MU-NLPC/Calc-aqua_rat huggingface dataset:
There are 3 numbers A, B and C. If A:B = 3/4, B:C = 4/5, C:D = 5/6, then A:D will be?  Pick one:
A) 1 : 2	B) 2 : 3	C) 2 : 5	D) 3 : 5	E) 3 : 7

Solution: Sol. A : B = 3 : 4, B : C = 4 : 5, C : D = 5 : 6   ∴A∶B∶C∶D= 3 : 4 : 5 : 6.   Thus, 1 : 2 : D = 3 : 6 or, 1 : 2   1 : 2
Answer: A
Ayesha's father was 28 years of age when she was born while her mother was 15 years old when her brother four years younger to her was born. What is the difference between the ages of her parents?  Pick:
A) 12 years	B) 17 years	C) 16 years	D) 18 years	E) 10 years

Solution: Explanation:   Mother's age when Ayesha's brother was born = 15 years.   Father's age when Ayesha's brother was born = (28 + 4)= 
(28 + 4) = 32
32 years.   Required difference= (32 - 15)= 
(32 - 15) = 17
17 years.   Answer: 17 years
Answer: B
Rs. 20 is the true discount on Rs. 260 due after a certain time. What will be the true discount on the same sum due after half of the former time ,the rate of interest being the same ?
Choose the correct choice from the following
A) Rs. 10
B) Rs. 10.40
C) Rs. 15.20
D) Rs. 13
E) None of these

Solution: Solution   S.I. on Rs. (260-20) for a given time =Rs. 7.34.   S.I. on Rs. 240 for half the time = Rs.10.   T.D. on Rs. 250 = Rs. 10.   ∴ T.D. on Rs. 260 = Rs. ( 10/250 x260 ) = Rs. 10.40.   Answer Rs. 10.40
Answer: B
A father said to his son, "I was as old as you are at the present at the time of your birth". If the father's age is 42 years now, the son's age five years back was Pick:
A) 13years B) 14years C) 15years D) 16years E) 17years

Solution: Let the son's present age be x years. Then, (42 - x) = x   2x = 42.   x = 21.   Son's age 5 years back (21 - 5)= 
(21 - 5) = 16
16 years.   16years)
Answer: D
An article is bought for Rs.675 and sold for Rs.1200, find the gain percent?
Choices.
A) 87%
B) 88%
C) 78%
D) 75%
E) 73%

Solution: 675 ---- 525   100 ---- ? =>   =78%   Answer:78%
Answer: C
Working in a North Side studio at a constant rate, Kanye can drop a full-length platinum LP in 5 weeks. Working at his own constant rate, Common can drop a full-length platinum LP in x weeks. If the two emcees work together at their independent rates, they can drop a full-length platinum compilation LP in 2 weeks. Assuming no efficiency is lost or gained from working together, how many weeks would it take Common, working alone, to drop a full-length platinum LP?	Choose the correct choice from the following.
A) 3 and 1/3 weeks B) 3 weeks C) 2 and 1/2 weeks D) 2 and 1/3 weeks E) 2 weeks

