MU-NLPC/Calc-aqua_rat huggingface dataset:
If a 3-number code is formed of the integers from 1 to 16 inclusively, and each of the numbers in the code is different, how many possible codes are there? Select the correct option
A) 3140	B) 3250	C) 3360	D) 3470	E) 3580

Solution: 16*15*14= 
16*15*14 = 3_360
3360   The answer is 3360.
Answer: C
Reena took a loan of Rs. 1200 with simple interest for as many years as the rate of interest. If she paid Rs. 432 as interest at the end of the loan period, what was the rate of interest?
Choose the correct choice from the following answers: A) 4 B) 6 C) 8 D) 5 E) 1

Solution: Let rate = R% and time = R years.   Then, (1200 * R * R) / 100 = 432   12R2 = 432   R2 = 36 => R = 6.   Answer: 6
Answer: B
How many integers are there between 55 and 95, inclusive?
Select the correct option
A) 41 B) 55 C) 56 D) 57 E) 58

Solution: I guess the easiest way to answer this is -   Say you have two positive integers, x and y where y > x   Then the number of integers between x and y is given by - (y - x) + 1   In this case, it's (95 - 55) + 1= 
(95 - 55) + 1 = 41
41. Option 41
Answer: A
In how many different ways can the letters of the word 'JUDGE' be arranged such that the vowels always come together?	Select:
A) None of these B) 48 C) 32 D) 64 E) 57

Solution: Explanation :   The word 'JUDGE' has 5 letters. It has 2 vowels (UE) in it and these 2 vowels should   always come together. Hence these 2 vowels can be grouped and considered as a single   letter. That is, JDG(UE).   Hence we can assume total letters as 4 and all these letters are different.   Number of ways to arrange these letters = 4!= 4 x 3 x 2 x 1 = 24   In the 2 vowels (UE), all the vowels are different.   Number of ways to arrange these vowels among themselves = 2! = 2 x 1 = 2   Total number of ways = 24 x 2 = 48. Answer : Option 48
Answer: B
Four different children have jelly beans: Aaron has 3, Bianca has 7, Callie has 8, and Dante has 11. How many jelly beans must Dante give to Aaron to ensure that no child has more than 1 fewer jelly beans than any other child?	Pick one:
A) 2	B) 3	C) 4	D) 5	E) 6

Solution: Since Bianca and Callie are both within 1 jelly bean of each other and Aaron has 5, Dante must provide 3 of his 11 jelly beans so each child has no more than 1 fewer jelly bean than any other child.   Dante + Aaron = 11+3= 
11+3 = 14
14/2= 
14/2 = 7
7   11-7= 
11-7 = 4
4 so Dante must provide 3 jelly beans to Aaron.   Answer (4)
Answer: C
At a party, everyone shook hands with everybody else. There were 66 handshakes. How many people were at the party?	Pick:
A) 12  B) 15  C) 17  D) 19  E) 11

Solution: In general, with n+1 people, the number of handshakes is the sum of the first n consecutive numbers: 1+2+3+ ... + n.   Since this sum is n(n+1)/2, we need to solve the equation n(n+1)/2 = 66.   This is the quadratic equation n2+ n -132 = 0. Solving for n, we obtain 11 as the answer and deduce that there were 12 people at the party.   Since 66 is a relatively small number, you can also solve this problem with a hand calculator. Add 1 + 2 = + 3 = +... etc. until the total is 66. The last number that you entered (11) is n.
Answer: A
A shopkeeper sells his goods at cost price but uses a faulty meter that weighs 900 grams. Find the profit percent.	Choices
A) 100/17%  B) 100/23%  C) 100/9%  D) 100/13%  E) None of these

Solution: Explanation:   (100 + g) / (100 + x) = True measure / Faulty measure   x = 0   true measure = 1000   faulty measure = 900   100 + g / 100 + 0 = 1000 / 900   100+g = 10/9*100   g = 100/9 %   ANSWER: 100/9%
Answer: C
The price of a T.V. set worth Rs. 40000 is to be paid in 20 installments of Rs. 2500 each. If the rate of interest be 6% per annum, and the first installment be paid at the time of purchase, then the value of the last installment covering the interest as well will be? Choose the most appropriate option
A) 29997	B) 28088	C) 27098	D) 37500	E) 2799

