MU-NLPC/Calc-aqua_rat huggingface dataset:
ABCE is an isosceles trapezoid and ACDE is a rectangle.AB=10 and EC=20.What is the length of AE.
Pick
A) 5	B) 10	C) 12	D) 15	E) 20

Solution: As ABCE is an isosceles trapezoid and EC is twice times AB, we can consider the given trapezoid as half of a regular hexagon(as length of diagonal in regular hexagon is always double the side).   Thus, sides AB=AE=BC. => AE = 10.   ANSWER:10
Answer: B
The length of the bridge, which a train 160 metres long and travelling at 45 km/hr can cross in 30 seconds, is?  Select
A) 876 m B) 157 m C) 215 m D) 156 m E) 167 m

Solution: Speed = [45 X 5/18] m/sec   = [25/2] m/sec Time = 30 sec Let the length of bridge be x metres. Then, (160 + x)/30 = 25/2   => 2(160 + x) = 750 => x   = 215 m.   Answer: 215 m
Answer: C
What is the dividend. divisor 17, the quotient is 9 and the remainder is 5 Choose one.
A) 134
B) 136
C) 140
D) 158
E) 160

Solution: 158 = d * Q + R   158 = 17 * 9 + 5   158 = 153 + 5   158 = 158
Answer: D
A company bought for its 7 offices 2 computers of brand N and 3 computers of brand M. In how many ways could computers be distributed among the offices if each office can have only 1 computer. Options:
A) 196  B) 210  C) 256  D) 292  E) 312

Solution: I solved it in a slightly different way. I would love feedback on the logic.   Again, this is a comb problem. So I though of it as follows.   From the seven offices, there will be 5 'winners' (of PCs) and 2'losers'. The number of ways they could be winners and losers is 7!/(5!2!) = 21   For the five winners, the 5 computers can be distributed in 5!/(2!3!) ways = 10.   If you have trouble seeing this, think of anagrams NNMMM (so 5! ways of ordering them but divide by 2! because 2 Ns are similar and 3! because 3 'M's are similar.)   The number of different combinations is then 21*10= 
21*10 = 210
210 -> 210.
Answer: B
In how many ways can the letters in mmmnnnppqq can be arranged with two n's together?
Pick one:
A) 15120 ways
B) 16120 ways
C) 14120 ways
D) 13120 ways
E) 12120 ways

Solution: MMMN(NN)PPQQ so taking two N's together we can get =9!/(3!*2!*2!) arrangements   bow this NN can be arranged in =2!/2!=1 ways   so total arrangements2 /2= 
2 /2 = 1
1 ways   so total arrangements=9!/(3!*2!*2!)=15120 ways   15120 waysNSWER:15120 ways
Answer: A
The product of two numbers is 168 and the sum of these two numbers is 26. What is the largest of these two numbers?
Choose the most appropriate option:
A) 22	B) 77	C) 88	D) 12	E) 62

Solution: Let the numbers be x and (26 – x).   Therefore, x (26 – x) = 168   x2 – 26x + 168 = 0   (x – 14) (x – 12) = 0   x = 14 or x = 12   So, the numbers are 14 and 12.   ANSWER: 12
Answer: D
A rectangular grass field is 70 m * 55 m, it has a path of 2.5 m wide all round it on the outside. Find the area of the path and the cost of constructing it at Rs.2 per sq m?	Pick.
A) 1350	B) 1971	C) 9676	D) 1300	E) 2691

Solution: Area = (l + b +2d) 2d   = (70 + 55 +2.5 * 2) 2*2.5 => 650   650 * 2 = Rs.1300   Answer:1300
Answer: D
Two persons start running simultaneously around a circular track of length 400 m from the same point at speeds of 20 km/hr and 20 km/hr. When will they meet for the first time any where on the track if they are moving in opposite directions ?  Options.
A) 27 sec	B) 87 sec	C) 67 sec	D) 47 sec	E) 36 sec