Solution: VERITAS PREPOFFICIAL SOLUTION:   Now, while your instinct may be to Go! and speed through your initial read of this rate problem, remember: slow motion (is) better than no motion. As you read each sentence, you should start jotting down variables and relationships so that by the time you get to the question mark you have actionable math on your noteboard and you don’t have to read the question all over again to get started. You should be thinking:   Working in a North Side studio at a constant rate, Kanye can drop a full-length platinum LP in 5 weeks.   Rate (K) = 1 album / 5 weeks   Working at his own constant rate, Common can drop a full-length platinum LP in x weeks.   Rate (C) = 1 album / x weeks   If the two emcees work together…   I’m adding these rates, so their combined rate is 1/5 + 1/x   …they can drop a full-length platinum compilation LP in 2 weeks.   And they’re giving me the combined rate of 1 album / 2 weeks, so 1/5 + 1/x = 1/2   Assuming no efficiency is lost or gained from working together, how many weeks would it take Common, working alone, to drop a full-length platinum LP?   I’m using that equation to solve for Common’s time, so I’m solving for x.   Now by this point, that slow motion has paid off – your equation is set, your variable is assigned, and you know what you’ve solving for. Your job is to solve for x, so:   1/5 + 1/x = 1/2, so let’s get the x term on its own:   1/x = 1/2 – 1/5. and we can combine the two numeric terms by finding a common denominator of 10:   1/x = 5/10 – 2/10   1/x = 3/10, and from here you have options but let’s cross multiply:   10 = 3x, so divide both sides by 3 to get x alone:   10/3 = x, and that doesn’t look like the answer choices so let’s convert to a mixed number: 3 and 1/3 (there’s that number again), for answer choice 3 and 1/3 weeks.
Answer: A
One man traveled a distance of 61 km in 9hrs. He traveled partly on footat 4 km/hr and partly on bicycle ta 9 km/hr. The distance traveled on foot is? Options.
A) 10 km	B) 12 km	C) 16 km	D) 17 km	E) 18 km

Solution: Let the distance travelled on foot be x km.   Then, distance travelled on bicycle = (61 -x) km.   So, x + (61 -x) = 9   4 9   9x + 4(61 -x) = 9 x 36   5x = 80   x = 16 km.   16 km
Answer: C
Which number can we add to 425897 to get a number exactly divisible by 456?  Choices:
A) 3 B) 5 C) 7 D) 9 E) 11

Solution: 425897 / 456 = 933 with a remainder of 449.   We need to add 456 - 449= 
456 - 449 = 7
7   The answer is 7.
Answer: C
There are 15 points in a given plane, no three of which are on the same line. If one of the points is represented as 'U', then how many triangles can be determined with the 15 points that contain the point U?  Choose the correct answer
A) 182	B) 105	C) 185	D) 210	E) 455

Solution: Fist point is U which is fixed so can be selected in 1 way   Second point can be selected in 14 ways   Third point can be selected in 13 ways   so total ways = 1x14x13 = 182   but answer is 91 which is 182/2=182
Answer: A
A train 240 m long passed a pole in 24 sec. How long will it take to pass a platform 750 m long? Choose the correct choice:
A) 78sec  B) 83sec  C) 95sec  D) 99sec  E) 100sec

Solution: Speed = 240/24= 
240/24 = 10
10 m/sec.   Required time= (240 + 750)/10= 
(240 + 750)/10 = 99
99 sec.   Answer:99sec
Answer: D
If x is a positive integer such that (x-1)(x-3)(x-5)....(x-93) < 0, how many values can x take?
Pick one:
A) 47	B) 23	C) 46	D) 21	E) 22

Solution: Solution   If x takes any value greater than 93, the expression will definitely be positive.   Therefore, the set of values that x takes should be from the set of positive integers upto 93   The expression(x-1)(x-3)(x-5)....(x-93) has a total of 47 terms.   When x = 1, 3, 5,7 ....93 the value of the express will be zero. i.e., for odd values of x, the expression will be zero.   We need to evaluate whether the expression will be negative for all even numbers upto 93   Let x = 2; first term (x-1) > 0; remaining 46 terms < 0.   The product of one positive number and 46 negative numbers will be positive (product of even number of negative terms will be positive).   So, x = 2 does not satisfy the condition.   Let x = 4; (x-1) and (x-3) are positive; the remaining 45 terms < 0.   The product of two positive numbers and 45 negative numbers will be negative. So, x = 4 satisfies the condition.   Let x = 6; first 3 terms (x-1), (x-3), and (x-5) are positive and the remaining 44 terms are negative.   Their product > 0. So, x = 6 does not satisfy the condition.   Let x = 8; first 4 terms positive; remaining 43 terms < 0. Their product < 0. x = 8 satisfies the condition.   Extrapolating what we have oberved with these 4 terms, we could see a pattern.   The expression takes negative values when x = 4, 8, 12, 16 ..... 92 (multiples of 4)   92, the last value that x can take is the 23rd multiple of 4. Hence, number of such values of x = 23   Answer 23
Answer: B
Walking at 8KMPH From Point E to Point railway station, mike will miss the train by 5 minutes. If he walks at 10KMPH he will reach the station by 5 minutes early.What is the distance between Point E to Railway station?  Choose the correct choice from the following answers
A) A)9KM	B) B)6.66KM	C) C)7.25KM	D) D)12.40KM	E) E)13KM