Solution: Money paid in cash = Rs. 2500   Balance payment = (40000- 2500) = Rs. 37500.   Answer:37500
Answer: D
Find out the C.I on Rs.5000 at 4% p.a. compound half-yearly for 1 1/2 years.  Choose the correct option:  A) Rs.420.20  B) Rs.319.06  C) Rs.306.04  D) Rs.294.75  E) Rs.295.75

Solution: A = 5000(51/50)3   = 5306.04   5000   -----------   306.04   ANSWER:Rs.306.04
Answer: C
From an island, it is possible to reach the mainland by either Ferry P or Ferry Q. Ferry P travels for 3 hours at 8 kilometers per hour, while Ferry Q takes a route that is three times longer. If Ferry P is slower than Ferry Q by 1 kilometer per hour, how many hours longer is the journey of Ferry Q compared with the journey of Ferry P?  Choose one:  A) 5  B) 7  C) 8  D) 10  E) 12

Solution: The distance traveled by Ferry P is 24 km.   Then the distance traveled by Ferry Q is 72 km. Ferry Q travels at a speed of 9 kph. The time of the journey for Ferry Q is  72/9= 
 72/9 = 8
8 hours, which is 5 hours more than Ferry P. The answer is 5.
Answer: A
Two pipes A and B can separately fill a tank in 2 minutes and 15 minutes respectively. Both the pipes are opened together but 4 minutes after the start the pipe A is turned off. How much time will it take to fill the tank?	Choose the correct answer: A) 8 B) 10 C) 12 D) 14 E) 15

Solution: 4/12 + x/15 = 1   x = 10 min   ANSWER 10
Answer: B
The average number of shirts with Salman, Ambani and Dalmiya is 60, if all of them reached a shopping mall in Delhi and purchased 6 shirts each of them then average number of shirt each of them now has
Choose the correct choice from the following answers:
A) 66	B) 63	C) 62	D) can't be determined	E) None of these

Solution: 66nswer   Required average   = Old average + New average   = 60 + 6= 
60 + 6 = 66
66   Correct Option: 66
Answer: A
If James has to pay 12 % interest per year on an amount of $60,000 for 12 year then what is total interest paid?	Options: A) 33000 B) 35410 C) 36074 D) 35973 E) 32158

Solution: For simple interest, I = P * N * R / 100   let Principle P = x   I = x * 12 * 12 / 100   I = 1.44 * x   Amount = P + I   60000 = 1.44 x + x   x = 24590.16 = P   I = 1.44 * 24590.16   I = 35409.83   35410
Answer: B
By approximately what percent is x greater than 5/11 if (4/11)(x) = 1? Choose the correct choice from the following
A) 730%  B) 560%  C) 410%  D) 505%  E) 209%

Solution: what percent is x greater than 5/11 if (4/11)(x) = 1?   => x = 11/4   % change =[(11/4 -5/11) /(5/11) ] * 100   = 505%   Ans ,505%
Answer: D
Find the expenditure on digging a well 14m deep and of 3m diameter at Rs.16 per cubic meter? Pick.
A) 2998  B) 2799  C) 2890  D) 1485  E) 1584

Solution: 22/7 * 14 * 3/2 * 3/2= 
22/7 * 14 * 3/2 * 3/2 = 99
99 m2   99 * 16= 
99 * 16 = 1_584
1584   Answer:1584
Answer: E
A farmer used 1,034 acres of land for beans, wheat, and corn in the ratio of 5 : 2 : 4, respectively. How many E acres were used for corn?  Answers:
A) 188  B) 258  C) 376  D) 470  E) 517

Solution: consider 5x acres of land used for bean   consider 2x acres of land used for wheat   consider 4x acres of land used for corn   Total given is 1034 acres   11x =1034   x = 94   land used for corn E= 4 * 94= 
4 * 94 = 376
376   correct option - 376
Answer: C
The cash difference between the selling prices of an book at a profit of 4% and 6% is $3. The ratio of the two selling prices is:	Answers: A) 55:23 B) 52:33 C) 52:53 D) 45:53 E) 51:34

