MU-NLPC/Calc-aqua_rat huggingface dataset:
How many different possible arrangements A can be obtained from the letters G, M, A, T, I, I, and T, such that there is at least one character between both I's? Choose the correct choice from the following
A) 360  B) 720  C) 900  D) 1800  E) 5040

Solution: Total ways for arranging without restriction = 7!/ (2!2!) { 2! is becoz of two T's and other 2! for two I's)   Restriction : atleast one character between I's = Possible ways - both I's together i.e.o character between I's   _ _ _ _ _ (I I)   Both I's Together = 6! (Assuming 2 I's as one unit) /2!(for 2 T's) * 2! (No of arrangements of 2 I's)/2! (for 2 I's)   =6!/2!   Therefore ans A= 7!/ (2!2!) -6!/2! = 900   HEN900E 900.
Answer: C
Find the simple interest on Rs.500 for 9 months at 6 paisa per month?  Select the correct option
A) 278	B) 270	C) 876	D) 279	E) 367

Solution: I = (500*9*6)/100= 
(500*9*6)/100 = 270
270   Answer: 270
Answer: B
. Ram sold two bicycles, each for Rs.990. If he made 10% profit on the first and 10% loss on the second, what is the total cost of both bicycles?	Select the correct option.
A) 2000 B) 2009 C) 2007 D) 20054 E) 2002

Solution: (10*10)/100= 
(10*10)/100 = 1
1%loss   100 --- 99   ? --- 1980=> Rs.2000   2000nswer: 2000
Answer: A
At 6′o a clock ticks 6 times. The time between first and last ticks is 20 seconds. How long does it tick at 12′o clock
Choose the correct answer.
A) 47  B) 76  C) 44  D) 66  E) 11

Solution: Explanation:   For ticking 6 times, there are 5 intervals.   Each interval has time duration of   20/5= 
  20/5 = 4
4 secs   At 12 o'clock, there are 11 intervals,   So total time for 11 intervals= 11 × 4 = 44 secs.   Answer: 44
Answer: C
How much 50% of 56 is greater than 30% of 50? Choose the correct choice from the following:
A) 18
B) 99
C) 13
D) 55
E) 71

Solution: (50/100) * 56 – (30/100) * 50   28 - 15= 
28 - 15 = 13
13   Answer: 13
Answer: C
A and B together can do a work in 6 days. If A alone can do it in 15 days. In how many days can B alone do it?
Choose the correct choice from the following options:
A) 10  B) 15  C) 12  D) 16  E) 18

Solution: Explanation:   1/6 â€“ 1/15 = 1/10 => 10   10NSWER IS 10
Answer: A
The closest approximation of F(69.28 × 0.004)/0.03 is
Choose one
A) 0.092	B) 0.92	C) 9.2	D) 92	E) 920

Solution: F(69.28 × 0.004)/0.03   1. 0.004 = 4 × 10^(-3)   2. 0.03 = 3 × 10^(-2)   3. (a × b)/c = a × (b/c)   4. 0.004/0.03 = 4 × 10^(-3)/ (3 × 10^(-2)) = 4 × 10^( -3 - (-2))/3 = 4 × 10^(-1) / 3 = (4/3) × 10^(-1) = 1.333 × 10^(-1)   Therefore,   (69.28 × 0.004)/0.03 = 69.28 × (0.004/0.03) = 69.28 × 1.33 × 10^(-1) = 69.28 × 1.33/10 = 6.928*1.33   Now,   7 × 2 = 14   7 × 1 = 7   or better:   6.9 × 1 = 6.9   6.9 × 2 = 13.8   hence,   6.9 <6.928 × 1.33 < 13.8   9.2 is the only answer that satisfies this condition.9.2
Answer: C
The number of natural numbers n such that (n+1)^2/(n+7) is an integer, is ?  Choose the most appropriate option:	A) 4	B) 5	C) 6	D) 7	E) 8