Solution: Since time differences given are in minutes so let's convert speed in Km per minute   8 kmph = 8/60 km per minute = (2/15) km per minute   10 kmph = 10/60 km per minute = (1/6) km per minute   Let, Time of train to depart from station = t minutes   Distance between Point E and Railway Station = Speed*Time = (2/15)*(t+5)   Distance between Point E and Railway Station = Speed*Time = (1/6)*(t-5)   i.e. (2/15)*(t+5) = (1/6)*(t-5)   i.e. 12t+60 = 15t - 75   i.e. 3t = 135   i.e. t = 45 minutes   i.e. Distance = (1/6)*(t-5) = (1/6)*(45-5) = 40/6 = 20/3 Km = 6.66 Km   Answer: Option 6.66KM
Answer: B
A tap can fill a tank in 6 hours. After half the tank is filled three more similar taps are opened. What is the total time taken to fill the tank completely? Choices:  A) 3 hrs 15 min  B) 3 hrs 45 min  C) 4 hrs  D) 4 hrs 15 min  E) 5 hrs

Solution: Time taken by one tap to fill the tank = 3 hrs.   Part filled by the taps in 1 hour = 4 * 1/6 = 2/3   Remaining part = 1 - 1/2 = 1/2   2/3 : 1/2 :: 1 : x   x = 1/2 * 1 * 3/2 = 3/4 hrs. i.e., 45 min   So, total time taken = 3 hrs 45 min.   ANSWER:3 hrs 45 min
Answer: B
If p is an even integer and q is an odd integer, which of the following must be an odd integer?	Choices:
A) p/q  B) pq  C) 2p+q  D) 2(p+q)  E) 3p/q

Solution: A. p/q   p = 6, q = 3 => p/q is odd integer   p = 4, q=3 =>p/q is not integer   B. pq   Must be even   C. 2p+q   2p must be even, q is odd=> 2p+q must be ODD: CORRECT   D. 2(p+q)   must be even   E. 3p/q   Same A   Answer: 2p+q
Answer: C
There are 6 chess amateurs playing in Villa's chess club tournament. If each chess amateur plays with exactly 4 other amateurs, what is the total number of chess games possible to be played in the tournament?	Answers:
A) 10
B) 20
C) 40
D) 60
E) 12

Solution: Method 2:   Each person is one participant of 4 games. So there are in all 4*6= 
4*6 = 24
24 instances of one participant games. But each game has 2 participants so total number of games= 24/2= 
24/2 = 12
12   12
Answer: E
Find the sum The difference between the compound and S.I. on a certain sum of money for 2 years at 10% per annum is Rs.18 of money?
Select the correct option
A) 1800  B) 1992  C) 9921  D) 2798  E) 2789

Solution: P = 18(100/10)2   => P = 1800   1800nswer: 1800
Answer: A
A can give B 80 meters start and C 200 meters start in a kilometer race. How much start can B give C in a kilometer race?
Choose the correct choice from the following choices:	A) 130.12	B) 130.43	C) 130.22	D) 111.0	E) 111.12