Solution: C   52:53   Let C.P. of the book be $x.   Then, required ratio = 104% of x / 106% of x   = 104/106 = 52/53 = 52:53
Answer: C
if z=100^2-x^2,then for how many value of x, z is divisible by 6.  Select the correct option:  A) 33  B) 66  C) 44  D) 55  E) 77

Solution: x can be negative also.   33*2= 
33*2 = 66
66   ANSWER:66
Answer: B
In how many ways can the letters of the word ACUMEN be rearranged such that the vowels alwaysappear together?
Options:
A) 124 ways B) 144 ways C) 134 ways D) 154 ways E) 164 ways

Solution: ACUMEN   AUE will come together as a group which can be arranged in 3!=6 ways.   AUE, C,M,N can be arranged in 4!=24 ways.   total possible arrangements = 24*6= 
24*6 = 144
144 ways   ANSWER:144 ways
Answer: B
How many cuboids of length 5 m, width 3 m and height 2 m can be farmed from a cuboid of 18 m length, 15 m width and 2 m height.  Choose the correct choice from the following choices:
A) 106
B) 109
C) 108
D) 101
E) 104

Solution: (18 × 15 × 12)/(5 × 3 × 2) = 108   Answer is 108.
Answer: C
A work which could be finished in 9 days was finished 3 days earlier after 10 more men joined. The number of men employed was?
Choose the correct choice from the following answers:
A) 22	B) 20	C) 99	D) 277	E) 12

Solution: x ------- 9   (x + 10) ---- 6   x * 9 = (x + 10)6   x = 20   Answer: 20
Answer: B
The present ages of three persons in proportions 4 : 7 : 9. Eight years ago, the sum of their ages was 56. Find their present ages (in years).  Choose the correct choice from the following options:  A) 8, 20, 28  B) 16, 28, 36  C) 20, 35, 45  D) 20, 35, 48  E) None of these

Solution: Let the present ages are 4x, 7x, 9x.   => (4x-8) + (7x-8) + (9x-8) = 56   => 20x = 80   => x = 4   So their present ages are: 16,28,36   ANSWER:16, 28, 36
Answer: B
The average (arithmetic mean) of six numbers is 5. If 3 is subtracted from each of four of the numbers, what is the new average?	Choose the correct choice from the following.
A) 1.5  B) 2  C) 3  D) 4  E) 4.5

Solution: Sum of 6 numbers = 6*5= 
6*5 = 30
30   If 3 is subtracted from each of four of the numbers , we subtract  3*4= 
 3*4 = 12
12 from the total sum   Sum of 6 number after subtracting 3 from each of four of the numbers= 30 - 12= 
30 - 12 = 18
18   New average= 18/6= 
18/6 = 3
3   Answer 3
Answer: C
9.6 , 9.6 , 10.0 , 10.0 , 10.0 , 10.1 , 10.2 , 10.5
The mean and the standard deviation of the 8 numbers shown above is 10 and 0.278 respectively. What percent of the 8 numbers are within 1 standard deviation of the mean? Choose the most appropriate option:
A) 62.5%
B) 85%
C) 80.67%
D) 75.50%
E) 90.30%

Solution: Within 1 standard deviation of the mean- means in the range {mean-1*sd; mean+1*sd} = {10-1*0.278; 10+0.278} = {9.722; 10.278}.   From the 8 listed numbers, 5 are within this range so 5/8=62.5%.   62.5%nswer: 62.5%.
Answer: A
Two different types of tea are mixed, at 6 Kg of type 1 and 4 Kg of type 2. One Kg of type 1 is Rs. 6 and that of type 2 is Rs. 7. The seller get 10% profit, by this action. Find at what price, he had sold the mixture/Kg?  Choose the most appropriate option:
A) Rs 5.04
B) Rs 7.04
C) Rs 6.04
D) Rs 8.04
E) Rs 9.04

Solution: CP of 6 kg tea of type 1= 6*6= 
6*6 = 36
36 Rs.   CP of 4 kg tea of type 2= 4*7= 
4*7 = 28
Rs 28   CP of 10 kg mixed tea= Rs Rs 64   SP of mixture for 10% profit = 64*1.1= 
64*1.1 = 70.4
Rs 70.4   SP of 1kg mixed tea= Rs 7.04   ANSWER:Rs 7.04
Answer: B
The distance between 2 cities A and B is 1000km. A train starts from A at 12 p.m. and travels towards B at 100 km/hr. Another starts from B at 1 p.m. and travels towards A at 150 km/hr. At what time do they meet?  Select:  A) 11am.  B) 12p.m.  C) 5pm.  D) 2p.m.  E) 1p.m.

