MU-NLPC/Calc-aqua_rat huggingface dataset:
QUANT 4-PACK SERIES Problem Solving Pack 4 Question 2 For every positive integer n...
For every positive integer n that is greater than 1, the function s(n) is defined to be the sum of all of the odd integers from 1 to n, inclusive. The s(n) could have any of the following units digits except…?
Choose one
A) 1	B) 2	C) 4	D) 6	E) 9

Solution: For every positive integer n that is greater than 1, the function s(n) is defined to be the sum of all of the odd integers from 1 to n, inclusive. The s(n) could have any of the following units digits except…?   Used brute force on this one to calculate. Not sure if there is a quicker way.   1+3= 
1+3 = 4
4 C is out   1+3+....15= 81 A is out   1+3+5+7= 
1+3+5+7 = 16
16 D is out   1+3+5= 
1+3+5 = 9
9 E i out   Answer: 2
Answer: B
Two trains of equal lengths take 10 sec and 20 sec respectively to cross a telegraph post. If the length of each train be 120 m, in what time will they cross other travelling in opposite direction?	Select: A) 16 sec B) 13 sec C) 17 sec D) 21 sec E) 23 sec

Solution: Speed of the first train = 120/10= 
120/10 = 12
12 m/sec.   Speed of the second train= 120/20= 
120/20 = 6
6 m/sec.   Relative speed= 12 + 6= 
12 + 6 = 18
18 m/sec.   Required time= (120 + 120)/18 = 13 sec.   Answer: 13 sec
Answer: B
A palindrome is a word or a number that reads the same forward and backward. For example, 2442 and 111 are palindromes. If 5-digit palindromes are formed using one or more of the digits 1 and 2, how many palindromes are possible? Choose the correct choice from the following choices.
A) 8  B) 12  C) 16  D) 24  E) 32

Solution: There are 2 choices for each of the first three digits.   The number of possible palindromes is 2^3=8.   The answer is 8.
Answer: A
If a number is formed by writing integers 1 to 150 one after another, like 12345...150. How many E digits does this integer consists of?
Choose the correct choice from the following choices:
A) 150 B) 339 C) 342 D) 359 E) 362

Solution: Number of single digit integers = 9   Number of 2 digit integers = 99 - 10 + 1= 
99 - 10 + 1 = 90
90   Number of 3 digit integers= 150 - 100 + 1= 
150 - 100 + 1 = 51
51   Number of digits in the integer E= 1*9 + 2*90 + 3*51 = 9 + 180 + 153= 
9 + 180 + 153 = 342
342   Answer: 342
Answer: C
If |y−12|<112|y−12|<112, which of the following could be a value of y? Choose the correct choice from the following:
A) -11  B) -11/2  C) 11/2  D) 11  E) 22

Solution: |y−12|<112|y−12|<112, is equivalent to −112<y−12<112−112<y−12<112. --="" 1212="" add="" each="" inequality:="" of="" part="" the="" to="" −112+12<y<112+12−112+12<y<112+12=""> −5<y<6−5<y<6.   Only answer C is from this range.   Answer: 11/2.</y−12<112−112<y−12<112.>
Answer: C
The speed of a boat in upstream is 60 kmph and the speed of the boat downstream is 80 kmph. Find the speed of the boat in still water and the speed of the stream?
Options.
A) 10 B) 99 C) 88 D) 66 E) 23

Solution: Speed of the boat in still water = (60+80)/2= 
(60+80)/2 = 70
70 kmph. Speed of the stream= (80-60)/2= 
(80-60)/2 = 10
10 kmph. 10nswer:10
Answer: A
The sum of two numbers is 40 and their product is 1050. What will be the sum of their reciprocals? Select.
A) (4/105)  B) (11/210)  C) (35/4)  D) (75/8)  E) None

