: B
Question: A and B together invested Rs. 20,000 in a business. At the end of the year, out of total profit is Rs. 5,000 B's share was Rs. 2000. A's investment was
Options:
A)s. 4,500
B)s. 8,250
C)s. 10,500
D)s. 11,250
E)s. 12,000
Rationale: A+B=20000
total profit=5000
5000-2000=3000
3000;2000=3:2
then 3*20000/5=12000
ANSWER:E
Answer: E
Question: The length of a rectangular plot is thrice its breadth. If the area of the rectangular plot is 867 sq m, then what is the breadth of the rectangular plot?
Options:
A)19 m
B)17 m
C)18 m
D)14 m
E)12 m
Rationale: Let the breadth of the plot be b m.
Length of the plot = 3 b m
(3b)(b) = 867
3b2 = 867
b2 = 289 = 172 (b > 0)
b = 17 m.
Answer: B
Answer: B
Question: Nine highschool teachers gather at allocacting the subject, Three subject of 3 people each will be created. How many ways are there to create these 3 teams?
Options:
A)45
B)51
C)90
D)175
E)280
Rationale: Arrange the 6 teachers in a straight line in 6! ways.
The first three form team 1, next three form team 2 and last three form team 3. But in each team, the boys are arranged in first, second third positions so you need to un-arrange them by dividing by 3! three times (once for each team). You get 6!/(2! * 2! * 2!)
Also, there are no distinct teams - team1, team2 and team3. You just have three teams. So you also need to un-arrange the three teams by dividing by another 3!.
You get 6!/(2! * 2! * 2!) * 2! = 45
Answer (A)
You get 6!/(2! * 2! * 2!) * 2!
Answer : A
Answer: A
Question: There are two circles of different radii. The are of a square is 784 sq cm and its side is twice the radius of the larger circle. The radius of the larger circle is seven - third that of the smaller circle. Find the circumference of the smaller circle?
Options:
A)65
B)17
C)12
D)18
E)15
Rationale: Let the radii of the larger and the smaller circles be l cm and s cm respectively. Let the side of the square be a cm.
a2 = 784 = (4)(196) = (22).(142)
a = (2)(14) = 28
a = 2l, l = a/2 = 14
l = (7/3)s
Therefore s = (3/7)(l) = 6 Circumference of the smaller circle = 2∏s = 12∏ cm.
Answer: C
Answer: C
Question: A company has 60 employees, of which 22 studied accounting, 15 studied finance and 14 studied marketing. Nine employees have done just two courses and only one made ​​the three courses. How many employees have no training?
Options:
A)A)0
B)B)9
C)C)10
D)D)20
E)E)26
Rationale: Total employees=60
studied accounting=22
studied finance=15
studied marketing=14
9 employees have been double counted and one employee has been counted thrice.
Therefore employees who have received training=22+15+14-9-(2*1)
=51-11
=40
Employees with no training
=60-40
=20
Ans=D
Answer: D
Question: The banker's discount on a bill due 4 months hence at 15% is Rs. 420. The true discount is:
Options:
A)400
B)277
C)268
D)191
E)123
Rationale: T.D.
=	B.D. x 100
100 + (R x T)
= Rs. 420 x 100
100 + 15 x	1
3
= Rs. 420 x 100
105
= Rs. 400.
Answer: A
Answer: A
Question: If a, b, and c are consecutive positive integers and a > b > c, which of the following must be true?
I. c - a = 2
II. abc is an even integer.
III. (a + b + c)/3 is an integer.
Options:
A) I only
B) II only
C) I and II only
D) II and III only
E) I, II, and III
Rationale: Since a, b, and c are consecutive positive integers and a < b < c, then a = c + 2, from which it follows that c - a = -2. So, I is false.
Next, out of 3 consecutive integers at least 1 must be even, thus abc=even. II is true.
Finally, since b = a + 1, and c = a + 2, then (a + b + c)/3 = (a + a + 1 + a + 2)/3 = a + 1 = integer. III is true as well.
Answer: D.
Answer: D
Question: The units digit of (35)^(87) + (93)^(47) is:
Options:
A)2
B)4
C)6
D)8
E)0
Rationale: The units digit of powers of 3, cycles in a group of 4: {3, 9, 7, 1}
47 has the form 4k+3, so the units digit of 93^47 is 7.
The units digit if powers of 5 is always 5.
7+5 = 12, so the units digit is 2.
The answer is A.
Answer: A
Question: Can you replace the question mark with the number to complete the series, provided the pair of numbers exhibits a similar relationship?
? : 4623 :: 9 : 647
Options:
A)?= 17
B)18
C)13
D)10
E)20
Rationale: A
17
The relationship holds for below formula :
pow(x,3) - pow(x,2) - 1
=> 9*9*9 - 9*9 - 1
=> 729 - 81 - 1
=> 647
Similarly,
17*17*17 - 17*17 - 1
=> 4913 - 289 - 1
=> 4623
Answer: A