Solution: Explanation:   Time taken to meet for the first time anywhere on the track   = length of the track / relative speed   = 400 / (20 + 20)5/18 = 400 x 18 / 40 x 5 = 36 seconds.   Answer: 36 sec
Answer: E
A man wears socks of two colours - Black and brown. He has altogether 20 black socks and 20 brown socks in a drawer. Supposing he has to take out the socks in the dark, how many must he take out to be sure that he has a matching pair ? Choose the correct choice from the following choices.
A) 3 B) 10 C) 20 D) 39 E) None of these

Solution: 3 socks must be taken out to be sure that he has a matching pair .   3NSWER:3
Answer: A
If the number 52,1n7, where n represents the tens digit, is a multiple of 3, then the value of n could be which of the following?  Select the correct option.
A) 7  B) 5  C) 2  D) 1  E) 0

Solution: The sum of the digits 5 + 2 + 1 + n + 7 must be a multiple of 3   15 + n must be a multiple of 3   substituting the numbers n must = 0   Aswer 0
Answer: E
For any number Z, Z* is defined as the greatest positive even integer less than or equal to y. What is the value of 6.15 – 6.15*?	Choose the correct answer:
A) 1.5
B) 0.15
C) 6.25
D) 0.25
E) 6.0

Solution: Since Z* is defined as the greatest positive even integer less than or equal to Z, then 6.15* =6 (the greatest positive even integer less than or equal to 6.15 is 6).   Hence, 6.15 – 6.15* = 6.15 - 6= 
6.15 - 6 = 0.15
0.15   Answer: 0.15.
Answer: B
The first doughnut is priced at $1 and then if you purchase additional doughnuts as dozens then the price is $6/dozen. What is the total number of doughnuts purchased if you paid $26?
Pick one:	A) 50	B) 52	C) 54	D) 56	E) 58

Solution: $26 = 4 * $6 + $2   The number of doughnuts is 4*12 + 2= 
4*12 + 2 = 50
50   The answer is 50.
Answer: A
A rectangular wall is covered entirely with two kinds of decorative tiles: regular and jumbo. 1/3 of the tiles are jumbo tiles, which have a length three times that of regular tiles and have the same ratio of length to width as the regular tiles. If regular tiles cover 50 square feet of the wall, and no tiles overlap, what is the area of the entire wall?
Choose the correct choice from the following answers.
A) 160	B) 275	C) 360	D) 440	E) 560

Solution: The number of jumbo tiles = x.   The number of regular tiles = 2x.   Assume the ratio of the dimensions of a regular tile is a:a --> area = a^2.   The dimensions of a jumbo tile is 3a:3a --> area = 9a^2.   The area of regular tiles = 2x*a^2 = 50.   The area of jumbo tiles = x*9a^2 = 4.5(2x*a^2 ) = 4.5*50= 
4.5*50 = 225
225.   Total area= 50 + 225= 
50 + 225 = 275
275.   Answer: 275.
Answer: B
The ratio of the present ages of a man and his wife is 4 : 3. Which of the following can't be a possible ratio of their ages 30 years ago?  Choose one:
A) 2: 4  B) 3: 4  C) 4:4  D) 5: 4  E) 6: 4

Solution: 4x-30/3x-30 = 5/4   Therefore x=-30   Age cannot be negative.   Answer: 5: 4
Answer: D
A can do a piece of work in 5 hours; B and C together can do it in 4 hours, while A and C together can do it in 3 hours. How long will B alone take to do it? Select:
A) 60/7 hours B) 70/6 hours C) 35/2 hours D) 90.8 hours E) none of the above

Solution: A's 1 hour's work = 1/5 ;   (B + C)'s 1 hour's work = 1/4 ;   (B + C)'s 1 hour's work = 1/3   (A + B + C)'s 1 hour's work = (1/5 + 1/4) = 9/20   B's 1 hour's work = (9/20 - 1/3) = 7/60   B alone will take 60/7 hours to do the work.   60/7 hoursnswer = 60/7 hours
Answer: A
A contractor undertakes to built a walls in 50 days. He employs 70 peoples for the same. However after 25 days he finds that only 40% of the work is complete. How many more man need to be employed to complete the work in time?  Choose the correct choice.
A) 105	B) 30	C) 35	D) 20	E) None of these