Solution: Solution   x+y=40 xy=1050 1/x+1/y=x+y/xy 40/1050 = (4/105).   (4/105)nswer (4/105)
Answer: A
A man invests some money partly in 9% stock at 96 and partly in 12% stock at 120. To obtain equal dividends from both, he must invest the money in the ratio: Choose the correct choice from the following answers.
A) 16:15 B) 15:16 C) 12:11 D) 11:13 E) 13:18

Solution: Let the Face Value of Stock giving dividend 9% be Rs. x, whose Market Value is Rs.96.   Let the Face Value of Stock giving dividend 12% be Rs. y, whose Market Value is Rs.120.   By given formula,   Face Value * Dividend % / Market Value = Annual income.   Annual Income from 1st Stock = 9x/96.   Annual Income from 2nd Stock = 12y/120.   To obtain equal dividends from both,   Annual Income from 1st Stock = Annual Income from 2nd Stock.   = 9x/96 = 12y/120.   = x/y = 96/90.   We find GCD of 96, 90 = 6.   = x/y = 16*6 / 15*6.   = Required ratio = x:y = 16:15.   answer : 16:15
Answer: A
0.05 x 0.03 = ? Choose the correct option.
A) 0.00015 B) 0.015 C) 0.0015 D) 0.15 E) 1.5

Solution: 5 x 3 = 15.   Sum of decimal places = 4   0.05 x 0.03 = 0.0015   Answer: Option 0.0015
Answer: C
Dan's age after 18 years will be 8 times his age 3 years ago. What is the present age of Dan?
Choose the correct choice from the following options:  A) 4  B) 6  C) 8  D) 10  E) 12

Solution: Let Dan's present age be x.   x+18 = 8(x-3)   7x = 42   x = 6   The answer is 6.
Answer: B
A zinc-copper alloy with 6 kg of pure zinc would contain 90% of zinc. The alloy with 3 kg of 90% zinc alloy contains 84% of zinc. Calculate the weight and percentage of zinc in the zinc-copper alloy.
Choose the correct option
A) 2.4 kg or 80%  B) 1.4 kg or 88%  C) 3.4 kg or 60%  D) 4.9 kg or 81.4%  E) 1.4 kg or 60%

Solution: Right Answer Explanation:   x : 6   y : 100   90   10 : 90 – y   (90-y)/6 = 10/x = ………..(1)   In the second case,   x 3   y 90   84   6 84-y   Therefore (84-y)/3 = 6/x ………..(2)   4.9 kg or 81.4%ividing (1) and (2)   =   270 – 3y = 840 – 10y   7y = 570   y = 81.4   x = 60/(90-80) = 60/10= 
60/10 = 6
6 kg   Quantity of zinc in x= 81.4% of x   = 0.814 6   = 4.9 kg   Weight and percentage of zinc is 4.9 kg or 81.4%   4.9 kg or 81.4%
Answer: D
A machine fills 150 bottles of water every 8 minutes. How many minutes it takes this machine to fill 675 bottles?	Choices
A) 12 min
B) 34 min
C) 32 min
D) 45 min
E) 29 min

Solution: 8 minutes are needed to fill 150 bottles. How many groups of 150 bottles are there in 675 bottles?   675 ÷ 150 = 4.5 = 4 and 1/2   For each of these groups 8 minutes are needed. For 4 groups and 1/2   8 × 4 + 4 = 32 + 4= 
32 + 4 = 36
36 minutes. (4 is for 1/2 a group that needs half time)   We can also find the final answer as follows   4.5 x 8= 32 minutes   correct answer is 32 min) 32 min
Answer: C
Set G consists of all even integers between 2 and 100, inclusive. Set X is derived by reducing each term in set G by 50, set Y is derived by multiplying each term in set G by 1.5, and set Z is derived by dividing each term in set G by -4. Which of the following represents the ranking of the three sets in descending order of standard deviation?
Choose the correct choice from the following choices.
A) X, Y, Z B) X, Z, Y C) Y, Z, X D) Y, X, Z E) Z, Y, X