Solution: A runs 1000 m while B runs 920 m and C runs 800 m.   The number of meters that C runs when B runs 1000 m,   = (1000 * 800)/920   = 869.56 m   B can give C = 1000 - 869.56   =130.43m.   Answer:130.43
Answer: B
A man is trying to fill up his pool and he has three different water sources, if he uses faucet A it takes 5 hours to fill up the pool, if he used faucet B it takes 20 hours to fill it up. He first runs the water from source A for 2 hours, then turning that off, he continues with faucet B for 10 hours. Then turning that off as well he uses Faucet C and in 3 hours the pool is filled up. How long does it take to fill up the pool only using the faucet C?
Choose the correct choice from the following answers
A) 10 hours	B) 20 hours	C) 30 hours	D) 40 hours	E) 5 hours

Solution: 2/5 +10/20 + 3/x = 1 x = 30ANSWER =30 hours
Answer: C
The age of Somu is one-third his father's. 5 years back he was one-fifth of his father's age. What is his persent age ?
Choose the correct choice
A) 11	B) 13	C) 14	D) 12	E) 10

Solution: Explanation :   Let Somu's age be x and that of his father be 3x.   So, x - 5 = 3x - 5/5 = x = 10   Answer : Option 10
Answer: E
It was calculated that 75 men could complete a piece of work in 10 days. When work was scheduled to commence, it was found necessary to send 25 men to another project. How much longer will it take to complete the work?
Pick one
A) 10 days. B) 20 days. C) 25 days. D) 12.5 days. E) 15 days.

Solution: One day work = 1 / 10   One man’s one day work = 1 / ( 10 * 75)   Now:   No. Of workers = 50   One day work = 50 * 1 / ( 10 * 75)   The total no. of days required to complete the work = (75 * 10) / 50= 
(75 * 10) / 50 = 15
15   Answer:15 days.
Answer: E
A and B invests Rs.6000 and Rs.9000 in a business. After 4 months, A withdraws half of his capital and 2 months later, B withdraws one-third of his capital. In what ratio should they share the profits at the end of the year? Choose the correct choice from the following answers:
A) 32:99
B) 82:31
C) 24:45
D) 34:89
E) 35:21

Solution: A : B   (6000*4)+(3000*8) : (9000*6)+(6000*6)   48000 : 90000   24 : 45   Answer:24:45
Answer: C
If y exceeds x by 20%, then x is less than y by?  Choose the correct option:
A) 16 2/38% B) 16 3/3% C) 16 2/3% D) 18 2/3% E) 126 2/3%

Solution: X=100	y=120   120------20   100-------? => 16 2/3%   Answer: 16 2/3%
Answer: C
Calculate the fourth proportional to 7.4, 8.1 and 9.8?
Choose one
A) 10.73 B) 13.73 C) 15.73 D) 11.73 E) 12.73

Solution: Explanation:   Formula = Fourth propotional = (b × c)/a   10.73 = 7.4 , B = 8.1 and C = 9.8   (8.1 × 9.8)/7.4 = 10.73   10.73nswer: Option 10.73
Answer: A
The sum of three numbers is 98. The ratio of the first to the second is 2/3, and the ratio of the second to the third is 5/8. The second number is:  Choose the correct choice from the following options
A) 20
B) 30
C) 60
D) 70
E) 10

Solution: B   30   Let the three numbers be x, y and z.   Sum of the numbers is 98.   x + y + z = 98………………(i)   The ratio of the first to the second is 2/3.   x/y = 2/3.   x = 2/3 × y.   x = 2y/3.   The ratio of the second to the third is 5/8.   y/z = 5/8.   z/y = 8/5.   z = 8/5 × y.   z = 8y/5.   Put the value of x = 2y/3 and z = 8y/5 in (i).   2y/3 + y + 8y/5 = 98   49y/15 = 98.   49y = 98 × 15.   49y = 1470.   y = 1470/49.= 
1470/49. = 30
30 .   Therefore, the second number is 30.
Answer: B
Dominos charges $6.25 for a veg pizza of std size that costs a total of $2.85 to make. Pizza Hut charges $5.80 for a similar pizza that costs $1.80 to make. If Dominos sells 2,000 pizzas, how many must Pizza Hut sell to make at least as much in total gross profit as its competitor does? Select:
A) 858  B) 1875  C) 14,667  D) 63,840  E) 146,667

