MU-NLPC/Calc-aqua_rat huggingface dataset:
The length of a train and that of a platform are equal. If with a speed of 72 k/hr, the train crosses the platform in one minute, then the length of the train (in meters) is?	Choose the correct choice:
A) 227
B) 299
C) 276
D) 600
E) 211

Solution: Speed = [72 * 5/18] m/sec = 20 m/sec; Time = 1 min. = 60 sec.   Let the length of the train and that of the platform be x meters.   Then, 2x/60 = 20 è x = 20 * 60 / 2= 
20 * 60 / 2 = 600
600   Answer: 600
Answer: D
Which of the following is a non-negative?  Choose one:
A) (b-0.9)(b-1)  B) (b-0.9)(b-0.9)  C) (b+0.9)(b+1)  D) (b+1)(b-1)  E) b(b+1)

Solution: 5-sec approach:   D. (b-0.9)(b-0.9) = (b-0.9)^2. The square of a number is always non-negative.   Answer: (b-0.9)(b-0.9).
Answer: B
When positive integer n is divided by 3, the remainder is 1. When n is divided by 11, the remainder is 9. What is the smallest positive integer k such that k+n is a multiple of 33?  Choose the correct choice from the following answers:
A) 2	B) 4	C) 6	D) 8	E) 10

Solution: n = 3p + 1 = 11q + 9   n+2 = 3p + 3 = 11q + 11   n+2 is a multiple of 3 and 11, so it is a multiple of 33.   The answer is 2.
Answer: A
A man can row upstream at 37 kmph and downstream at 53 kmph, and then find the speed of the man in still water?
Select the correct option.
A) 29	B) 92	C) 30	D) 32	E) 45

Solution: US = 37   DS = 53   M = (53 + 37)/2= 
(53 + 37)/2 = 45
45   Answer:45
Answer: E
In a Lake, there is a patch of lily pads. Every day, the patch doubles in size. It takes 39 days for the patch to cover the entire lake, how many days would it take the patch to cover half of the lake?  Choose the correct choice:	A) 36	B) 2^4*3	C) 24	D) 38	E) 47

Solution: Working backward from the day it's covered:   day 39: fully covered   day 38: half covered   So 38 days   ANSWER:38
Answer: D
a girl scout sold 5 macadamia cookies, 10 peanut butter cookies and 15 butter cookies. what is the ratio of the peanut butter cookies to the total sold?
Pick.
A) 1/2 B) 1/3 C) 5/10 D) 10/15 E) 5/15

Solution: total # of cookies is 5+10+15= 
5+10+15 = 30
30; ratio of peanut butter cookies sold is 10/30= 1/3   ANSWER:1/3
Answer: B
If the volume of two cubes are in the ratio 125:1, the ratio of their edges is:	Choose the correct choice from the following answers
A) 3:1  B) 5:1  C) 3:5  D) 3:7  E) None of these

Solution: Explanation:   Let the edges be a and b of two cubes, then   a3/b3=125/1   =>(a/b)3=(5/1)3   a/b=5/1   =>a:b=5:1   Option 5:1
Answer: B
A and B invests Rs.3000 and Rs.4000 respectively in a business. If A doubles his capital after 6 months. In what ratio should A and B divide that year's profit? Choose the most appropriate option:
A) 9:10
B) 9:8
C) 3:4
D) 39:49
E) 38:49

Solution: (3*6 + 6*6): (4*12)   54:48 => 9:8   ANSWER:9:8
Answer: B
At what percentage above the C.P must an article be marked so as to gain 33% after allowing a customer a discount of 5%?	Choose the correct choice from the following answers
A) 38%
B) 40%
C) 43%
D) 48%
E) 50%

Solution: Let C.P = Rs. 100, Then S.P = Rs.133.   Let the marked price be x   Then , 95% of x = 133, 95 x/ 100 =133, x = 133*100/95= 
133*100/95 = 140
140   Marked price= 40% above C.P   ANSWER:40%
Answer: B
If each term in the sum a1+a2+a3+.....+an is either 7 or 77 and the sum equals 336, which of the following could be equal to n?	Choose the correct choice from the following answers:	A) 38	B) 39	C) 40	D) 41	E) 42

Solution: Since, there is no 48 in the answer choices (336/7 = 48), we know there is at least one 77.   336 - 77= 
336 - 77 = 259
259   259/7= 
259/7 = 37
37   37+1= 
37+1 = 38
38   If 38 wasn't there, I would have subtracted 77 from 259 and continued in a similar way.   Ans. 38
Answer: A
A company has two models of computers, model M and model N. Operating at a constant rate, a model M computer can complete a certain task in 36 minutes and a model N computer can complete the same task in 18 minutes. If the company used the same number of each model of computer to complete the task in 1 minute, how many model M computers were used? Choose one: A) 12 B) 11 C) 10 D) 9 E) 8