Solution: we can use (n+1)^2 greater than (n+7) which gives n>2,-3........now there are four integers -2.-1,0,1 in between -3 and 2.   so answer is 4.   4NSWER:4
Answer: A
Mary, Peter, and Lucy were picking chestnuts. Mary picked twice as much chestnuts than Peter. Lucy picked 2 kg more than Peter. Together the three of them picked 26 kg of chestnuts. How many kilograms did each of them pick?
Choose the most appropriate option: A) 5, 12, and 8 kg B) 6, 12, and 8 kg C) 7, 12, and 8 kg D) 8, 12, and 8 kg E) None

Solution: Solution:   Let x be the amount Peter picked. Then Mary and Lucy picked 2x and x+2x+2, respectively. So   x+2x+x+2=26   4x=24   x=6   Therefore, Peter, Mary, and Lucy picked 6, 12, and 8 kg, respectively.   Answer 6, 12, and 8 kg
Answer: B
A chair is bought for Rs.600/- and sold at a loss of 10% find its selling price?	Choose the correct choice from the following answers.
A) Rs.540/-
B) Rs.560/-
C) Rs.580/-
D) Rs.590/-
E) Rs.600/-

Solution: 100 % ------> 600 (100 * 6 = 600)   90 % ------> 540 (90 * 6 = 540)   Selling price = Rs.540/-   Option 'Rs.540/-'
Answer: A
A single discount equivalent to the discount series of 15%, 10% and 5% is?
Choose the correct option:  A) 27.325  B) 31.0  C) 31.6  D) 31.1  E) 31.5

Solution: 100*(85/100)*(90/100)*(95/100)   = 68.4   100 - 72.675= 
100 - 72.675 = 27.325
27.325   27.325nswer: 27.325
Answer: A
If n is a prime number, which of the following could be true  Choose the correct choice from the following answers
A) n^n=n B) n^2/4= is even C) (n)(n^n) = is negative D) n^n/4 = 1^(n-1) E) n^2+n^3= n^5

Solution: D should be the answer.   2^2/4 = 1^(2-1)
Answer: D
What is the product of the greatest 2 digit multiple of 13 and the greatest 2 digit prime number?
Choices
A) 9,312
B) 9,408
C) 9,506
D) 8,827
E) 9,702

Solution: the greatest 2 digit multiple of 13: 91   the greatest 2 digit prime numebr: 97   97*91.   8827   8,827
Answer: D
In the rectangular coordinate system, what is the area of triangle CDE with points
C=(3,3)
D=(1,4)
E=(8,0)	Answers:
A) 0.6	B) 0.75	C) 0.9	D) 0.5	E) 0.3

Solution: Use the formula of the distance formula   square root (x2-x1)^2+(y2-y1)^2   0.5o this for each of the sides and then the value is given as 0.5.
Answer: D
H, Be, F, S, Mn, Kr, In, Gd, Tl, ?
What's the next in the sequence ?  Choose the correct choice from the following.
A) Fm  B) Ks  C) gh  D) kl  E) Zd

Solution: A   Fm.   These are the chemical elements whose atomic numbers are perfect squares.   1, 4, 9, 16, 25, 36, 49, 64, 81, 100
Answer: A
Pipe A can fill a tank in 12 hours. Due to a leak at the bottom, it takes 18 hours for the pipe A to fill the tank. In what time can the leak alone empty the full tank?  Choose the most appropriate option.
A) 36 B) 87 C) 40 D) 37 E) 86

Solution: Let the leak can empty the full tank in x hours 1/12 - 1/x = 1/18   => 1/x = 1/12 - 1/18 = (3 - 2)/36 = 1/36   => x = 36.   36nswer: 36
Answer: A
A man has Rs. 160 in the denominations of one-rupee notes, five-rupee notes and ten-rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has ?
Select:	A) 45	B) 60	C) 30	D) 90	E) 95

Solution: Let number of notes of each denomination be x.   Then x + 5x + 10x = 160   16x = 160   x = 10.   Hence, total number of notes = 3x = 30.   Answer: Option 30
Answer: C
Two cars cover the same distance at the speed of 50 and 63 kmps respectively. Find the distance traveled by them if the slower car takes 1 hour more than the faster car.  Choose the correct answer:
A) 212 km
B) 214 km
C) 224 km
D) 216 km
E) 231 km