Solution: Dominos : Profit/pizza = 6.25-2.85 = 3.75   : No of pizza = 2,000   : Gross Profit = 2,000*3.75 = 7,500   Pizza Hut : Profit/pizza = 4   : Gross Profit = 7,500   : No of Cups = 7,500/4 = 1875   Answer 1875
Answer: B
What is the least number of squares tiles required to pave the floor of a room 4 m 5 cm long and 2 m 25 cm broad?
Pick one
A) 14	B) 20	C) 40	D) 44	E) 45

Solution: Length of largest tile = H.C.F. of 405 cm and 225 cm = 45 cm.   Area of each tile = (45 x 45) cm2.   Required number of tiles =405 x 225/(45^2)= 45.   ANSW45R:45
Answer: E
If n=4p where p is a prime number greater than 3, how many different positive even divisors does n have, including n?  Choose the correct choice from the following answers
A) 2  B) 6  C) 4  D) 8  E) 10

Solution: We're told that N = 4P and that P is a prime number greater than 3. Let's TEST P = 4; so N = 16   The question now asks how many DIFFERENT positive EVEN divisors does 16 have, including 16?   16:   1,16   2,8   4,4   How many of these divisors are EVEN? 2,8,4,16…..4 even divisors.   ANSWER:4
Answer: C
If Henry were to add 6 gallons of water to a tank that is already 3/4 full of water, the tank would be 7/8 full. How many gallons of water would the tank hold if it were full?	Select the correct option.
A) 25	B) 48	C) 64	D) 80	E) 96

Solution: 7/8x-3/4x=6galls   1/8*x=6gallons   x=48 gallons   Answer 48
Answer: B
Three machines operating independently, simultaneously, and at the same constant rate can fill a certain production order in 52 hours. If one additional machine were used under the same operating conditions, in how manyfewerhours of simultaneous operation could the production order be fulfilled? Options:
A) 6
B) 9
C) 12
D) 27
E) 13

Solution: If 3 Machines can do the work in 36 hr then 4 Machines can do the work in   3/4*52= 
  3/4*52 = 39
39 Hrs. hence time saved will be 13hr   option 13 is the correct answer
Answer: E
The average of four consecutive even numbers is 27. find the largest of these numbers? Choose the most appropriate option
A) 10  B) 20  C) 30  D) 40  E) 50

Solution: let the numbers be x,x+2,x+4 andx+6. then,   (x+(x+2)+(x+4)+(x+6))/4) = 27   (4x+12)/4 = 27   x+3=27   x=24.   Therefore the largest number=(x+6)=24+6= 
24+6 = 30
30.   Option 30
Answer: C
There are 2 sections with 6 questions each. If two questions are selected from each section, the chance of getting different questions is________  Choose the correct choice from the following answers.
A) 10 B) 100 C) 240 D) 225 E) 6000

Solution: we have to select two questions from each section so the chances are 6C2.6C2=225   ANSWER:225
Answer: D
Find the least number which when divided by 35 and 11 leaves a remainder of 1 in each case. Choose the most appropriate option:
A) 384
B) 391
C) 388
D) 397
E) 386

Solution: The least number which when divided by different divisors leaving the same remainder in each case   = LCM(different divisors) + remainder left in each case.   Hence the required least number   = LCM(35, 11) + 1 = 386.   ANSW386R:386
Answer: E
Bag A contains red, white and blue marbles such that the red to white marble ratio is 1:3 and the white to blue marble ratio is 2:3. Bag B contains red and white marbles in the ratio of 1:4. Together, the two bags contain 28 white marbles. How many red marbles could be in bag A? Choices:
A) 1
B) 3
C) 4
D) 6
E) 7