Solution: 70 men complete 0.4 work in 25 days.   105pplying the work rule, m1 × d1 × w2 = m2 × d2 × w1   we have,   70 × 25 × 0.6 = m2 × 25 × 0.4   or m2 = 70×25×0.6/25×0.4 = 105 men   105nswer105
Answer: A
A certain kind of necklace is made from 9 blue, 6 red, and 3 pink beads. What is the maximum number of these necklaces that can be made from 54 beads of each color ? Pick
A) 5	B) 6	C) 7	D) 8	E) 9

Solution: Atleast 9 blue breads are needed to make a necklace, so irrespective of the combinations of red and pink beads, the number of necklaces that can be formed will be   54/9= 
54/9 = 6
6   Answer:- 6
Answer: B
A bag contains 3 red, 5 yellow and 4 green balls. 3 balls are drawn randomly. What is the probability that balls drawn contain exactly two green balls? Answers:  A) 9/16  B) 7/18  C) 12/55  D) 14/67  E) 19/87

Solution: Total number of balls = 3+5+4= 
3+5+4 = 12
12   n(S)= 1212/553 = 12*11*10 / 3*2 = 220   n(E) = 412/552* 812/551 = 6*8= 
6*8 = 48
48   Probability= 48/220 = 12/55   Answer is 12/55
Answer: C
George can do a piece of work in 8 hours. Paul can do the same work in 10 hours, Hari can do the same work in 12 hours. George, paul and hari start the same work at 9 am, while george stops at 11 am, the remaining two complete the work. What time will the work complete?  Choose the correct choice from the following.
A) 12:00 Pm
B) 1:00 Pm
C) 2:00 Pm
D) 3:00 Pm
E) 4:00 Pm

Solution: ((1/8)+(1/10)+(1/12))2+((1/10)+(1/12))(x-2)=1   x=4 hrs   work started at 9 am..   takes 4 hrs to complete 9am + 4hrs =1:00 Pm   ANSWER:1:00 Pm
Answer: B
A 270 metres long train running at the speed of 120 kmph crosses another train running in opposite direction at the speed of 80 kmph in 9 seconds. What is the length of the other train? Choose the correct choice from the following choices
A) 230 m B) 240 m C) 260 m D) 320 m E) 330 m

Solution: Relative speed = (120 + 80) km/hr   =	(200 x(5/18))m/sec   =	(500/9)m/sec.   Let the length of the other train be x metres.   Then,	(x + 270)/9 = 500/9   x + 270 = 500   x = 230.   230 m
Answer: A
If A lends Rs.2800 to B at 15% per annum and B lends the same sum to C at 18.5% per annum then the gain of B in a period of 3 years is?  Answers
A) 294
B) 289
C) 240
D) 233
E) 200

Solution: (2800*3.5*3)/100= 
(2800*3.5*3)/100 = 294
> 294   294nswer: 294
Answer: A
The number of meters in QB is equal to the square root of the number of centimeters in QB. What is the length of QB (1 meter=100 centimeters)?	Select:
A) 100 meters B) 10 meters C) 100 centimeters D) 10 centimeter E) 1 centimeter

Solution: I'd plug in the options for this question.   Check option A: if the number of meters in QB is 100, then the number of centimeters is 100*100. The square root of 100*100 is 100: 100 = 100.   100 metersnswer: 100 meters.
Answer: A
From the integer n, if n*n*n*n*n is odd, then what is true from below options? Choose the correct choice from the following choices.
A) n*n is odd B) n is odd and n*n*n is even C) n is even D) n is odd E) n*n is even

Solution: n is odd and n*n is even   Option n is odd and n*n*n is even
Answer: B
The smallest prime number in the list: Answers:
A) 5
B) 7
C) 10
D) 14
E) 18