Solution: Suppose they meet x hrs after 12 p.m.   Distance moved by first in x hrs + Distance moved by second in (x-1)hrs = 1000   100x + 150 (x-1) = 1000   x = 4.60 = 5 hrs   They meet at 10+5 = 5 p.m.   Answer is 5pm.
Answer: C
If a – b = 3 and a2 + b2 = 29, find the value of ab.	Choose the correct choice from the following options.
A) 10 B) 12 C) 15 D) 18 E) 19

Solution: EXPLANATION   2ab = (a2 + b2) – (a – b)2   = 29 – 9 = 20   ab = 10.   10nswer 10
Answer: A
A trader purchased two colour televisions for a total of Rs. 35000. He sold one colour television at 30% profit and the other 40% profit. Find the difference in the cost prices of the two televisions if he made an overall profit of 30%?	Pick.
A) Rs. 28985
B) Rs. 40985
C) Rs. 20985
D) Rs. 21000
E) Rs. 30985

Solution: Let the cost prices of the colour television sold at 30% profit and 40% profit be Rs. x and Rs. (35000 - x) respectively.   Total selling price of televisions = x + 30/100 x + (35000 - x) + 40/100 (35000 - x)   => 130/100 x + 140/100 (35000 - x) = 35000 + 30/100 (35000)   x = 27985   35000 - x = 6985   Difference in the cost prices of televisions = Rs. 20985   ANSWER:Rs. 20985
Answer: C
If f(x) = Log(x), then f -1(x) =	Select.
A) 10 x
B) -10 -x
C) 1 / 10 x
D) x 10
E) NONE

Solution: Solution   y = Log(x) if and only if   x = 10y   Interchange x and y   y = 10x   Hence   f -1(x) = 10x   10 xnswer 10 x
Answer: A
An aeroplane covers a particular distance at a speed of 240 kmph in 5 hours. To cover the same distance in 1 hour, it must travel at a speed of
Choices
A) 300 kmph  B) 720 kmph  C) 700 kmph  D) 450 kmph  E) 500 kmph

Solution: distance=(240*5)= 
(240*5) = 1_200
1200 km   speed=dist/time   req speed = 1200/(5/3)= 
1200/(5/3) = 720
>720km/hr   ANSWER 720 kmph
Answer: B
Machine A takes 100 hours to complete a certain job and starts that job at 6AM. After ten hour of working alone, machine A is joined by machine B and together they complete the job at 6PM. How long would it have taken machine B to complete the job if it had worked alone for the entire job? Choose the correct answer
A) 24.65
B) 22.27
C) 2.273
D) 11.62
E) 21.13

Solution: Let us assume total job = 100 units   A finishes 100 units in 100 hrs(given)   Hence A (working rate)= 1 units /hr   Now Given that A works for 10 hr( so 10 units done) then A and B finish total work in 12 hours. Hence A and B finish 90 units in 2 hours. Of these 1x2=2 units were done by A. Hence B did 88units in 2 hours.   Hence B(working rate)= 44 units /hr   Hence B takes 100/44 = 2.273 hours to complete the job.   Answer 2.273.
Answer: C
A pipe can empty 3/4th of a cistern in 12mins. In 8 mins, what part of the cistern will be empty?	Choose the most appropriate option: A) 1/2 B) 3/7 C) 4/9 D) 3/8 E) 4/7

Solution: 3/4 ---- 12   ? ----- 8 ==> 1/2   1/2
Answer: A
The population of a town is 176400. If it increase at the rate of 5% per annum. What was its population 4 years ago?	Choose the most appropriate option:
A) 152460
B) 214560
C) 145125
D) 210000
E) 200000