Solution: Set G - {2, 4, ..., 100};   Set X - {-48, -46, ..., 50};   Set Y - {3, 6, ..., 150};   Set Z - {-2/4, -4/4, ..., -100/4} = {-1/2, -1, -3/2, ..., -25}.   If we add or subtract a constant to each term in a set the SD will not change, so sets G and X will have the same SD.   If we increase or decrease each term in a set by the same percent (multiply by a constant) the SD will increase or decrease by the same percent, so set Y will have 1.5 times greater SD than set G and set Z will have 4 times less SD than set G (note SD can not be negative so SD of Z wil be SD of G divided by 4 not by -4).   So, the ranking of SD's in descending order is: Y, G=X, Z.   Answer: Y, X, Z.
Answer: D
The area of a rectangular field is equal to 300 square meters. Its perimeter is equal to 70 meters. Find the width of this rectangle.	Pick
A) 5  B) 10  C) 15  D) 20  E) 25

Solution: L * W = 300 : area , L is the length and W is the width.   2 L + 2 W = 70 : perimeter   L = 35 - w : solve for L   (35 - W) * W = 300 : substitute in the area equation   W = 15 and L = 20 : solve for W and find L using L = 35 - w.   correct answer 15
Answer: C
A military garrison in a wild frontier has 60 men who have provisions to last 26 weeks. At the end of 6 weeks they are joined by another 30 men. How long will the provisions last?	Choose one
A) 13 1/3	B) 12 1/3	C) 11 3/3	D) 12 1/2	E) 12 3/4

Solution: Total provisions=600*26*7=10920   Provisions used for in 6 weeks=6*7*600=2520   remaining provisions=8400   remaining provisions need to be split between 90(60+30) people.   Number of provisions per person= 8400/90   we need to find the answer in terms of weeks=(8400/90)/7=40/3   13 1/3nswer:13 1/3
Answer: A
By selling an article at Rs.900, a shopkeeper makes a profit of 25%. At what price should he sell the article so as to make a loss of 25%? Choose the correct option
A) s.600 B) s.480 C) s.500 D) s.540 E) s.550

Solution: SP = 900   Profit = 25%   CP = (SP)*[100/(100+P)]   = 900 * [100/125]   = 720   Loss 900 *  100/125= 
900 *  100/125 = 720
720   Loss= 25% = 25% of 720 = Rs.180   SP = CP - Loss = 720 - 180 = Rs.540   ANSWER:s.540
Answer: D
xy=2 then what is (2^(x+y)^2) / (2^(x-y)^2)	Choose one:
A) 2 B) 4 C) 8 D) 16 E) 256

Solution: (x+y)^2 - (x-y)^2   (x+y+x-y)(x+y-x+y)   (2x)(2y)   4xy   8   2^8 = 256   Answer 256
Answer: E
If x < y < z and y - x > 5, where x is an even integer and y and z are odd integers, what is the least possible value A of z - x? Choose the correct choice from the following:
A) 6  B) 7  C) 8  D) 9  E) 10

Solution: x<y<z and="" be="" can="" closest="" could="" each="" even="" find="" for="" if="" is="" least="" minimum="" need="" number="" number,="" odd="" other.="" possible="" some="" that="" the="" then="" to="" value="" values="" we="" what="" x="" y-x="" z="" z-x;="" z.="">5; y>x+5; minimum value for y</y<z>=x+5+2=x+7[Note: x+5 is as even+odd=odd and nearest odd greater than x+5 is x+5+2]   Minimum value for z=y+2=x+7+2=x+9 [Note: z=y+2 because both z and y are odd. 9ifference between two odd numbers is 2]   A=z-x = x+9-x= 9   Ans:9
Answer: D
I have 150 pieces of cake. There are 50 friends in my house. I would like to give each friend the same amount of cake, how much should I give to each friend?
Choose the correct choice from the following options.
A) 12
B) 7
C) 9
D) 15
E) 3

Solution: 150/50= 
150/50 = 3
3   The answer is 3.
Answer: E
Working together, Jose and Jane can complete an assigned task in 12 days. However, if Jose worked alone and complete half the work and then Jane takes over the task and completes the second half of the task, the task will be completed in 48 days. How long will Jose take to complete the task if he worked alone? Assume that Jane is more efficient than Jose Choose the correct choice from the following choices
A) 25 days B) 30 days C) 60 days D) 65 days E) 36 days