Solution: 5   5
Answer: A
A man has $ 10,000 to invest. He invests $ 4000 at 5 % and $ 3500 at 4 %. In order to have a yearly income of $ 500, he must invest the remainder at: Choose one
A) 4%  B) 6%  C) 6.4%  D) 7%  E) 8.2%

Solution: C   6.4%   Income from $ 4000 at 5 % in one year = $ 4000 of 5 %.   = $ 4000 × 5/100.   = $ 4000 × 0.05.   = $ 200.   Income from $ 3500 at 4 % in one year = $ 3500 of 4 %.   = $ 3500 × 4/100.   = $ 3500 × 0.04.   = $ 140.   Total income from 4000 at 5 % and 3500 at 4 % = $ 200 + $ 140 = $ 340.   Remaining income amount in order to have a yearly income of $ 500 = $ 500 - $ 340.   = $ 160.   Total invested amount = $ 4000 + $ 3500 = $7500.   Remaining invest amount = $ 10000 - $ 7500 = $ 2500.   We know that, Interest = Principal × Rate × Time   Interest = $ 160,   Principal = $ 2500,   Rate = r [we need to find the value of r],   Time = 1 year.   160 = 2500 × r × 1.   160 = 2500r   160/2500 = 2500r/2500 [divide both sides by 2500]   0.064 = r   r = 0.064   6.4%hange it to a percent by moving the decimal to the right two places r = 6.4 %   Therefore, he invested the remaining amount $ 2500 at 6.4 % in order to get $ 500 income every year.
Answer: C
The areas, in kilometers squared, of some countries are given below. USA: 9,629,091, Russia: 17,098,242, China: 9,598,094, Canada: 9,984,670, the UK: 242,400 and India: 3,287,263.
What is the difference between the areas of Russia and China?	Select:
A) 5,500,148 kilometers squared
B) 8,500,148 kilometers squared
C) 7,500,148 kilometers squared
D) 6,500,148 kilometers squared
E) 3,500,148 kilometers squared

Solution: he difference between the areas of Russia and 7,500,148 kilometers squaredhina is given by   17,098,242 - 9,598,094 = 7,500,148 kilometers squared   correct answer 7,500,148 kilometers squared
Answer: C
The price of a jacket is reduced by 15%. During a special sale the price of the jacket is reduced another 30%. By approximately what percent must the price of the jacket now be increased in order to restore it to its original amount?  Answers:	A) 60	B) 65	C) 69	D) 68.25	E) 67.5

Solution: 1) Let the price of jacket initially be $100.   2) Then it is decreased by 15% , therefore bringing down the price to $85.   3) Again it is further discounted by 30%, therefore bringing down the price to $59.5   4) Now 59.5 has to be added byX %in order to equal the original price.   59.5 + ( X% ) 59.5 = 100.   Solving this eq for X, we get X = 68.25   Ans is 68.25
Answer: D
A lighting store is stocked with 410 fixtures. Some of the fixtures are floor lamps and the rest are table lamps. If 5% of the floor lamps and 30% of the table lamps are imported, what is the smallest possible number T of imported lamps stocked at the store?  Choose the correct answer
A) 3	B) 10	C) 13	D) 20	E) 23

Solution: We want to minimize not maximize the expression,.   T=x/20+(410-x)*3/10=123+x/20-3x/10=123-5x/20 --> maximize x to minimize the expression --> x must be the greatest multiple of 20 less than 410, so 400 --> 123-5*400/20=23.   But i'm guessing 123-5x/20 can be written as 123- x/4   if x has to be the greatest multiple of 4 less then 410, then it would be 408.   Hence 123-408/4 --> 123-102 -->21   Yes, you cannot reduce in this case. If x=408, then 5/100*x and (410-x)*3/10 won't be integers.23
Answer: E
The average of a couple was 26Yrs when they were married 6Yrs ago.The avg age of
the couple and a child, who was born during the interval, is 22Yrs now. How old is the
child now ?
Answers:
A) 2 Yrs
B) 4 Yrs
C) 3 Yrs
D) 1 Yrs
E) None of these