Solution: population 2 years ago = 176400/(1 + 5/100)^4   Answer is 145125
Answer: C
Frank is 13 years younger then John. In 5 years John will be twice as old as Frank. How old will Frank be in four years? Choose the correct choice from the following answers
A) 8
B) 10
C) 12
D) 14
E) 16

Solution: Frank is 15 years younger then John --> F+13=J;   In 5 years John will be twice as old as Frank (in 5 year John will be J+5 years old and Frank will be F+5 years old) --> J+5=2*(F+5) --> (F+13)+5=2*(F+5) --> F=8;   In 4 years Frank will be 8+4= 
8+4 = 12
12 years old.   Answer: 12.
Answer: C
In a certain game there are 7 steps, referred to as step 1, step 2, and so on with the final step being step 7. The steps are played one after the other. In each step a score of 1, 2,3 or 4 is obtained. Mary played the game, getting at least one score of each of 1, 2, 3 and 4 and never getting the same score in consecutive steps. What is the greatest possible score that Mary could have gotten?  Choose the correct choice from the following options: A) 20 B) 19 C) 17 D) 18 E) 16

Solution: There are two conditions:   1. Mary got at least one score of each of 1, 2, 3 and 4.   2. She never got the same score in consecutive steps.   Taking that into account, the greatest possible score that Angel could have gotten is  4 + 1 + 4 + 2+4+3= 
 4 + 1 + 4 + 2+4+3 = 18
18   Answer: 18.
Answer: D
A 200 meter long train running at the speed of 120 kmph crosses another train running in the opposite direction at the speed of 80 kmph in 9 seconds.What is the lenght of other train.  Options
A) 210m
B) 300m
C) 230m
D) 240m
E) 250m

Solution: Relative speeds=(120+80)km/hr   =200km/hr=(200*5/18)m/s=(500/9)m/s   let length of train be xm   x+200/9=500/9   x=300   Ans is 300m   ANSWER:300m
Answer: B
A train running at the speed of 54 km/hr crosses a pole in 9 seconds. Find the length of the train?  Choose the correct choice.
A) 135 B) 272 C) 278 D) 277 E) 112

Solution: Speed = 54*(5/18) m/sec = 15 m/sec   Length of Train (Distance) = Speed * Time     (15) * 9= 
  (15) * 9 = 135
135 meter   135nswer: 135
Answer: A
From given equation find the value of x: 2x² + 9x − 5	Choose the most appropriate option.
A) −5 B) -4 C) -3 D) 3 E) 4

Solution: That quadratic is factored as follows:   2x² + 9x − 5 = (2x − 1)(x + 5).   Lesson 17.   Now, it is easy to see that the second factor will be 0 when x = −5.   As for the value of x that will make   2x − 1 = 0,   we must solve that little equation. (Lesson 9.)   We have:   2x = 1   x = 1   2   The solutions are:   x = 1/2 or −5   −5
Answer: A
A and B working separately can complete a piece of work in 9 and 12 days respectively. If they work alternatively starting from A in how many days will the work be completed?  Choose the correct choice: A) 10.21 days B) 10.23 days C) 18.25 days D) 10.25 days E) 40.25 days

Solution: Explanation:   A takes 9 days to complete a piece of work. B takes 12 days to complete a piece of work.   => In one day A came complete 1/9th of the task(x/9)   => In one day B can complete 1/12th of the job.(x/12)   First day x/9th work will be done next day x/12th and so on:   Together A and B can do x/9 + x/12 work.   =>(x/9) + (x/12) = 7/36th work done   In 10 days 35/36th of the work will be done.   On 11th day it will be A’s chance. It takes A 1 day to complete 1/9th work.   So, 1/36th work will be done in 1/4 days.   =>10.25 days   ANSWER: 10.25 days
Answer: D
Find the value of (875 233/899) × 899  Select
A) 788658 B) 786858 C) 788865 D) 786588 E) None of them

Solution: =(875 233/899) × 899   =(786625 + 233)/899 × 899   =786858/899 × 899   =786858   Answer is 786858.
Answer: B
If c = (1/4)a and b = 7c, then which of the following represents the average (arithmetic mean) of a, b, and c, in terms of c ?  Choose the correct choice from the following answers:
A) 2b
B) 3b
C) 4b
D) 5b
E) 12b

