MU-NLPC/Calc-aqua_rat huggingface dataset:
Bob finishes the first half of an exam in four sixth the time it takes him to finish the second half. If the whole exam takes him an hour, how many minutes does he spend on the first half of the exam? Choose one.
A) 12
B) 24
C) 27
D) 36
E) 40

Solution: Many times, it is easiest to think of problems like this conceptually (as opposed to formulaically). Conceptually, if the first half of the exam takes 4/6's the time of the second half (6/6's), we can see that the hour the entire exam took to finish can be broken down into tenth's. (Another way to look at this problem is via ratio's - first half is 4:10 and the second half is 6:10). With each tenth of an hour being 6 minutes (60/10), the first half of the exam would have taken 12 minutes. Correct answer is 12.
Answer: A
Excluding stoppages, the speed of a bus is 54 km/hr and including stoppages, it is 45 km/hr. For how many minutes does the bus stop per hour?	Choose one
A) 11 min B) 10 min C) 37 min D) 17 min E) 16 min

Solution: Due to stoppages, it covers 9 km less.   Time taken to cover 9 km   = 9/54 * 60= 
9/54 * 60 = 10
10 min.   Answer: 10 min
Answer: B
The sum of ages of 5 children born at the intervals of 3 years each is 50 years. What is the age of the youngest child?
Choose the correct choice from the following choices:
A) 4
B) 5
C) 6
D) 7
E) 8

Solution: Let the ages of children be x, (x + 3), (x + 6), (x + 9) and (x + 12) years.   Then, x + (x + 3) + (x + 6) + (x + 9) + (x + 12) = 50   5x = 20   x = 4.   Age of the youngest child = x = 4 years.   4nswer:4
Answer: A
A is thrice as efficient as B and is, therefore, able to finish a piece of work 10 days earlier than B. In how many days A and B will finish it together?	Options.
A) 6
B) 7
C) 87
D) 5
E) 34

Solution: WC = 3:1   WT = 1:3   x 3x   1/x – 1/3x = 1/10   x = 20/3   3/20 + 1/20 = 1/5 => 5 days   Answer:5
Answer: D
How long does a train 110 m long running at the speed of 90 km/hr takes to cross a bridge 132 m length?  Choose the correct choice from the following answers
A) 82.1 sec B) 9.68 sec C) 16.1 sec D) 13.1 sec E) 12.15sec

Solution: Speed = 90 * 5/18= 
90 * 5/18 = 25
25 m/sec   Total distance covered= 110 + 132= 
110 + 132 = 242
242 m.   Required time= 242/25= 
242/25 = 242/25 = around 9.68
9.68 sec.   Answer:9.68 sec
Answer: B
A person buys an article at Rs.500. At what price should he sell the article so as to make a profit of 20%?  Select.
A) 600 B) 882 C) 772 D) 652 E) 271

Solution: Cost price = Rs.500   profit = 20% of 500 = Rs.100   Selling price = Cost price + Profit   = 500 + 100= 
500 + 100 = 600
600   600nswer:600
Answer: A
A computer simulation of a 12 hour analog clock keeps perfect time while it is running, and
has two hands—an hour hand and a minute hand—both of which move continuously around
the 12 hour dial. (For example, at 2:30, the hour hand will be exactly halfway between 2 and
3.) Because of careless programming, the minute hand looks exactly like the hour hand, so
that the two are indistinguishable.
On one day, the clock stops at some time after 12am and before 12pm. How many times could
it have stopped without it being possible after 12pm to tell what time it stopped?  Options
A) 11  B) 12  C) 66  D) 132  E) 708