Solution: (a+b-6-6)/2=26;   a+b=64;   a+b+c/3=22;   solving both c=2   2 YrsNSWER:2 Yrs
Answer: A
Calculate the value of z from the below equation: z^2âˆ’4z+6=0  Options.
A) 6 B) 5 C) 2 D) 1 E) 3

Solution: Use elimination method to find the correct option. you find that of all the options 2 is the correct value for z   Answer: 2
Answer: C
Find the value of x in [(17.28/x) / (3.6*0.2)] = 2 Select.
A) 11	B) 12	C) 13	D) 14	E) 15

Solution: (17.28/x) = 2*3.6*0.2   x = (17.28/1.44)   = (1728/14)   = 12.   Option 12
Answer: B
x varies inversely as square of y. Given that y = 2 for x = 1. The value of x for y = 6 will be equal to:	Pick
A) 1/2 B) 1/3 C) 1/5 D) 1/9 E) 1/3

Solution: Given x = k/y2, where k is a constant.   Now, y = 2 and x = 1 gives k = 4.   x = 4/y2 => x = 4/62, when   y = 6 => x = 4/36 = 1/9.   Answer: 1/9
Answer: D
An inspector rejects 0.08% of the meters as defective. How many will be examine to project ? Pick one:
A) 2000  B) 2300  C) 2700  D) 2500  E) 250

Solution: Let the number of meters to be examined be x.   Then, 0.08% of x =2   [(8/100)*(1/100)*x] = 2   x = [(2*100*100)/8= 
(2*100*100)/8 = 2_500
2500   Answer is 2500.
Answer: D
In a circuit board factory, all circuit boards that pass a verification process are certified. Every board that fails the verification process is indeed faulty, but 1/8 of those that pass are also faulty.
Approximately how many faulty circuit boards exist in a group of 400 circuit boards where 64 fail inspection?	Options:
A) 106  B) 192  C) 200  D) 256  E) 264

Solution: Total of 400 boards. All that fail verification are indeed faulty. So the 64 are indeed faulty. 1/8 those that pass are also faulty.   From the 400 we know 64 fail. So 336 must pass. Of these 1/8 are faulty. 336 divided by 8 gives you 42.   What one must do now is to add to the 42 which were not detected the actually detected faulty ones, namely the 64.   Total faulty: 106.   106nswer: 106
Answer: A
A vessel contains 20 liters of a mixture of milk and water in the ratio 3:2. 10 liters of the mixture are removed and replaced with an equal quantity of pure milk. If the process is repeated once more, find the ratio of milk and water in the final mixture obtained?	Choose the correct choice from the following
A) 9:1	B) 9:3	C) 9:3	D) 5:2	E) 4:1

Solution: Milk = 3/5 * 20= 
3/5 * 20 = 12
12 liters, water= 8 liters   If 10 liters of mixture are removed, amount of milk removed = 6 liters and amount of water removed = 4 liters.   Remaining milk = 12 - 6= 
12 - 6 = 6
6 liters   Remaining water= 8 - 4= 
8 - 4 = 4
4 liters   10 liters of pure milk are added, therefore total milk= (6 + 10)= 
(6 + 10) = 16
16 liters.   The ratio of milk and water in the new mixture= 16:4 = 4:1   If the process is repeated one more time and 10 liters of the mixture are removed, then amount of milk removed = 4/5 * 10= 
4/5 * 10 = 8
8 liters.   Amount of water removed= 2 liters.   Remaining milk = (16 - 8)= 
(16 - 8) = 8
8 liters.   Remaining water= (4 -2)= 
(4 -2) = 2
2 liters.   The required ratio of milk and water in the final mixture obtained= (8 + 10):2 = 18:2 = 9:1.   9:1nswer:9:1
Answer: A
kamal purchased 7kg of grapes at the rate of 70 per kg and 9 kg of mangoes at the rate of 55 per kg. How much amount did he pay to the shopkeeper?  Options.
A) A)980	B) B)1065	C) C)1070	D) D)1075	E) E)1080