Solution: Assume:   Jose does 1 job in x days, so Jose does 1/x job in a day   Jane does 1 job in y days, so Jane does 1/y job in a day   Together, they does (x+y)/xy job in a day. This is equals to 1/20. So   (x+y)/xy = 1/12   12(x+y) = xy   Next, we're told 1 job takes 48 days to complete if Jose and Jane each does half the work. So since Jose does 1 job in x days, he wil need x/2 days to do half the job. Jane similarly will need y/2 days to do the other half.   x/2 + y/2 = 48   x+y = 96   So   xy = 1152   The answer choices are:   25 days   30 days   60 days   65 days   36 days   From the answer choices, So I'll go for 36 days for Jose and 32 days for Jane.   Answer : 36 days
Answer: E
In a race of 1000 m, A can beat by 100 m, in a race of 800m, B can beat C by 100m. By how many meters will A beat C in a race of 600 m ?
Choices.
A) 127.5 m	B) 254 m	C) 184 m	D) 212 m	E) 314 m

Solution: Explanation:   When A runs 1000 m, B runs 900 m and when B runs 800 m, C runs 700 m.   When B runs 900 m, distance that C runs = (900 x 700)/800 = 6300/8= 
6300/8 = 1_575/2 = around 787.5
787.5 m.   In a race of 1000 m, A beats C by   (1000 - 787.5)= 
  (1000 - 787.5) = 212.5
212.5 m to C.   In a race of 600 m, the number of meters by which A beats C= (600 x 212.5)/1000 = 127.5 m.   127.5 mNSWER IS 127.5 m
Answer: A
There are a total of 11 students in Mr. Michael's gym class. Over the course of a badminton unit, each of the 11 students will compete exactly once against every other student in the class. How many total games of badminton will be played?
Choose the correct choice from the following answers.
A) 58 B) 51 C) 52 D) 55 E) 59

Solution: there are 11 students , if each play with all other members .   then total games can be calculated as 10+9....+1 = 55.   alternate approach is to choose 2 distinct out of 11 = 11c2 = 55   Answer is 55.
Answer: D
J is faster than P. J and P each walk 24 km. Sum ofthe speeds of J and P is 7 kmph. Sum of time taken by them is 14 hours. Then J speed is equal to?
Pick
A) 4  B) 5  C) 6  D) 7  E) 8

Solution: let j's speed is x then p's speed would be 7-x.   and given,   sum of time taken by them is 14 hours   =>(24/x)+(24/(7-x)=14   =>x=4,3   therefore j's speed will be 4 as j walks faster than p.   4NSWER:4
Answer: A
A box contains 2 red balls and 5 black balls. One by one, every ball is selected at random without replacement. What is the probability that the fourth ball selected is black?  Choose one:
A) 1/4  B) 7/5  C) 1/2  D) 5/8  E) 2/3

Solution: My complicated version of your simple approach   Let the 5 black balls be 7/57/57/57/57/5 and 2 Red 7/5alls be RRR   They can be arranged in 8 slots _ _ _ _ _ _ _ _   in (7!)/ (5!x2!)   If the fourth slot is 7/5lack ball then the arrangement will be to fill   _ _ _ 7/5 _ _ _ _   we have 6 slots and 4 7/5lack (7/57/57/57/5) and 2 Red (RRR)   They can be arranged in (7!)/ (4!x2!)   Hence required probability = [(7!)/ (5!x2!)]/[(6!)/ (4!x2!)]=7/5   7/5
Answer: B
A dress on sale in a shop is marked at $D. During the discount sale its price is reduced by 55%. Staff are allowed a further 50% reduction on the discounted price. If a staff member buys the dress what will she have to pay in terms of D ? Choose the correct choice from the following:  A) 0.275D  B) 0.225D  C) 0.265D  D) 0.245D  E) 0.205D