Solution: 50(x + 1) = 63x   X = 3.85   60 * 3.85= 
60 * 3.85 = 231
231 km   ANSW231 kmR:231 km
Answer: E
A pump can fill a tank with water in 2 hours. Because of a leak, it took 2 1/3 hours to fill the tank. The leak can drain all the water in ? Choose the correct choice from the following:
A) 10hr B) 14hr C) 12hr D) 9hr E) 15hr

Solution: Work done by the leak in 1 hour = 1/2 - 3/7 = 1/14   Leak will empty the tank in 14 hrs   Answer is 14hr
Answer: B
Two trains are running in opposite directions in the same speed. The length of each train is 120 meter. If they cross each other in 12 seconds, the speed of each train (in km/hr) is Select
A) 42	B) 36	C) 28	D) 20	E) 24

Solution: Explanation:   Distance covered = 120+120= 
120+120 = 240
240 m   Time= 12 s   Let the speed of each train = v. Then relative speed = v+v = 2v   2v = distance/time = 240/12= 
240/12 = 20
20 m/s   Speed of each train= v = 20/2= 
20/2 = 10
10 m/s= 10×36/10 km/hr = 36 km/hr   Answer: Option 36
Answer: B
If 5a + 7b = l, where a and b are positive integers, what is the largest possible value of l for which exactly one pair of integers (a, b) makes the equation true? Choose the correct choice from the following
A) 35 B) 48 C) 69 D) 70 E) 74

Solution: 5*a1 + 7*b1 = l   5*a2 + 7*b2 = l   5*(a1 - a2) = 7*(b2 - b1)   since we are dealing with integers we can assume that a1 - a2 = 7*q and b2 - b1 = 5*q where q is integer, so whenever we get a pair for (a;b) we can find another one by simply adding 7 to a and subtracting 5 from b or vice versa, subtracting 7 from a and adding 5 to b.   Lets check how it works for our numbers, starting from the largest:   E)74 = 5*12 + 7*2 (a1 = 12, b1 = 2), subtract 7 fromaand add 5 tobrespectively, so a2 = 5 and b2 = 7, second pair - bad   70)70 = 5*7 + 7*5 (a1 = 7, b1 = 5), if we add 7 toawe will have to subtract 5 from b but b can't be 0, so - no pair, if we subtract 7 froma, we'll get a = 0 which also isn't allowed - no pair, thus this is the only pair for (a;b) that works,good!, thus   70 is the answer
Answer: D
An even positive integer 'x' has 'y' positive integral factors including '1' and the number itself. How many positive integral factors does the number 4x have? Choose one
A) 4y	B) 3y	C) 16y	D) 5y	E) Cannot be determined

Solution: Let’s express x as a product of its prime factors:   x=2a∗3b∗5c∗…x=2a∗3b∗5c∗…   Total number of its positive divisors will be   (a+1)∗(b+1)∗(c+1)∗…=y(a+1)∗(b+1)∗(c+1)∗…=y   Now we’ll do the same for the 4x   4x=22∗2a∗3b∗5c∗…=2a+2∗3b∗5c…4x=22∗2a∗3b∗5c∗…=2a+2∗3b∗5c…   Total number of positive divisors of 4x will be   (a+3)∗(b+1)∗(c+1)…=y′(a+3)∗(b+1)∗(c+1)…=y′   For easier calculations let’s take (b+1)∗(c+1)∗…=z(b+1)∗(c+1)∗…=z   We have: (a+3)∗z=y′(a+3)∗z=y′   (a+1+2)∗z=y′(a+1+2)∗z=y′   (a+1)∗z+2∗z=y′(a+1)∗z+2∗z=y′   y+2∗z=y′y+2∗z=y′   So, as we can see, in order to find out the total # of positive divisors of 4x we need to know # of odd divisors of x, which is not given in the question.   Answer Cannot be determined.
Answer: E
What is Sonia’s present age?
I.	Sonia’s present age is five times Deepak’s present age.
II.	Five years ago her age was twenty-five times Deepak’s age at that time.	Choose the correct answer:
A) I alone sufficient while II alone not sufficient to answer
B) II alone sufficient while I alone not sufficient to answer
C) Either I or II alone sufficient to answer
D) Both I and II are not sufficient to answer
E) Both I and II are necessary to answer