Solution: Let's say 1 work is processing 36 gb of data.   Model M : 1 gb per min   Model N : 2 gb per min   Working together, 1 M and 1 N = 3 gb per min   So, 12 times as many computers would work at 36 gb per min.   So no. of M =12   12nswer is 12
Answer: A
How many positive integer solutions does the equation 5x+10y = 100 have?	Choose the correct choice from the following choices:	A) 2	B) 33	C) 38	D) 35	E) 14

Solution: formula: (constant)/(lcm of two nos)   =100/(5*10)= 
100/(5*10) = 2
2   2NSWER:2
Answer: A
Two trains 200m and 300m long run at the speed of 70kmph and 50kmph in opposite directions in parallel tracks. The time which they take to cross each other is?	Choose the correct choice from the following answers.
A) 10sec	B) 15sec	C) 18sec	D) 20sec	E) 22sec

Solution: Relative speed = 70+50= 
70+50 = 120
120kmph * 5/18= 100/3 m/s   Distance covered in crossing each other = 200+300= 
200+300 = 500
500m   Required time= 500*3/100= 
500*3/100 = 15
15sec   Answer is 15sec
Answer: B
If the three-digit number 5W2 is evenly divisible by 8, which of the following could be the digit W ?	Choose the correct choice from the following choices
A) 5
B) 4
C) 3
D) 2
E) 1

Solution: Tried to locate a '0' ending multiple of 8 between 500599   Only 560 is present   560 is divisible by 8, so (560 - 8) is also divisible by 8 = 5   5NSWER 5
Answer: A
If 350!/10^n is an integer, what is the largest possible value of n? Select:
A) 88 B) 82 C) 86 D) 87 E) 80

Solution: The question actually asks the highest power of 10 which divides 350! ( For a number to be an integer - Without any remainder all the trailing zeroe's must be divided by the denominator)   10 = 2 x 5   350 factorial will have 86 as -   350/5= 
350/5 = 70
70   70/5= 
70/5 = 14
14   14/5=2   So answer will be (86) 86
Answer: C
A person travels through 5 cities - A, B, C, D, E. Cities E is 2 km west of D. D is 3 km north-east of A. C is 5 km north of B and 4 km west of A. If this person visits these citiesin the sequence B - C - A - E - D, what is the effective distance between cities B and D?	Choose the correct answer:
A) 12	B) 13	C) 14	D) 15	E) 16

Solution: make diagram first, then traverse according to 13 C A E D   u can find  5+4= 
 5+4 = 9
9 (13 to A)   A to E is not given but u can see it as 1.5 or 2 km so 13 to E is 10 km   now E to D is 2 km   total=5+4+1.5+2= 
5+4+1.5+2 = 12.5
12.5   or 5+4+2+2= 
5+4+2+2 = 13
13   ANSWER:13
Answer: B
In a group of ducks and Cows, the total number of legs are 16 more than twice the no. of heads. Find the total no.of buffaloes.  Select.
A) 10	B) 12	C) 8	D) 12	E) 14

Solution: Let the number of buffaloes be x and the number of ducks be y   => 4x + 2y = 2 (x + y) + 16   => 2x = 16 => x = 8   8
Answer: C
What profit percent is made by selling an article at a certain price, if by selling at 2/3rd of that price, there would be a loss of 12%?
Pick
A) 20%
B) 29%
C) 32%
D) 80%
E) 90%

Solution: SP2 = 2/3 SP1   32%P = 100   SP2 = 88   2/3 SP1 = 88   SP1 = 132   100 --- 32 => 32%   Answer: 32%
Answer: C
If the cost price of 12 pencils is equal to the selling price of 8 pencils, the gain percent is:	Choose one:
A) 30 B) 40 C) 50 D) 60 E) 70

Solution: C   50%   Let C.P. of each pencil be $ 1.   Then, C.P. of 8 pencils = $8; S.P. of 8 pencils = $12.   Gain % = 4/8 * 100= 
4/8 * 100 = 50
50%
Answer: C
A box contains 100 balls, numbered from 1 to 100. If three balls are selected at random and with replacement from the box, what is the probability that the sum of the three numbers on the balls selected from the box will be odd?  Choose the correct choice.
A) 1/4  B) 3/8  C) 1/2  D) 5/8  E) 3/4