Solution: Cost of 7 kg grapes = 70 × 7 = 490.   Cost of 9 kg of mangoes = 55 × 9 = 490.   Total cost he has to pay = 490 + 490= 
490 + 490 = 980
980   980
Answer: A
A man in a train notices that he can count 21 telephone posts in one minute. If they are known to be 50 metres apart, at what speed is the train travelling?  Pick
A) 61 km/hr B) 60 km/hr C) 56 km/hr D) 63 km/hr E) 62 km/hr

Solution: Explanation:   The man in the train notices that he can count 21 telephone posts in one minute.   Number of gaps between 21 posts are 20 and Two posts are 50 metres apart.   It means 20 x 50 meters are covered in 1 minute.   Distance = 20×50 meter = (20×50)/1000 km = 1 km   Time = 1 minute = 1/60hour   Speed = Distance/Time=1(1/60) = 60 km/hr   Answer: Option 60 km/hr
Answer: B
3889 + 17.952 - ? = 3854.002  Choices.
A) 52.95  B) 49.75  C) 45.97  D) 47.59  E) 45.79

Solution: Let 3889 + 17.952 - x = 3854.002.   Then x = (3889 + 17.952) - 3854.002   = 3906.952 - 3854.002   = 52.95.   52.95nswer is 52.95
Answer: A
The probability of a lottery ticket being a prized ticket is 0.2. When 4 tickets are purchased, the probability of winning a prize on atleast one ticket is ?	Pick one
A) 0.5989	B) 0.5904	C) 0.5929	D) 0.5938	E) 0.5907

Solution: P(winning prize atleast on one ticket)   = 1 - P("Losing on all tickets")   = 1 - (0.8)4 = (1 + (0.8)2)(1 - (0.8)2)   = (1.64)(0.36) = 0.5904   Answer:0.5904
Answer: B
In what ratio must rice at Rs.30 per kg mixed with rice at Rs.10.80 per kg so that the mixture be worth Rs.10per kg Ans	Select the correct option:
A) 8:7  B) 8:8  C) 8:3  D) 8:2  E) 8:1

Solution: If 2 ingredients are mixed, then the required ratio is given by, the rule of allegation C.P of a unit quantity of cheaper (c) C.P. of a unit quantity of dearer (d)   Mean Price (m) d-m m-c  Required ratio is cheaper quantity : dearer quantity = (d-m) : (m-c) Answer with Explanation: By the rule of allegation i. C.P of 1 Kg of rice of I kind (p) = 930 ii. C.P of 1 Kg of rice of II kind (p) = 1080 iii. Mean price (p) = 1000 iv. d – m = 1080-1000= 
1080-1000 = 80
80 v. m – c= 1000 – 930 = 70  Required ratio = 80 : 70   = 8 : 7   8:7nswer:8:7
Answer: A
A car traveled 462 miles per tankful of gasoline on the highway and 336 miles per tankful of gasoline in the city. If the car traveled 12 fewer miles per gallon in the city than on the highway, how many miles per gallon did the car travel in the city?
Select:  A) 14  B) 16  C) 21  D) 22  E) 32

Solution: I treat such problems as work ones.   Work=Rate*Time   Mileage(m)=Rate(mpg)*Gallons(g)   X gallons is a full tank   {462=RX   {336=(R-12)X solve for R, R=44   44-12= 
44-12 = 32
32 mpg   32
Answer: E
A trader marks his articles 20% more than the cost price. If he allows 20% discount, then find his gain or loss percent?  Choices.
A) 7 B) 6 C) 5 D) 9 E) 4

Solution: Let CP of an article = RS. 100   MP= Rs. 120   Discount = 20%   SP = M[(100 - d%)/100] = 120(80/100) = Rs. 96   Clearly, the trader gets 4% loss.   Answer: 4
Answer: E
Three numbers are in the ratio 3:5:7. The largest number value is 42. Find difference between Smallest & largest number is?	Pick one:
A) 18
B) 22
C) 24
D) 26
E) 28