Solution: A configuration of the hands is called “ambiguous” if you cannot use this broken clock to   distinguish the minute hand from the hour hand.   In the above diagram it must be the minute hand that is pointing to 6 and the hour hand that   is pointing midway between 2 and 3. (If the hour hand were to point to 6, the minute hand   would have to point to 12.) 2:30 is not an ambiguous configuration.   Let m 2 (0; 1) represent the fraction of the way around the clock face for the minute hand and   h 2 (0; 1) the corresponding fraction for the hour hand. For example, 2:30 hasm = 1=2 = 0:5   and h = 2:5=12 = 0:2083.   As the minute hand moves 12 times as fast as the hour hand, a configuration is ambiguous if   m and 12h have the same fractional part. Because the hands are indistinguishable, a time is   also ambiguous when h and 12m have the same fractional part. We express these conditions   as: 12h m( mod 1) and 12m h( mod 1). Thus 144h h( mod 1), and so 143h 0(   mod 1). There are 142 solutions to this equation in the open interval (0; 1): h 2 H1 := f k   143 :   k = 1; 2; : : : ; 142g.   Times when the hour and minute hand perfectly overlap (h = m) are in H1, but these are not   ambiguous times. These configurations occur when 12h h( mod 1). That is, 11h 0(   mod 1). There are 10 such times: h 2 H2 :=   k   11 : k = 1; 2; : : : ; 10   The number of ambiguous times is the cardinality of H1nH2. As H2 H1 the cardinality of   H1nH2 is 142 􀀀 10 = 132, which is answer (d).   correct answer 132
Answer: D
The volume of a sphere with radius r is (4/3)*pi*r^3 and the surface area is 4*pi*r^3. If a sperical balloon has a volume of 288 pi cubic centimeters, what is hte surface area of the balloon in square centimeters? Choose the correct choice from the following options.
A) a. 40
B) b. 100
C) c. 400
D) d. 1,000
E) e. 10,000

Solution: The surface area is 4.pi.r^2 (its area remember not volume)   as 4/3.pi.r^3=288pi   r=6   so area = 4.pi.r^2= 144.pi= 324 x 3.14 = 400 (approx)   c. 400
Answer: C
How many 4 digit numbers can be formed if the tens and thousands digits are even, and the hundreds and units digits are odd?
Answers.
A) 100	B) 200	C) 300	D) 400	E) 500

Solution: Thousands digit: 2, 4, 6, 8   Hundreds digit: 1, 3, 5, 7, 9   Tens digit: 2, 4, 6, 8, 0   Units digit: 1, 3, 5, 7, 9   =4*5*5*5= 
4*5*5*5 = 500
500   ANS:500
Answer: E
What are the number of ways to select 3 men and 2 women such that one man and one woman are always selected?	Choose the correct choice from the following options:
A) 60 ways
B) 40 ways
C) 30 ways
D) 10 ways
E) 20 ways

Solution: Explanation:   The number of ways to select three men and two women such that one man and one woman are always selected = Number of ways selecting two men and one woman from men and five women   = â´Câ‚‚ * âµCâ‚ = (4 * 3)/(2 * 1) * 5= 
(4 * 3)/(2 * 1) * 5 = 30
30 ways.   Answer: 30 ways
Answer: C
4 professors and 6 students are being considered for membership on a supervisory committee which must consist of 3 people. If the committee has to include at least 4 professor, how many ways can this committee be formed?	Pick:  A) 36  B) 64  C) 72  D) 80  E) 100

Solution: you count up combinations twice.   4*9*8... and let me name 6 with students A,B,C,..,F   after choosing a professor, when you choose Student A and B, you can choose A first, then B. Or B first, then A. Both combination are same.   I don't think that's the only mistake.   64 is a factor of = 2^2*4^2   144 is a factor of = 2^4*3^2.   These are very different numbers and you cannot divide 144 with something to get to 64. ans 64
Answer: B
Lottery balls numbered consecutively from one through one hundred are placed in a spinner. If one ball is drawn at random, what is the probability that it will have the number 3 on it exactly once?  Select the correct option
A) 18/100 B) 1/10 C) 11/100 D) 19/100 E) 1/5