Solution: # of Red marbles in Bag A can be either 2 or 6. No 2 in the choices, so 6. D.   Bag A:   R:W:B = 2:6:9   Bag B   R:W = 1:4   6X + 4Y = 28 i.e 3X + 2Y = 14   X has to be odd to make an odd sum from the eq.   X = 2 , Y = 4 OR X = 4, Y = 1   So R can be 2X i.e 4 or 8.   Answer 4
Answer: C
From a corner of a ground of 20m*30m, a boy hits a ball that travels maximum 14m. What is the area of the football ground through which the ball can pass by the hit of that boy from that corner ?	Select:
A) 132
B) 140
C) 150
D) 154
E) 168

Solution: Area covered by ball = Pi*r^2/4 ( here we divide by 4 because ball is hit from the corner of the ground and only 1/4 part the ball can go)   where r= 14 m = length of pass   So area = (22/7)*14*14/4= 
(22/7)*14*14/4 = 154
154 sq m   answer :154
Answer: D
If n is a multiple of 5, n=p^2q, where p and q are prime numbers. Which of the following must be a multiple of 25?
Choose the correct answer.
A) p^2	B) q^2	C) pq	D) p^2q^2	E) p^3q

Solution: You are given that n = p^2 * q, which is a multiple of 5. Therefore p^2 * q is a multiple of 5. Since 5 is a prime number, p OR q must be a multiple of 5. Therefore, in order to be a multiple of 25, you must have a MINIMUM of p^2 * q^2 in the answer, since you don't know whether p or q is the multiple of 5. The only answer which satisfies this condition is D. The answer is p^2q^2: p^2*q^2.
Answer: D
(x —1)(x + 3) > 0
(x +5)(x—4) < 0
Which of the following values of x satisfy both inequalities shown?
I. 3
II. -6
III. 2
IV. 5  Choose the correct choice
A) I and II only	B) I and III only	C) II and III only	D) II and IV only	E) I, II, III, and IV

Solution: (x - 1)(x + 3) > 0 --> x<-3 or x>1.   (x + 5)(x - 4) < 0 --> -5<x<4.   Among choices only 3 and 2 satisfy both inequalities.   Answer: I and III only.
Answer: B
6persons enter a lift on the ground floor of a 9floor apartment. Assuming that each of them independently & with equal probability can leave the lift at any floor beginning with the first, what is the probability that all the 6persons are leaving the lift at different floors? Pick:
A) 7P6/8^6 B) 5P6/8^6 C) 8P6/8^6 D) 9P6/8^2 E) 8P6/8^3

Solution: Apart from the ground floor, there are 8 floors   Let's find out the total number of ways in which all the six persons can leave the   lift at eight different floors   The 1st person can leave the lift in any of the 8 floors (8 ways)   The 2nd person can leave the lift in any of the remaining 7 floors (7 ways)   The 3nd person can leave the lift in any of the remaining 6 floors (6 ways)   ...   The 6th person can leave the lift in any of the remaining 3 floors (3 ways)   Total number of ways = 8 × 7 × 6 × 5 × 4 × 3 = 8P6   (In fact, from the definition of permutations itself,   we will be able to directly say that the number of ways in which all the six persons   can leave the lift at 8 different floors = 8P6)   n(E)= Total Number of ways in which all the six persons can leave the lift at eight   different floors = 8P6   Now we will find out the total number of ways in which each of the six persons   can leave the lift at any of the eight floors   The 1st person can leave the lift in any of the 8 floors (8 ways)   The 2nd person can leave the lift in any of the 8 floors (8 ways)   The 3nd person can leave the lift in any of the 8 floors (8 ways)   ...   The 6th person can leave the lift in any of the 8 floors (8 ways)   Total number of ways = 8 × 8 × 8 × 8 × 8 × 8 = 86   i.e., The total number of ways in which each the six persons can leave the lift   at any of the eight floors = n(S) = 86   P(E) = n(E)n(S)=8P6/8^6   8P6/8^6
Answer: C
An army’s recruitment process included N rounds of selection tasks. For the first A rounds, the rejection percentage was 60 percent per round. For the next B rounds, the rejection percentage was 50 percent per round and for the remaining rounds, the selection percentage was 70 percent per round. If there were 20000 people who applied for the army and 196 were finally selected, what was the value of N?	Choices.
A) 4
B) 5
C) 6
D) 8
E) 10