Solution: == 3:5:7   Total parts = 15   = The largest number value is 42   = The largest number is = 7   = Then 7 parts -----> 42 ( 7 * 6 = 42 )   = smallest number = 3 & Largest number = 7   = Difference between smallest number & largest number is = 7 - 3= 
7 - 3 = 4
4= Then 4 parts -----> 24 (4 * 6 = 24)   24
Answer: C
Salaries of Ravi and Sumit are in the ratio 2 : 3. If the salary of each is increased by Rs. 4000, the new ratio becomes 40 : 57. What is Sumit's salary?	Choose the correct answer:
A) 32000 B) 34000 C) 38000 D) 35000 E) 36000

Solution: Let the original salaries of Ravi and Sumit be Rs. 2x and Rs. 3x respectively.   Then,2x + 4000/3x + 4000	= 40/57   57(2x + 4000) = 40(3x + 4000)   6x = 68,000   3x = 34,000   Sumit's present salary = (3x + 4000) = Rs.(34000 + 4000) = Rs. 38,000.   ANSWER 38000
Answer: C
Mohit sold an article for Rs. 18000. Had he offered a discount of 10% on the selling price, he would have earned a profit of 8%. What is the cost price of the article?  Choose the correct choice from the following choices: A) 15000 B) 28277 C) 12002 D) 28821 E) 12000

Solution: Explanation:   Let the CP be Rs. x.   Had he offered 10% discount, profit = 8%   Profit = 8/100 x and hence his SP = x + 8/100 x = Rs. 1.08x = 18000 - 10/100(18000) = 18000 - 1800 = Rs. 16200   => 1.08x = 16200   => x = 15000   15000nswer:15000
Answer: A
At a particular pizza shop, a pizza can be created from any combination of 2 different types of spice, 7 different types of meat, among which are pepperoni and anchovies, and 4 different types of cheese. If a customer at the shop decides to order a pizza with 1 type of spice, 2 types of cheese, and 4 types of meat but without pepperoni and anchovies together, how many possible ways to garnish the pizza are available to the customer?  Choose the correct answer:
A) 6 B) 35 C) 300 D) 450 E) 740

Solution: Number of possible ways to select 1 type of spice = 2c1 = 2   Number of possible ways to select 2 types of cheese = 4c2 = 6   (Here we can pick our answer as D- 450 since it is the only answer that is divisible by   3*6= 
  3*6 = 18
18 , but most likely on the GMAT there will be more another answer that will be divisible by 18 )   Number of possible ways to select 4 types of meat but without pepperoni and anchovies together= Total number of ways without any restriction - Total number of ways in which pepperoni and anchovies together   = 7c4 - 5c2   =35 - 10= 
35 - 10 = 25
25   Possible ways to garnish the pizza are available to the customer= 2*6 * 25= 
2*6 * 25 = 300
300   Answer 300
Answer: C
Ten percent of Ram's monthly salary is equal to eight percent of Shyam's monthly salary. Shyam's monthly salary is twice Abhinav's monthly salary. If Abhinav's annual salary is Rs. 1.92 lakhs, find Ram's monthly salary? Choose the correct answer:
A) Rs.25638	B) Rs.25638	C) Rs.25600	D) Rs.25624	E) Rs.25602

Solution: Let the monthly salaries of Ram and Shyam be Rs. r and Rs. s respectively.   10/100 r = 8/100 s   r = 4/5 s   Monthly salary of Abhinav = (1.92 lakhs)/12 = Rs. 0.16 lakhs   s = 2(0.16 lakhs) = 0.32 lakhs   r = 4/5(0.32 lakhs) = Rs.25600   Answer:Rs.25600
Answer: C
A person travels equal distances with speeds of 3 km/hr, 4 km/hr and 5 km/hr and takes a total time of 47 minutes. The total distance is?
Answers.
A) 2 B) 3 C) 4 D) 5 E) 6

Solution: Explanation:   Let the total distance be 3x km.   Then, x/3 + x/4 + x/5 = 47/60   47x/60 = 47/60 => x = 1.   Total distance = 3 * 1= 
3 * 1 = 3
3 km.   ANSWER IS 3
Answer: B