Solution: Probability = No of balls with exactly one 1 / total number of balls   = {3,13, 23, 30,31, 32, 34 to 39, 43,53,63,73,83,93}/100   = 18/100   18/100nswer is 18/100
Answer: A
A cylindrical can has a radius of 3 centimeters and a height of 24 centimeters. What is the area, in square centimeters, of a rectangular label that completely covers the curved surface of the can without over-lapping?	Choose the correct answer
A) 16 pi  B) 64 pi  C) 96 pi  D) 144 pi  E) 576 pi

Solution: They are asking the lateral surface area of the cylinder.   the Lateral surface area = 2* pi * r *h   = 2*pi*3*24=144 pi   Answer is 144 pi.
Answer: D
The bus that travels from St. Louis to Chicago and back comes to St. Louis every 3 hours while the bus that travels from St. Louis to Springfield and back comes to St. Louis every 4 hours. If at 6:00 o'clock both bused arrived at St. Louis, at what time will they meet in St. Louis again?	Choose the correct choice from the following.
A) 16:00.
B) 18:00.
C) 20:00.
D) 22:00.
E) 24:00.

Solution: Time taken by bus to travel from St. Louis to Chicago and back comes to St. Louis = 3 hours   Time taken by bus to travel from St. Louis to Springfield and back comes to St. Louis = 4 hours   Time taken by both buses to meet again in St. Louis will be LCM of 3 and 4 = 12   If the buses start at 6:00 o'clock from St. Louis , they will meet again in St. Louis at 18:00 hours   Answer 18:00.
Answer: B
We run a business that rents out canoes and kayaks. A canoe rental costs $12 per day, and a kayak rental costs $18 dollars per day. One day, our business rents out 3 canoes for every 2 kayaks and receives a total of $504 in revenue. How many more canoes than kayaks were rented out?  Choose one:
A) 5
B) 6
C) 7
D) 8
E) 9

Solution: Let x be the number of canoes.   Then 2x/3 is the number of kayaks.   12x+(2x/3)*18=504   12x+12x=504   24x=504   x=21 (canoes)   2x/3=14 (kayaks)   There were   21-14= 
  21-14 = 7
7 more canoes rented out.   The answer is 7.
Answer: C
Of three numbers, the third is twice the second and the second is 4 times the first. If their average is 78, the smallest of the three numbers is:	Choose the correct choice from the following answers:  A) 18  B) 19  C) 20  D) 21  E) 22

Solution: Explanation:   Let first number be x.   So,2nd no. = 4x & 3rd no.=8x.   So,x+4x+8x=78 × 3 = 234.   13x = 234   x = 234/13   Hence,smallest Number x=18.   18nswer: 18
Answer: A
What is the unit digit in 4^100?
Pick.
A) 0	B) 1	C) 6	D) 3	E) 5

Solution: Unit digit in 4^100 = unit digit in [(4^4)^25 ]But unit digit in 4^4=6unit digit 4^100= 6Answer is 6
Answer: C
A fruit seller sells mangoes at the rate of Rs.5 per kg and thereby loses 20%. At what price per kg, he should have sold them to make a profit of 5%  Choose the correct option.
A) Rs 6.56
B) Rs 9.56
C) Rs 10.56
D) Rs 11.56
E) None of these

Solution: Explanation:   80 : 5 = 105 : x   x= (5×105/80)   = Rs 6.56   Option Rs 6.56
Answer: A
How many integers from 0 to 53, inclusive, have a remainder of 1 when divided by 3 ? Pick
A) 15	B) 16	C) 17	D) 18	E) 19

Solution: My ans is also C.17.   Explanation:   1 also gives 1 remainder when divided by 3, another number is 4, then 7 and so on.   Hence we have an arithmetic progression: 1, 4, 7, 10,..... 52, which are in the form 3n+1.   Now we have to find out number of terms.   tn=a+(n-1)d, where tn is the nth term of an AP, a is the first term and d is the common difference.   so,52 = 1+(n-1)3   or, (n-1)3 = 51   or, n-1 = 17   or, n = 18   18
Answer: D
How many ways are there to select a subcommittee of 8 members from among a committee of 17?
Select:  A) 22888  B) 24310  C) 28791  D) 27711  E) 12111