Solution: a = (4)c and b =7c.   The mean = (a + b + c)/3 = (4c + 7c + b)/3 = 4b.   Answer is 4b
Answer: C
A train of length 230 metres takes 58 seconds to cross a tunnel of length 60 metres. What is the speed of the train in km/hr?  Select the correct option:  A) 58 km/hr.  B) 60 km/hr.  C) 30 km/hr.  D) 18 km/hr.  E) None

Solution: Sol.   Speed = [230 + 60 / 58] m/sec = [290 /58 * 18/5] km/hr = 18 km/hr.   Answer 18 km/hr.
Answer: D
If x, y, and z are distinct positive prime numbers, then (x^3)(y)(z) has how many different positive factors greater than 1?
Answers:	A) a. 8	B) b. 9	C) c. 12	D) d. 15	E) e. 17

Solution: Let Number is (x^3)(y)(z) = (3^3)(4)(5) = 180   We can write 180 as product of two numbers in following ways   1*180   2*90   3*60   4*45   5*36   6*30   9*20   10*18   12*15 9 cases = 9*2 i.e. 18 factors (including 1)   Factors greater than 1 = 17   Answer: Option e. 17
Answer: E
Two pipes can fill a tank in 18 and 12 hours, while third pipe will make the tank empty in 20 hours. If all three pipes operate simultaneously. In how many hours the tank will be filled ?	Choose one.
A) 5.25 Hours B) 7.25 Hours C) 8.25 Hours D) 9.25 Hours E) 11.25 Hours

Solution: In 1 hour it fill 1/18 + 1/12 - 1/20 = 4/45   So fill tank fill up in 45/4= 
45/4 = 45/4 = around 11.25
11.25 Hours   ANSW11.25 HoursR:11.25 Hours
Answer: E
The speed of a boat in upstream is 30 kmph and the speed of the boat downstream is 70 kmph. Find the speed of the boat in still water and the speed of the stream?  Choose the correct choice: A) 22 kmph B) 20 kmph C) 21 kmph D) 26 kmph E) 28 kmph

Solution: Speed of the boat in still water = (30+70)/2= 
(30+70)/2 = 50
50 kmph. Speed of the stream= (70-30)/2= 
(70-30)/2 = 20
20 kmph.   Answer:20 kmph
Answer: B
The average of the marks of 12 students in a class is 36. If the marks of each student are doubled, find the new average?
Options:
A) 72	B) 82	C) 97	D) 268	E) 27

Solution: Sum of the marks for the 12 students = 12 * 36= 
12 * 36 = 432
432. The marks of each student are doubled, the sum also will be doubled.   The new sum= 432 * 2= 
432 * 2 = 864
864. So, the new average= 864/12= 
864/12 = 72
72.   72nswer:72
Answer: A
A sum of money is to be distributed among A, B, C, D in the proportion of 5 : 2 : 4 : 3. If C gets Rs. 1000 more than D, what is B's share? Answers:  A) 500  B) 1500  C) 2000  D) 1220  E) 1000

Solution: Let the shares of A, B, C and D be Rs. 5x, Rs. 2x, Rs. 4x and Rs. 3x respectively.   Then, 4x - 3x = 1000   x = 1000.   B's share = Rs. 2x = Rs. (2 x 1000) = Rs. 2000.   so the answer is option 2000) 2000
Answer: C
In a family 19 people eat only vegetarian, 9 people eat only non veg., 12 people eat both veg and non veg.. How many people eat veg in the family? Options.
A) 20
B) 31
C) 9
D) 31
E) 21

Solution: Total people eat veg = only veg + both veg and non veg   Total= 19+12= 
19+12 = 31
31   Answer= 31
Answer: B
The traffic lights at 3 different roads change after every 36 sec, 72 sec, 108 sec respectively. If they all change simultaneously at 9:15 AM then at what time will they again change simultaneously.	Choose the correct choice from the following options.
A) 9:18:36	B) 9:42:15	C) 10:15:24	D) 9:54:12	E) 10:01:20