Solution: EXPLANATION   I. S = 5D D = s/5….(i)   II. S – 5 = 25 (D – 5) <=> S = 25D – 120 ….(ii)   Using (i) in (ii), we get S =(25 x S/5) - 120   4S = 120.   S = 30.   Thus, I and II both together give the answer. answer is (Both I and II are necessary to answer).
Answer: E
6 boys and 4 girls appeared in a exam. If 4 students are failed how many chances at least one girl is failed?
Select the correct option
A) 198
B) 200
C) 190
D) 195
E) 180

Solution: 4 girls and 6 boys. Four students is failed   It is always better to subtract the total from none in case of at least one problems.   Total ways = 10C4 = 210   Total ways without any girls = 6C4 = 15   Hence ways in which at least one man will be present = 210 - 15= 
210 - 15 = 195
195   Correct option: 195
Answer: D
How long will a boy take to run round a square field of side 30 meters, if he runs at the rate of 12km/hr?  Select the correct option:
A) 52sec
B) 45sec
C) 60sec
D) 25sec
E) 36sec

Solution: Speed = 12 km/hr = 12*5/18 = 10/3 m/sec   Distance = 30*4= 
30*4 = 120
120m   Time taken= 120*3/10= 
120*3/10 = 36
36sec   Answer is 36sec
Answer: E
A motor pool has 800 vehicles of which 30 percent are trucks. 20 percent of all the vehicles in the motor pool are diesel, including 15 trucks. What percent of the motor pool is composed of vehicles that are neither trucks nor diesel?
Choices:
A) 65%
B) 52%
C) 45%
D) 30%
E) 10%

Solution: Trucks = 30% of 800 = 240   Other Vehicles (Excluding Trucks) = 800-240= 
800-240 = 560
560   Diesel Vehicle= 20% of 800 = 160 (Including 15 Trucks)   Other Diesel Vehicles (Excluding Trucks) = 160-15= 
160-15 = 145
145   Trucks that are NOT diesel= 240 - 15= 
240 - 15 = 225
225   Other Vehicles that are NOT diesel Vehicles= 560-145= 
560-145 = 415
415   Required %= (415/800)*100 = 51.87%=52%   Answer: option 52%
Answer: B
Angelo and Isabella are both salespersons. In any given week, Angelo makes $570 in base salary plus 8 percent of the portion of his sales above $1,000 for that week. Isabella makes 10 percent of her total sales for any given week. For what amount of weekly sales would Angelo and Isabella earn the same amount of money?  Options
A) 23,500  B) 24,500  C) 25,500  D) 26,500  E) 27,500

Solution: Let the weekly sales of both = x   570+(x−1000)8/100=10/100x   x = 24500   ANSWER:24,500
Answer: B
A 300 m long train crosses a platform in 39 sec while it crosses a signal pole in 18 sec. What is the length of the platform?	Choose the correct option.
A) 350  B) 300  C) 400  D) 450  E) 500

Solution: Speed = 300/18 = 50/3 m/sec.   Let the length of the platform be x meters.   Then, (x + 300)/39 = 50/3   3x + 900 = 1950 => x = 350 m.   350NSWER 350
Answer: A
The probability that a brand A widget is defective is x, the probability that a brand B widget is defective is 0.06, and the probability that a brand C widget is defective is 0.08. There are 40 brand A widgets, 35 brand B widgets, 25 brand C widgets, and nothing else in a container. If a widget is selected at random from the container, the probability that the widget selected is defective is 0.053. What is the value of x?
Choose the correct choice from the following:  A) 0.03  B) 0.04  C) 0.048  D) 0.05  E) 0.12