Solution: Explanation:   Since it does not matter what order the committee members are chosen in, the combination formula is used.   Committees are always a combination unless the problem states that someone like a president has higher hierarchy over another person. If the committee is ordered, then it is a permutation.   C(17,8)= 24310   Answer: 24310)
Answer: B
The area of rectangular field of length 90 meters and breadth 80 meters is equal to the area of a square plot. What will be the length of the diagonal of the square plot? Answers
A) 100m B) 120m C) 95m D) 80m E) 150m

Solution: Given that the length of the rectangular field l = 90 m and breadth = b = 80 m.   Then its area lb = 90 x 80 sq.m   We know that the area of square = (1/2)x(diagonal)2   from the given question, we have area of square plot = area of rectangular field   That is, 90 x 80 = 1/2 x diagonal2   diagonal^2 = 2 x 7200 = 14400 = (120)2   diagonal = 120 m.hence 120m
Answer: B
Which of the following is equal to 5^k*7^(k-1)?  Choose the correct choice from the following choices:
A) 5*35^(k-1)
B) 5*35^(k-1)
C) 35^k
D) 5*35^k )
E) 35^(2k-1)

Solution: 5^k*7^(k-1) = 5*5^(k-1)*7^(k-1) = 5*35^(k-1)   The answer is 5*35^(k-1).
Answer: A
The ratio of the area of a square to that of the square drawn on its diagonal is Choose the correct choice from the following answers: A) 1:2 B) 1:0 C) 1:7 D) 1:5 E) 1:6

Solution: 1:2nswer: 1:2) 1:2
Answer: A
If x,y ,and z are positive real numbers such that x+y-z = 62, y-z+x =82 , and z-x+y = 100, then find the x+y+z value?	Choices:
A) 80
B) 91
C) 62
D) 74
E) 82

Solution: x+y-z = 62, ------1)   y-z+x =82 , ------2)   z-x+y = 100------3)   from (1)&(2)   2z=20   z=10   from (2)&(3)   2y = 182   y=91   then x=62-81= -19   x+y+z = 82   correct option is 82
Answer: E
A man can row 18 kmph in still water.it takes him thrice as long to row up as to row down the river.find the rate of stream. Select the correct option:  A) 2 km/hr  B) 3 km/hr  C) 7 km/hr  D) 9 km/hr  E) 5 km/hr

Solution: Let man’s rate upstream be x kmph.then ,his rate downstream=3xkmph.   So,2x=18 or x=9.   Rate upstream=9 km/hr,rate downstream=27 km/hr.   Hence,rate of stream=1/2(27-9)km/hr=9 km/hr.   ANSWER 9 km/hr 9 km/hr
Answer: D
Look at this series: 31, 29, 24, 22, 17, ... What number should come next? Choose the most appropriate option
A) 15  B) 14  C) 13  D) 12  E) 11

Solution: Explanation: This is a simple alternating subtraction series, which subtracts 2, then 5.   15nswer: Option 15
Answer: A
At 3:40, the hour hand and the minute hand of a clock form an angle of	Choose the correct answer: A) 10º B) 75º C) 90º D) 130º E) 180º

Solution: Hence the angle   =30(40/5-3)-40/2   =30(8-3)-20   =30 X5-20=130 °   Answer 130º
Answer: D
If an article is sold at 19% profit instead of 12% profit, then the profit would be Rs. 105 more. What is the cost price?	Select the correct option.
A) 1509	B) 1528	C) 1500	D) 1598	E) 1512

Solution: Let the cost price of an article be Rs. x.   (19% of x) - (12% of x) = 105   19x/100 - 12x/100 = 105 => 7x = 105 * 100   => x = 1500   Cost price = Rs. 1500.Answer:1500
Answer: C
A train 75 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is?  Answers
A) 28	B) 50	C) 88	D) 22	E) 32