Solution: The sum of the three numbers on the balls selected from the box to be odd one should select either three odd numbered balls (Odd+Odd+Odd=Odd) or two even numbered balls and one odd numbered ball (Even+Even+Odd=Odd);   P(OOO)=(1/2)^3;   P(EEO)=3*(1/2)^2*1/2=3/8 (you should multiply by 3 as the scenario of two even numbered balls and one odd numbered ball can occur in 3 different ways: EEO, EOE, or OEE);   So finally P=1/8+3/8=1/2.   Answer: 1/2.
Answer: C
The units digit of (10)^(87) + (5)^(46) is:
Choose one.
A) 2  B) 4  C) 6  D) 8  E) 0

Solution: any power of anything ending in 5 always has a units digit of 5. So the first term has a units digit of 5. Done.   The second term anything power to 10 unit digit will be zero   then   5 + 0= 
  5 + 0 = 5
5,   0
Answer: E
If a 6 cm cube is cut into 1 cm cubes, then what is the percentage increase in the surface area of the resulting cubes?  Choose the correct choice from the following choices
A) 300% B) 400% C) 500% D) 600% E) 750%

Solution: The area A of the large cube is 6*6*6= 
6*6*6 = 216
216 square cm.   The area of the 216 small cubes is 216*6= 6A, an increase of 500%.   The answer is 500%.
Answer: C
The winning relay team in a high school sports competition clocked 48 minutes for a distance of 13.2 km. Its runners A, B, C and D maintained speeds of 18 kmph, 19 kmph, 20 kmph, and 21 kmph respectively. What is the ratio of the time taken by B to than taken by D?	Choose the correct choice from the following options:
A) 5:16 B) 5:17 C) 9:8 D) 8:9 E) None of these

Solution: Explanation :   Since it is a relay race, all the runners ran the same distance.   Hence for a same distance, (ratio of times) = 1/(ratio of speeds).   Hence ratio of times taken by B t& D = 21 : 19   Answer : None of these
Answer: E
Two goods trains each 500 m long are running in opposite directions on parallel tracks. Their speeds are 45 km/hr and 45 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) 93 C) 26 D) 23 E) 12

Solution: Relative speed = 45 + 45= 
45 + 45 = 90
90 km/hr.   90 * 5/18= 
90 * 5/18 = 25
25 m/sec.   Distance covered= 500 + 500= 
500 + 500 = 1_000
1000 m.   Required time= 1000 /25= 
1000 /25 = 40
40 sec.   40nswer:40
Answer: A
Stacy and Heather are 5 miles apart and walk towards each other along the same route. Stacy walks at constant rate that is 1 mile per hour fast than heather's constant rate of 5 miles/hour. If Heather starts her journey 24 minutes after Stacy, how far from the original destination has Heather walked when the two meet?.	Pick one.
A) 2.5mile
B) 1.9mile
C) 1.7mile
D) 1.5mile
E) 1.18mile

Solution: Ss - Stacy's speed = 6m/hr   Sh - Heather's speed = 5m/hr   In 24 minutes Stacy will cover = (24/60)*6= 
(24/60)*6 = 12/5 = around 2.4
2.4miles   Now since both are walking in opposite directions, add their speeds - 6+5=11m/hr and distance to cover is  5 -2.4= 
 5 -2.4 = 2.6
2.6   Time taken= Distance/ Speed = 2.6/11 = 0.23 hrs   Heather will cover = 5*0.23 = 1.18miles.   Answer 1.18mile
Answer: E
In how many ways can 6 people, A, B, C, D, E, F be seated in a row such that C and D are not seated next to each other as well as A and B are not seated next to each other?	Answers
A) 384 B) 396 C) 576 D) 624 E) 696

Solution: Total # of arrangements of 6 people in a row is 6!;   Now, let's find # of arrangements where C and D as well as A and B ARE seated next to each other. Consider them as a single unit: {AB}, {CD}, E, F. Now, these 4 units can be arranged in 4!, but we should multiply this number by 2*2 as A and B, as well as C and D within their unit can be arranged in two ways: {AB} or {BA}, and {CD} or {DC}. Hence total for this case is 4!*2*2;   So, {# of arrangements}={total}-{restriction}=6!-4!*2*2=624.   Answer: 624.
Answer: D
When four dice are thrown, what is the probability that the same number appears on each of them ?
Pick one:
A) 1/36  B) 1/18  C) 1/216  D) 1/5  E) 1/8