Solution: Probability of Brand A defective is x   Probability of Brand B defective is 0.06 which 6/100. Which tells you there are 2 defective piece in a lot of 33, for 35 lot it is approx - 2.12   Probability of Brand C defective is 0.08 which 8/100. Which tells you there are 2 defective piece in a lot of 25   Total = 40 + 25 + 25 = 100   Probability of having defective piece in a lot of 100 ( All brands ) = 0.053   Hence 5.3 defective piece out 100 lot.   So 40x + 2.12 + 2 = 5.3   x = 0.03   0.03NSWER :Opt 0.03.
Answer: A
Victor gets 80 % marks in examinations. If these are 240 marks, find the maximum marks. Answers:
A) 334  B) 300  C) 376  D) 288  E) 271

Solution: Let the maximum marks be m   Then 80 % of m = 240   ⇒ 80/100 × m = 240   ⇒ m = (240 × 100)/80   ⇒ m = 24000/80= 
24000/80 = 300
300   Therefore, maximum marks in the examinations are 300   Answer:300
Answer: B
Mr. Smith calculated the average of 10 three digit numbers. But due to a mistake he reversed the digits of a number and thus his average increased by 59.4. The difference between the unit digit and hundreds digit of that number is :	Options.
A) 3	B) 4	C) 5	D) 6	E) 7

Solution: Since the average increased by 59.4 and there were a total of 10 numbers, it means the incorrect number was 297 greater than the correct number.   Say, the correct number was abc (where a, b and c are the digits of the 3 digit number)   Then the incorrect number was cba.   100c + 10b + a - (100a + 10b + c) = 594   99c - 99a = 99(c - a) = 594   594 = 99*6 = 99(c - a)   So c - a = 6   Answer (6)
Answer: D
If a train, travelling at a speed of 90 kmph, crosses a pole in 5 sec, then the length of train is? Pick one:
A) 128 m	B) 125 m	C) 198 m	D) 276 m	E) 279 m

Solution: D = 90 * 5/18 * 5= 
90 * 5/18 * 5 = 125
125 m   Answer: 125 m
Answer: B
John has taken four (8) tests that have an average of 82. In order to bring his course grade up to a ‘B’, he will need to have a final average of 87. What will he need to average on his final two tests to achieve this grade?	Choose the correct choice from the following choices.
A) 87 B) 90 C) 92 D) 107 E) 97

Solution: 87-82= 
87-82 = 5
5*8= 
5*8 = 40
40 points    2*87= 
 2*87 = 174
174   174+40= 
174+40 = 214
214 points to be scored in the 2 tests.   Avg of 2 tests= 214/2= 
214/2 = 107
107   Answer: 107   Traditional Method:   Total scored till now   82*8= 
  82*8 = 656
656   Total score to avg 87 in 10 tests= 87*10= 
87*10 = 870
870   Total to be scored on 2 tests= 870-656= 
870-656 = 214
214   Avg on 2 tests= 214/2= 
214/2 = 107
107   Answer 107
Answer: D
If the average (arithmetic mean) of a list of numbers is 12 and the standard deviation of that list of numbers is 1.3, then which of the following numbers is more than two standard deviations from the mean?
I. 13.2
II. 12.3
III. 9.3 Choose the correct choice:  A) I only  B) I and II only  C) II only  D) III only  E) I and III only

Solution: Mean = 12   SIII only = 1.3   2 SIII only above mean = 12+2*1.3= 
12+2*1.3 = 14.6
14.6   2 SIII only below mean= 12-2*1.3= 
12-2*1.3 = 9.4
9.4   12.3 and 13.2 lies in the range of 2SIII only from mean   Answer: Option III only
Answer: D
If Shreehari walks in the speed of 4.5 km/hr from his house, in what time will he reach his school which is 750 m long from his house?
Choose the most appropriate option.
A) 5  B) 30  C) 10  D) 12  E) 15

Solution: Speed = 4.5 * 5/18= 
4.5 * 5/18 = 1.25
1.25 m/sec   Time taken= 750/1.25= 
750/1.25 = 600
600 sec ie. 10 mins.   Answer:10
Answer: C
At Company K, 15 percent of the employees are secretaries and 60 percent are salespeople. If there are 60 other employees of Company K, how many employees does Company K have?  Choose the correct choice from the following choices:
A) 240
B) 180
C) 190
D) 200
E) 400