Solution: Speed of the train relative to man = (75/10) m/sec = (15/2) m/sec. [(15/2) * (18/5)] km/hr = 27 km/hr. Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr. x - 5 = 27 ==> x   = 32 km/hr.Answer:32
Answer: E
Two trains 140 m and 160 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions on parallel tracks. The time which they take to cross each other is?	Choose the correct choice
A) 22.9  B) 10.8  C) 17.2  D) 21.1  E) 12.6

Solution: Relative speed = 60 + 40= 
60 + 40 = 100
100 km/hr.= 100 * 5/18 = 250/9 m/sec.   Distance covered in crossing each other = 140 + 160= 
140 + 160 = 300
300 m.   Required time= 300 * 9/250 = 54/5= 
54/5 = 54/5 = around 10.8
10.8 sec.Answer: 10.8
Answer: B
The average of 20 numbers is zero. Of them, at the most, how many may be greater than zero ?
Answers.
A) 0
B) 8
C) 3
D) 7
E) 1

Solution: Explanation:   Average of 20 numbers = 0.   Sum of 20 numbers = (0 * 20)= 
(0 * 20) = 0
0.   It is quite possible that 19 of these numbers may be positive and if their sum is a, then 20th number is (- a).   0nswer: 0
Answer: A
A cistern can be filled by a tap in 5 hours while it can be emptied by another tap in 9 hours. If both the taps are opened simultaneously, then after how much time will the cistern get filled ?	Choose the correct choice from the following:
A) 4.5 hrs	B) 5 hrs	C) 6.5 hrs	D) 7.25 hrs	E) 11.25 hrs

Solution: Net part filled in 1 hour= 1/5 -1/9= 4/45   Therefore the cistern will be filled in 45/4 hours or 11.25 hours.   ANSW11.25 hrsR:11.25 hrs
Answer: E
If there are only 2 wheelers and 4 wheelers parked in a school located at the heart of the city, find the number of 4 wheelers parked there if the total number of wheels is 58?
Choose the correct choice from the following options
A) 11 B) 12 C) 13 D) 14 E) 15

Solution: four wheeler=14*4= 
14*4 = 56
56(max)   2 wheel=1   so no of 4 wheeler=14   ANSWER:14
Answer: D
A, B and C start a business each investing 10,000. After 6 months A withdrew 5000, B withdrew 4000 and C invests 6000 more. At the end of the year, a total profit of 34,200 was recorded. Find the share of B.	Choose one.
A) 9,600	B) 21,200	C) 28,200	D) 20,500	E) None of these

Solution: Ratio of the capitals of 9,600, B and C   = 10000 Ã— 6 + 5000 Ã— 6 : 10000 Ã— 6 + 6000 Ã— 6 : 10000 Ã— 6 + 16000 Ã— 6   =90000 : 96000 : 156000 = 90 : 96 : 156   Bâ€™s share = (34200 Ã— 96â„342) = 9600   9,600nswer 9,600
Answer: A
If yesterday was Monday, when will Wednesday be? Pick:	A) The day after tomorrow	B) Two days before today	C) Today	D) Tomorrow	E) none

Solution: Explanation:   Yesterday was Monday   =>Today is Tuesday   => Tomorrow is a Wednesday   Answer: Option Tomorrow
Answer: D
An unbiased die is tossed. Find the probability of getting a multiple of 5
Options
A) 1/4 B) 1/6 C) 2/5 D) 5/6 E) 3/7

Solution: Here S = {1,2,3,4,5,6}   E = event of getting a multiple of 5   E = {5}   P(E) = 1/6   Answer is 1/6
Answer: B
A man can row with a speed of 30 kmph in still water. If the stream flows at 11 kmph, then the speed in downstream is? Pick one: A) 22 B) 28 C) 20 D) 41 E) 34

Solution: M = 30   S = 11   41S = 30 + 11= 
30 + 11 = 41
41.Answer:41
Answer: D
The distance from Steve's house to work is 20 Km. On the way back Steve drives twice as fast as he did on the way to work. Altogether, Steve is spending 6 hours a day on the roads. What is Steve's speed on the way back from work?
Choose the correct choice from the following answers:
A) 5.	B) 10.	C) 14.	D) 15.	E) 20.