Solution: Effective discount = a + b + ab/100 = - 55 - 50 + (-55)(-50)/100 = 77.5   Sale price = D * ( 1 - 77.5/100)   Sale price = .225 * D   Answer (0.225D)
Answer: B
If the number 481 * 673 is completely divisible by 9, then the smallest whole number in place of * will b Choose the correct choice from the following options:
A) 4
B) 5
C) 7
D) 8
E) 9

Solution: Sum of digits = (4 + 8 + 1 + x + 6 + 7 + 3) = (29 + x), which must be divisible by 9.   x = 7.   7)
Answer: C
Two trains of equal length, running with the speeds of 60 and 90 kmph, take 50 seconds to cross each other while they are running in the same direction. What time will they take to cross each other if they are running in opposite directions?	Choose the correct choice
A) 3.2  B) 2.6  C) 6.6  D) 32.2  E) 42.2

Solution: RS = 60 -40= 
60 -40 = 20
20 * 5/18= 100/18   T = 50   D = 50 * 100/18 = 2500/9   RS = 60 + 90= 
60 + 90 = 150
150 * 5/18   T= 2500/9 * 18/750 = 6.6 sec.Answer: 6.6
Answer: C
If a^2x = b^y, then	Choices
A) log a/b= x/y	B) log a/ log b = x/y	C) log a/ log b = y/2x	D) log b/a = x/y	E) log b/a = y/x

Solution: a^2x = b^y => log a^2x = log b^y => 2x log a = y log b   => log a/ log b = y/2x   ANSWER:log a/ log b = y/2x
Answer: C
A can complete the job in 4 hours and B can complete the same job in 3 hours. A works for 1 hour and then B joins and both complete the job. What fraction of the job did B complete  Choose the correct choice from the following choices:  A) 1/7  B) 3/10  C) 1/2  D) 5/6  E) 8/9

Solution: 1/7=1/7
Answer: A
A , B , and C started a partnership business by investing $45,000 , $63,000 , and $72,000 respectively. At the end of the year, the profit was distributed among them. If C's share of profit is $20,000, what is the total profit? Pick.
A) $38,000	B) $42,000	C) $46,000	D) $50,000	E) $54,000

Solution: A:B:C = 45000:63000:72000 which is a ratio of 5:7:8.   Let the total profit be x.   x * 8/20 = 20000   x = 20000*20/8 = 50,000.   The answer is $50,000.
Answer: D
the sum of 2nd and 19th term of A.P. is equal to the sum of 8th , 15th and 12 th term . find the term which is 0
Choose the correct choice from the following answers.
A) 12
B) 13
C) 14
D) 15
E) 16

Solution: t2 + t19 = t8 + t15 + t12   => a+d + a+18d = a+7d + a+14d + a+11d   => a + 13d = 0   => t14 = 0 i.e. 14th term is zero.   ANSWER:14
Answer: C
A retailer buys 40 pens at the market price of 36 pens from a wholesaler ,if he sells these pens giving a discount of 1% ,what is the profit % ?
Choose the correct choice from the following answers.
A) 15%	B) 5%	C) 10%	D) 25%	E) 19%

Solution: let the market price of each pen be Rs 1   then,10%.P of 40 pens = Rs 36   S.P of 40 pens =99% of Rs 40=Rs 39.60   profit %=((3.60*100)/36)= 
((3.60*100)/36) = 10
10%   Answer is 10%.
Answer: C
In an examination 80% failed in Math and 20% failed in French. If 24% failed in both. What % of students passed in both. Pick one
A) 25%  B) 24%  C) 20%  D) 30%  E) 10%

Solution: Passed in Math = 100 - 80= 
100 - 80 = 20
20%   Passed in French= 100 - 20= 
100 - 20 = 80
80%   Students who passed Math or French= 100 -24= 
100 -24 = 76
76%   Students passed in Math and French= (Passed in Math) + (Passed in French) - (Students who passed Math or French) = 20+80-76= 
20+80-76 = 24
24%   ANSWER:24%
Answer: B
The grade point average of the entire class is 80. If the average of one fourth of the class is 92, what is the average of the rest of the class?  Choose the correct answer:  A) 73  B) 74  C) 75  D) 76  E) 77