Solution: Let the total number of employees in the company be x   % of secretaries = 15%   % of salespeople = 60%   % of of employees other than secretaries and salespeople = 100 - 75= 
100 - 75 = 25
25%   But this number is given as 60   so 25% of x= 60   x = 240   Therefore there a total of 240 employees in the company K   Correct answer - 240
Answer: A
Two goods trains each 500 m long are running in opposite directions on parallel tracks. Their speeds are 45 km/hr and 30 km/hr respectively. Find the time taken by the slower train to pass the driver of the faster one? Choose the most appropriate option:  A) 40  B) 45  C) 48  D) 51  E) 44

Solution: Relative speed = 45 + 30= 
45 + 30 = 75
75 km/hr.   75 * 5/18= 125/6 m/sec.   Distance covered = 500 + 500= 
500 + 500 = 1_000
1000 m.   Required time= 1000 * 6/125= 
1000 * 6/125 = 48
48 sec.   Answer: Option 48
Answer: C
How many minutes does it take Sharuk to type 25 words if he types at the rate of 5 words per minute? Choose the correct choice from the following answers:
A) 3	B) 5	C) 8	D) 15	E) 7

Solution: time*rate=job --> time*5=25 --> time=25/5= 
25/5 = 5
5.   Answer: 5.
Answer: B
96% of the population of a village is 23040. The total population of the village is?  Choose the correct option:
A) 24000 B) 25000 C) 15000 D) 1750 E) 2589

Solution: Explanation:   X * (96/100) = 23040   X = 240 * 100= 
240 * 100 = 24_000
24000   24000
Answer: A
The 4 sticks in a complete bag of Pick-Up Sticks are all straight-line segments of negligible width, but each has a different length: 1 inch, 2 inches, 3 inches, and 4 inches, respectively. If Tommy picks a stick at random from each of 3 different complete bags of Pick-Up Sticks, what is the probability C that Tommy CANNOT form a triangle from the 3 sticks?
Choose the correct choice from the following answers:  A) 11/32  B) 13/32  C) 15/32  D) 17/32  E) 19/32

Solution: In order to form a triangle, the sum of two sides must be greater than the third side.   So we can choose the combination of numbers which will NOT result in a triangle.   Favorable outcomes:   1,1,4 (4>1+1): 3 ways of arriving at this (1,1,4), (1,4,1), (4,1,1) or   1,2,4 (4>1+2): 6 ways of arriving at this (1,2,4), (1,4,2), (2,1,4), (2,4,1), (4,1,2), (4,2,1) which is same as 3!   1,3,4 (4=1+3): 6 ways of arriving at this   2,2,4 (4=2+2): 3 ways of arriving at this   1,1,3 (3>1+1): 3 ways of arriving at this   1,2,3 (3=1+2): 6 ways of arriving at this   1,1,2 (2+1+1): 3 ways of arriving at this   Overall favourable outcomes: 30   Total outcomes:  4*4*4= 
 4*4*4 = 64
64 (4 ways of choosing a stick from each of the 3 bags)   Probability 15/32 that a triangle is not formed= 30/64 = 15/32   15/32 is the correct option here.
Answer: C
I remember during the school days , the teacher asked the class "can you tell me the sum of the first 50 odd numbers ?".
I ran quickly to the teacher and told her "the answer is 2500". The teacher replied "lucky guess".
She then asked me "can you tell me the sum of first 75 odd numbers ?".
I wait for approx 10 seconds and replied with the correct answer.
How can i answer so quickly and whats the correct answer ?  Choices:
A) 8715 B) 0152 C) 3581 D) 5625 E) 9126

Solution: D   5625   n^1   75 * 75= 
75 * 75 = 5_625
5625 (sum of first 75 odd numbers).   50 * 50= 
50 * 50 = 2_500
2500 (sum of first 50 odd numbers).
Answer: D
Expenditures of a Company (in Lakh Rupees) per Annum Over the given Years.
Year	Item of Expenditure
Salary	Interest on Loans and Transport	Bonus	Fuel	Taxes
1998	288	98	3.00	23.4	83
1999	342	112	2.52	32.5	108
2000	324	101	3.84	41.6	74
2001	336	133	3.68	36.4	88
2002	420	142	3.96	49.4	98
The total amount of interest on loans paid by the company during the given period is approximately what percent of the total amount of salary paid during this period?	Choices
A) A)0.5%	B) B)1.5%	C) C)1.25%	D) D)3%	E) E)1%