Solution: Time is in the ratio 2:1 :: to: fro office   Therefore, 2x+1x=6 hrs   Time take to come back - 2 hrs, distance travelled - 20km => Speed = 10kmph   10.
Answer: B
At a dinner party, 6 people are to be seated around a circular table. 2 seating arrangements are considered different only when the positions of the people are different relative to each other. what is the total number of different possible seating arrangements for the group?
Choose the correct choice.
A) 5
B) 10
C) 24
D) 32
E) 120

Solution: Soln: Since the arrangement is circular and 2 seating arrangements are considered different only when the positions of the people are different relative to each other, we can find the total number of possible seating arrangements, by fixing one person's position and arranging the others.   Thus if one person's position is fixed, the others can be arranged in 5! =120 ways.   Ans is 120.
Answer: E
In how many ways can 5 different toys be packed in 3 identical boxes such that no box is empty, if any of the boxes may hold all of the toys ?  Pick one: A) 33 B) 25 C) 77 D) 28 E) 29

Solution: Explanation:   The toys are different; The boxes are identical   If none of the boxes is to remain empty, then we can pack the toys in one of the following ways   a. 2, 2, 1   b. 3, 1, 1   Case a. Number of ways of achieving the first option 2 - 2 - 1   Two toys out of the 5 can be selected in \inline {\color{Black} 5C_{2}} ways. Another 2 out of the remaining 3 can be selected in \inline {\color{Black} 3C_{2}} ways and the last toy can be selected in \inline {\color{Black} 1C_{1}} way.   However, as the boxes are identical, the two different ways of selecting which box holds the first two toys and which one holds the second set of two toys will look the same. Hence, we need to divide the result by 2   Therefore, total number of ways of achieving the 2 - 2 - 1 option is ways \inline {\color{Black} 5C_{2}\times 3C_{2}}= 15 ways   Case b. Number of ways of achieving the second option 3 - 1 - 1   Three toys out of the 5 can be selected in \inline {\color{Black} 5C_{3}} ways. As the boxes are identical, the remaining two toys can go into the two identical looking boxes in only one way.   Therefore, total number of ways of getting the 3 - 1 - 1 option is \inline {\color{Black} 5C_{3}} = 10 = 10 ways.   Total ways in which the 5 toys can be packed in 3 identical boxes   = number of ways of achieving Case a + number of ways of achieving Case b   = 15 + 10= 
15 + 10 = 25
25 ways.   Answer: 25) 25
Answer: B
The price of lunch for 15 people was $207 including a 15% gratuity for service. What was the average price per person, EXCLUDING the gratuity?  Answers:
A) 11.73  B) 12  C) 13.8  D) 14  E) 15.87

Solution: x -> Price without Gratuity   207 = x + 0.15x   => x = 207/1.15= 
207/1.15 = 180
180   So average price per person,excluding the gratuity= 180/15= 
180/15 = 12
12   The answer is 12.
Answer: B
Given that E and F are events such that P(E) = 15, P(F) = 10 and P(E n F) = 15,
find P (E|F) and P(F|E) Choose the correct answer.
A) 3/2
B) 4/5
C) 6/2
D) 8/5
E) 8/9

Solution: Here, E and F are events   P(E|F) = P(EnF)/P(F) = 15/5 = 1   P(F|E) = P(EnF)/P(E) = 15/10 = 3/2.   3/2)
Answer: A
Five years ago, the average age of A, B, C and D was 45 yr. with E joining them now, the average of all the five is 52 yr. How old is E?
Choose the correct answer.
A) 25 yr  B) 62 yr  C) 45yr  D) 64 yr  E) NOne