Solution: Let x be the number of students in the class.   Let P be the average of the rest of the class.   80x = (1/4)92x + (3/4)(P)x   320 = 92 + 3P   3P = 228   P = 76.   The answer is 76.
Answer: D
Of the three numbers, the first is twice as second and three times the third. The average of the three numbers is 66, and the three numbers in order are? Choose the correct choice from the following options:
A) 116,58,36
B) 98,49,33
C) 126,63,36
D) 108,54,36
E) None of these

Solution: Explanation :   Solution: Let A =x,   B =x/2, C = x/3.   =x + x/2 + x/3 / 3 = 66   By solving we will get x = 108.   Hence A= 108   B= 108/2= 
108/2 = 54
54   C= 108/3= 
108/3 = 36
36   Answer : 108,54,36
Answer: D
A bag contains nine yellow balls, three white balls and four red balls. In how many ways can two balls be drawn from the bag?	Choose the correct choice from the following options: A) ⁹C₂ B) ³C₂ C) ¹⁶C₂ D) ¹²C₂ E) ¹⁴C₂

Solution: Explanation:   Total number of balls = 9 + 3 + 4   Two balls can be drawn from 16 balls in ¹⁶C₂ ways.   ANSWER IS ¹⁶C₂
Answer: C
Given a unit square, two points are chosen uniformly at random within the square. Compute
the probability that the line segment connecting those two points touches both diagonals of the
square.
Options.
A) 1/4
B) 2/4
C) 3/4
D) 4/4
E) 5/4

Solution: If we draw both diagonals, then the desired event happens if and only if the two   points appear in dierent triangles that do not share an edge. Given the triangle where one   point lands, the other point has probability   1/4   of landing in the other triangle.   correct answer 1/4
Answer: A
Set X consists of 5 integers and has median of 20 and a range of 20. What is the value of the greatest possible integer that can be present in the set?  Choose the correct option
A) 20  B) 37  C) C.40  D) 43  E) 50

Solution: Note that both median and range do not restrict too many numbers in the set. Range is only concerned with the smallest and greatest. Median only cares about the middle.   Quick check of each option starting from the largest:   (E) 50   Range of 20 means the smallest integer will be 30. So 20 cannot lie in between and hence cannot be the median.   (D) 43   Range of 20 means the smallest integer will be 23. So 20 cannot lie in between and hence cannot be the median.   (C) 40   Range of 20 means the smallest integer will be 20. 20 can lie in between such as:   20, 20, 20, 20, 20   This is possible. Hence it is the greatest such number.   20nswer (20)
Answer: A
A train is running at a speed of 40 km/hr and it crosses a post in 25.2 seconds. What is the length of the train? Options.
A) 190 metres  B) 160 metres  C) 280 metres  D) 120 metres  E) 250 metres

Solution: Speed of the train, v = 40 km/hr = 40000/3600 m/s = 400/36 m/s   Time taken to cross, t = 25.2 s   Distance 280 metresovered, d = vt = (400/36)Ã— 25.2 = 280 m   Distance covered is equal to the length of the train = 280 m   280 metresorrect answer is 280 metres   280 metres
Answer: C
A circular path of 19 m radius has marginal walk 2 m wide all round it. Find the cost of leveling the walk at 25p per m2?  Choose the correct choice:
A) rs.49.25  B) rs.40.50  C) rs.44.20  D) rs.62.85  E) rs.43.10

Solution: Explanation:   π (21^2 - 19^2) = 22/7 * (441-361) = 251.43   251.43 * 1/4 = Rs.62.85   Answer: Option rs.62.85
Answer: D
Find large number from below question The difference of two numbers is 1365. On dividing the larger number by the smaller, we get 4 as quotient and the 15 as remainder	Answers
A) 1235 B) 1346 C) 1378 D) 1635 E) 1815