Solution: step(1) 8000 accepted.   step(2) another 40%of 8000=3200 accepted.   here it is quiet observable that if we further deduct candidate by 60% it would change our probablity of easy going 2000 candidate.   so i would get to second stage of recruitment where 50 % is accepted   step(3) 50% of 3200=1600   step(4) 50% of 1600=800   step(5) 50% of 800=400   Step(6) 50% of 400=200   70% of 400=280   and last step of accepting 70% of 280=196(our target)   total 8 steps required.   Ans 8
Answer: D
1254,1254,627,209,52.25,? Pick:
A) 1.29
B) 10.45
C) 3.58
D) 4.96
E) 3.87

Solution: Explanation :   Terms are continuously divided by 1,2,3 ,4, and so on   1254   1254 Ã· 1 = 1254   1254 Ã· 2 = 627   627 Ã· 3 = 209   209 Ã· 4= 52.25   52.25Ã·5=10.45   Answer : Option 10.45
Answer: B
How many integer values R are there for x such that 1 < 3x + 5 < 17?
Choose the correct option:
A) Two
B) Three
C) Four
D) Five
E) Six

Solution: 1 < 3x + 5 < 17   => -4 < 3x < 12   => -4/3 < x < 4   x can take integer values R -1,0 , 1 , 2 , 3   Answer Five
Answer: D
Alfred buys an old scooter for Rs. 4700 and spends Rs. 800 on its repairs. If he sells the scooter for Rs. 5800, his gain percent is Choices
A) 6/19% B) 6/17% C) 5 5/11% D) 3 5/11% E) None of these

Solution: Explanation:   Whenever we get this type of question, we should have formula in mind that,   Gain% = (gain/cost)*100   Cost = 4700 + 800 = Rs. 5500   S.P. = Rs. 5800   Profit = 5800 - 5500= 
5800 - 5500 = 300
300   Gain%=300/5500∗100=5 5/11%   Option 5 5/11%
Answer: C
How many options are there for license plate numbers if each license plate can include 2 digits and 3 letters (in that order), or 3 digits and 2 letters (in that order)? (Note: there are 26 letters in the alphabet)
Select the correct option
A) 37×260^2  B) 36×260^2  C) 36×270^2  D) 10^2×26^3  E) 10^3×26^2

Solution: We are given that License plate could be either of the form DDLLL or DDDLL   Now, every D could be filled in 10 ways and every L could be filled in 26 ways.   or Number of ways for DDLLL = 10 * 10 * 26 * 26 * 26 --(1)   Number of ways for DDDLL = 10 *10*10*26*26 --(2)   Total ways = (1) +   (2)   = \(36×260^2\)   Answer s 36×260^2.
Answer: B
The average of seven numbers is 18. The average of first three numbers is 14 and the average of last three numbers is 19. What is the middle number?	Choose the correct answer.
A) 26  B) 27  C) 29  D) 32  E) 36

Solution: The total of seven numbers = 7X18 = 126   The total of first 3 and last 3 numbers is = 3 X 14+3 X 19 = 99   So, the middle number is  (126 - 99 )= 
 (126 - 99 ) = 27
27   27
Answer: B
If -2x+3y=8 and 4x-3y=20, what is the sum of x and y?  Choices
A) 24	B) 28	C) 18	D) 26	E) 32

Solution: Given -2x+3y=8 ---Eq 1   4x -3y =20 -- Eq 2   Sum both eqns we get 2x = 28 => x = 14   Sub 2x in eq 1 => -28 + 3y = 8.   => y = 12   Now X+Y = 12 + 14= 
12 + 14 = 26
26   Option 26 is correct answer.
Answer: D