Solution: Solution:   Total present age of A, B, C and D,   = (45*4)+(4*5)= 
(45*4)+(4*5) = 200
200 yr;   Total age present age of A, B, C, D and E,= 52*5 = 262 yr.   So, age of E = 62 yr.   Answer: Option 62 yr
Answer: B
Kevin plants corn and cotton. Once he harvests the crops, he has 30 pounds of corn and x
pounds of cotton. Corn sells for $5 per pound and cotton sells for $10 per pound. If Kevin sells
all his corn and cotton for a total of $640, then compute x.
Pick:
A) 39
B) 49
C) 59
D) 69
E) 79

Solution: Kevin sells his corn for 305 dollars and his cotton for x10 dollars. Thus 30-5+x*10 =   640, so x = 640-30*5/10 = 490/10= 
490/10 = 49
49 .   correct answer 49
Answer: B
A batsman in his 9th inning makes a score of 75 and their by increasing his average by 7. What is his average after the 9th inning?
Choose the correct option
A) 12
B) 19
C) 26
D) 33
E) 40

Solution: 8x + 75 = 9(x + 7)   x = 12 + 7= 
12 + 7 = 19
19   Answer:19
Answer: B
P runs 20% faster than Q so P gives Q a 300 meter head start. If the race ends in a tie, how far (in meters) did P run in the race? Options.
A) 1500
B) 1600
C) 1700
D) 1800
E) 1900

Solution: Let D be the race distance that P ran.   Let T be the time it took to complete the race.   Let V be Q's speed.   T = D/1.2V = (D-300) / V   D=1.2D-360   0.2D=360   D=1800 meters.   The answer is 1800.
Answer: D
How many positive integers between 1 and 100 are there such that they are multiples of 13?
Pick one
A) 6 B) 5 C) 4 D) 7 E) 3

Solution: Multiples of 13 = 13,26,39,-----91   Number of multiples of 13 => 13*7= 
13*7 = 91
91   Answer is 7
Answer: D
Of the 75 employees of a certain company, twice as many are in the sales department as are in all of the other departments combined. What is the number of employees in the sales department?	Choose the correct answer.
A) 15 B) 20 C) 30 D) 40 E) 50

Solution: This is ratio problem solving question.   I will prefer to use RMV box.   R M V   Sales 2 25 50   Other 1 25 25   Total 3 25 75   Answer is 50. i.e 50
Answer: E
Which is the following is divisible by 11  Pick one.
A) A)3052  B) B)4825  C) C)4805  D) D)4905  E) E)4906

Solution: Explanation:   Sum of first 'n' natural numbers = n(n + 1)/2   Sum of first 8 natural numbers = 7(7+ 1)//2 = 7 x 4 = 28   Sum of first 88 natural numbers = 77(77 + 1)//2 = 77 x 40 = 3080   3080 - 28= 
3080 - 28 = 3_052
3052   3052nswer: Option 3052
Answer: A
In how many different number of ways a combination of 3 men and 2 children can be selected from 6 men and 5 children ?  Choices
A) 20	B) 22	C) 24	D) 26	E) 28

Solution: 6C3   = 6!/(3! . 3!)   = (6 × 5 × 4)/(3 × 2)   = 5 × 4 = 20.   20)
Answer: A
If A,B,C are three integers and AB+C is even ; which of the following must be true?
A)A+C is even
B)B+C is even
C)ABC is even  Select the correct option:  A) Only C  B) Both A and B  C) Both B and C  D) All of them  E) None of them

Solution: Case 1:-   AB+C= None of themven   None of them+None of them= None of them   O*None of them + None of them= None of them   None of them*O +None of them= None of them   Case 2:-   AB+C= None of themven   O+O= None of them   O*O +O= None of them   A)A+C is even- Only possible with Case 2   B)B+C is even- Only Possible with Case 2   C)ABC is even- Only Possible with case 1   No option is 'MUST BNone of them TRUNone of them'   None of them is the answer
Answer: E