Solution: Let the smaller number be x. Then larger number = (x + 1365).   x + 1365 = 4x + 15   3x = 1350   x = 450   Large number = 450+1365= 
450+1365 = 1_815
1815   1815
Answer: E
Rahul went to a shop and bought things worth Rs. 26, out of which 30 Paise went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items?  Choose the correct choice:
A) 19.7
B) 20.7
C) 22
D) 21.4
E) 21.5

Solution: Total cost of the items he purchased = Rs.26   Given that out of this Rs.26, 30 Paise is given as tax   => Total tax incurred = 30 Paise = Rs.30/100   Let the cost of the tax free items = x   Given that tax rate = 6%   ∴ (26−30/100−x)6/100 = 30/100   ⇒ 6(26 −0.3 −x) = 30   ⇒ (26 − 0.3 − x) = 5   ⇒ x = 26 − 0.3 − 5 = 20.7   20.7
Answer: B
The average weight of a group of boys is 30 kg. After a boy of weight 38 kg joins the group, the average weight of the group goes up by 1 kg. Find the number of boys in the group originally ? Choose the most appropriate option:	A) 4	B) 8	C) 5	D) 2	E) 7

Solution: Let the number off boys in the group originally be x.   Total weight of the boys = 30x   After the boy weighing 38 kg joins the group, total weight of boys = 30x + 38   So 30x + 38 + 31(x + 1) = > x = 7.   Answer: 7
Answer: E
How many of the positive divisors of 480 are also multiples of 4 not including 480? Options:
A) 15  B) 16  C) 19  D) 20  E) 24

Solution: 480 = 2^6 * 3 * 5 = (4) * 2^3 * 3 * 5   Besides (4), the exponents of 2, 3, and 5 are 3, 1, and 1.   There are (3+1)(1+1)(1+1) = 16 ways to make multiples of 4.   We must subtract 1 because one of these multiples is 480.   The answer is 15.
Answer: A
.
On dividing a number by 357, we get 39 as remainder. On dividing the same number 17, what will be the remainder ?
Choose the correct choice from the following choices: A) 0 B) 3 C) 5 D) 8 E) 11

Solution: Let x be the number and y be the quotient. Then,   x = 357 x y + 39   = (17 x 21 x y) + (17 x 2) + 5   = 17 x (21y + 2) + 5)   Required remainder = 5.   Answer: Option 5
Answer: C
x percent of y percent of z is decreased by y percent. find the result?	Pick one.
A) (xz - y) / 100 B) (100xyz - xy^2z) /1,000,000 C) (xz - y) / 10,000 D) (xyz - 2y) / 100 E) (xyz - 2y) / 10,000

Solution: We're told that X percent of Y percent of Z is DECREASED by Y percent. We're asked for the result of all of this math.   IF....   X = 10   Y = 50   Z = 100   First, 50% of 100 = 50   Next, 10% of 50 = 5   Finally, 5 decreased by 50% of itself is 2.5   So we're looking for an answer that equals 2.5 when X=10, Y=50 and Z=100.   Answer A. (100xyz - xy^2z) / 1,000,000 = (5,000,000 - 2,500,000)/1,000,000 = 2,500,000/1,000,000 = 2.5   Anwer is (100xyz - xy^2z) /1,000,000
Answer: B
There are 7 boxes numbered from 1 to 7. Either a red ball or a green ball will be placed in each box in such a way that at least 1 box contains a green ball and the boxes containing green balls are consecutively numbered. How many different ways can this be done? Choose the correct choice from the following choices.
A) 26  B) 28  C) 30  D) 32  E) 34

Solution: 1 green ball: 7 ways   2 green balls: 6 ways   3 green balls: 5 ways   4 green balls: 4 ways   5 green balls: 3 ways   6 green balls: 2 ways   7 green balls: 1 way   The total number of ways is   7*8/2= 
  7*8/2 = 28
28   The answer is 28.
Answer: B