Solution: Required percentage   =	(288 + 342 + 324 + 336 + 420)   =	[	17	x 100	]	%   1710   ~= 1%.   Answer : 1%
Answer: E
Paul and John are in a relay race. Paul runs the first leg of the course in 22 seconds. Ben runs the second leg of the course in 53 seconds. What was the average time they took to run a leg of the course?
Choose the correct choice from the following answers:
A) 36.5 B) 37.5 C) 38.5 D) 39.5 E) 40.5

Solution: (22 seconds +53 seconds)/2= 37.5 seconds   Correct option is: 37.5
Answer: B
How many two-digit numbers are there such that all two digits are different and the first digit is not zero?
Choices:
A) 50
B) 64
C) 72
D) 79
E) 81

Solution: All two digits are different and first digit is not zero.   So first digit can be filled in 9 ways.   And, second digit can be filled in 8 ways.   Total ways = 9*8= 
9*8 = 72
72   Hence option (72).
Answer: C
A child want to buy 5 new toys. If there are 15 toys that satisfy the child's criteria,in how many different ways can the child select the 5 new toys if the order of selection doesn't matter.	Choose the correct choice from the following answers.
A) 210  B) 1365  C) 3003  D) 5005  E) 3030

Solution: The number of ways of choosing 5 toys out of 15 are counted by = 1530035 ways = 3003   Answer: Option 3003
Answer: C
The length of the bridge, which a train 130 metres long and travelling at 45 km/hr can cross in 30 seconds, is?	Choose the correct choice from the following:  A) 288  B) 277  C) 245  D) 266  E) 261

Solution: Speed = [45 X 5/18] m/sec = [25/2] m/sec Time   = 30 sec Let the length of bridge be x metres. Then, (130 + x)/30   = 25/2 => 2(130 + x)   = 750 => x = 245 m.   Answer: 245
Answer: C
what is the next term of this series6,10,9,15,12...? Choose the correct choice from the following:
A) 9  B) 20  C) 11  D) 12  E) 15

Solution: 3&2=6;    5*2= 
 5*2 = 10
10;    3*3= 
 3*3 = 9
9;    3*5= 
 3*5 = 15
15   3*4= 
3*4 = 12
12   5*4= 
5*4 = 20
20.   ANSWER:20
Answer: B
For 600 km journey it will take 8hrs, if 120 km is done by bus and the rest by car. It takes 20 minutes more, if 200 km is done by busand the rest by car. The ratio of the speed of the train to that of the cars is?	Choose the most appropriate option:
A) 1 : 2 B) 3 : 4 C) 2:5 D) 5:7 E) 7:9

Solution: Let the speed of the train be x km/hr and that of the car be y km/hr.   Then, 120 + 480 = 8 1 + 4 = 1 ....(i)   x y x y 15   And, 200 + 400 = 25 1 + 2 = 1 ....(ii)   x y 3 x y 24   Solving (i) and (ii), we get: x = 60 and y = 80.   Ratio of speeds = 60 : 80 = 3 : 4.   3 : 4
Answer: B
If g(x) = ax^5 + bx^3 + 2, and g(5) = 10, then g(–5) =? Choose the correct choice
A) – 10  B) – 8  C) – 6  D) 0  E) 4

Solution: g(5) = 10   or, 5^5 a + 5^3 b + 2 = 10   or, 5^5 a + 5^3 b = 8   g(-5) = -5^5 a - 5^3 b + 2 = - (5^5 a + 5^3 b) + 2 = - 8 + 2 = - 6 = (– 6)
Answer: C
A 70 cm long wire is to be cut into two pieces so that one piece will be 2/5th of the other, how many centimeters will the shorter piece be?
Select the correct option
A) 21	B) 20	C) 17	D) 12	E) 18

Solution: 1: 2/5 = 5: 2   2/7 * 70= 
2/7 * 70 = 20
20   Answer: 20
Answer: B