Solution: LCM of 36,72,108 = 216 = 3mnts 36sec   The lines will change every 3m 36sec   The light will change again after 9:15 9:18:36M is = 9:15+0:03:36 = 9:18:36   9:18:36nswer is 9:18:36
Answer: A
A cistern is filled by pipe A in 20 hours and the full cistern can be leaked out by an exhaust pipe B in 25 hours. If both the pipes are opened, in what time the cistern is full?
Select the correct option: A) 50hrs B) 60hrs C) 70hrs D) 80hrs E) 100hrs

Solution: time taken to full the cistern=(1/20-1/25)hrs   =1/100   =100hrs   ANSW100hrsR:100hrs
Answer: E
What is the greatest value of n such that 24^n is a factor of 24! ?	Choose the correct choice from the following choices
A) 1  B) 2  C) 3  D) 4  E) 8

Solution: Another way to solve this question :   We know that 18 = 2 *3^2.   Hence, we need to find total number of 3s in 18! ( As out of 3 and 2 , we will have count of 3 least)   No. of 3s = 18/3= 
18/3 = 6
6/3= 
6/3 = 2
2.   Add the numbers in Bold, you will get total number of 3s= 8.   Hence, total number of 4^2 = 16/2= 
16/2 = 8
8.   Hence, answer is 8. 8
Answer: E
20 14 8
10 5 10
5 ? 3  Choose the most appropriate option: A) 2 B) 3 C) 4 D) 5 E) 6

Solution: difference bet 20&14=6 and 14&8=6   10&5=5 and 5&10=5   similarly   5&4=1 and 4&3=1   ans is 4   ANSWER:4
Answer: C
find value for x from given equation ? x + 1 = -3	Pick
A) 1 B) x=-4 C) -3 D) -5 E) 5

Solution: 1. Subtract 1 from both sides:   x + 1 - 1 = -3 - 1   2. Simplify both sides:   x = -4   x=-4
Answer: B
Solve This
6 + 7 = 12
8 + 9 = 16
5 + 6 = 10
7 + 8 = 14
Then, 9 + 3 = ??  Answers:
A) 11 B) 12 C) 13 D) 14 E) 18

Solution: 11   11NSWER:11
Answer: A
A boat can move upstream at 20 kmph and downstream at 34 kmph, then the speed of the current is? Choose the correct choice from the following answers
A) 7	B) 6	C) 8	D) 4	E) 2

Solution: US = 20   DS = 34   M = (34 - 20)/2= 
(34 - 20)/2 = 7
7 7nswer:7
Answer: A
The percentage profit earned by selling an article for Rs. 1920 is equal to the percentage loss incurred by selling the same article for Rs. 1280. At what price should the article be sold to make 25% profit?	Choose the correct choice from the following answers:
A) Rs.1000
B) Rs.1500
C) Rs.6000
D) Rs.3000
E) Rs.2000

Solution: Explanation:   Let C.P. be Rs. x.   Then,1920-x/x*100=x-1280/x*100   1920 - x = x - 1280   2x = 3200   x = 1600   Required S.P. = 125% of Rs. 1600 = Rs.(125/100*1600) Rs.2000   ANSWRs.2000R:Rs.2000
Answer: E
A man is walking at a speed of 10 km per hour. After every kilometre, he takes rest for 6 minutes. How much time will be take to cover a distance of 6 kilometres?	Choose the correct choice:  A) 48 min.  B) 50 min.  C) 66 min.  D) 55 min.  E) None of these

Solution: Rest time = Number of rest Ã— Time for each rest   = 5 Ã— 6 = 30 minutes   Total time to cover 6 km   = (6â„10 Ã— 60)minutes + 30 minutes = 66 minutes   Answer 66 min.
Answer: C
3 friends A, B, C went for week end party to McDonald’s restaurant and there they measure there weights in some order In 7 rounds. A, B, C, AB, BC, AC, ABC. Final round measure is 175kg then find the average weight of all the 7 rounds?	Answers: A) 100 kgs B) 88.5 kgs C) 86.5 kgs D) 67.5 kgs E) 88.2 kgs

Solution: 100 kgsverage weight = [(a + b + c + (a+b) + (b+c) + (c+a)+(a+b+c)] / 7 = 4 (a+b+c) /7 = 4 x 175/7 = 100 kgs   100 kgsnswer:100 kgs
Answer: A