Solution: Explanation :   When four dice are rolled the total no of outcomes are : 64   All dice show up same number in the following cases: (1,1,1,1), (2,2,2,2), (3,3,3,3), (4,4,4,4), (5,5,5,5), (6,6,6,6)   So in above six cases, all dice will show up the same number.   Required probability: 6/64 = 1/216   Answer : 1/216
Answer: C
If the least common multiple of two prime numbers x and y is 10, where x < y, then the value of 3x + y is	Select:
A) 7 B) 9 C) 11 D) 12 E) 21

Solution: LCM (x,y) = 10 and both x an y are prime.   The only values of x and y can be 2 and 5 (x = 2 and y = 5)   3x + y = 3*2 + 5= 
3*2 + 5 = 11
11   11orrect Option: 11
Answer: C
The ages of two persons differ by 24 years. If 5 years ago, the elder one be 5 times as old as the younger one, their present ages (in years) are respectively
Select the correct option
A) 20,20
B) 20,10
C) 25,15
D) 35,11
E) None of these

Solution: Explanation:   Let their ages be x and (x + 24) years.   5 (x - 5) = (x + 24 - 5) or 4x = 44 or x = 11.   Their present ages are 35 years and 11 years   Option 35,11
Answer: D
Express a speed of 36 kmph in meters per second?  Choose the correct answer:
A) 10 mps	B) 17 mps	C) 97 mps	D) 17 mps	E) 18 mps

Solution: 36 * 5/18= 
36 * 5/18 = 10
10 mps   10 mpsnswer: 10 mps
Answer: A
Every year an amount increases by 1/8th of itself. How much will it be after two years if its present value is Rs.64000?  Choose the correct choice from the following answers:
A) Rs.81000 B) Rs.80000 C) Rs.75000 D) Rs.64000 E) Rs.68000

Solution: 64000* 9/8 * 9/8= 
64000* 9/8 * 9/8 = 81_000
81000   Rs.81000NSWER:Rs.81000
Answer: A
How many 3-digit numbers can be formed with the digits 1,4,7,8 and 9 if the digits are not repeated?  Choose the correct choice from the following: A) 20 B) 40 C) 60 D) 80 E) 100

Solution: Three digit numbers will have unit's, ten's and hundred's place.   Out of 5 given digits any one can take the unit's place.   This can be done in 5 ways ------- (i)   After filling the unit's place, any of the four remaining digits can take the ten's place.   This can be done in 4 ways ------- (ii)   After filling in ten's place, hundred's place can be filled from any of the three remaining digits.   This can be done in 3 ways ------- (iii)   => By counting principle, the number of 3 digit numbers =5Ã—4Ã—3==5Ã—4Ã—3= 60   ANSWER 60
Answer: C
16 ltr of water is added with 24 ltr of a solution containing 90%of alcohol in the water. The %of alcohol in the new mixture is?  Select
A) 48% B) 52% C) 54% D) 60% E) 70%

Solution: We have a 24 litre solution containing 90% of alcohol in the water.   => Quantity of alcohol in the solution   =24Ã—90/ 100   Now 16 litre of water is added to the solution.   => Total quantity of the new solution = 24 + 16= 
24 + 16 = 40
40   Percentage of alcohol in the new solution=24Ã—90/100   40   Ã—   100   =24Ã—9010040Ã—100   =24Ã—2.25/100   =54%   54%
Answer: C
In how many ways can you seat 6 people on a bench if one of them does not want to sit at either end?  Choose one.
A) 360 B) 400 C) 440 D) 480 E) 520

Solution: One person can choose 4 possible chairs to sit. The remaining 5 people can sit in 5! ways.   The number of arrangements is 4*5! = 480.   The answer is 480.
Answer: D
Find the smallest number which should be divided with 3872 to make it a perfect square.  Choices.
A) 8
B) 6
C) 2
D) 4
E) 1

Solution: 3872 = 11*11*2*2*2*2*2   Required smallest number = 2   2 is the smallest number which should be divided with 3872 to make it a perfect square.   ANSWER:2
Answer: C
x is a positive integer less than 400. When x is divided by 7, the remainder is 1; when x is divided by 3, the remainder is 2. How many x are there? Choose the correct choice from the following choices.
A) 21
B) 22
C) 23
D) 24
E) 25

Solution: the nubmer which when divided by 7 leaves remainder 1 should be of the form 7k+1   this number when divided by 3 leaves remainder 2.   so,   (7k+1)-2 should be divisible by 3 or 7k-1 should be divisible by 3.   we now put the values of k starting from 0 to find first number divisible by 3   we find 1st number at k= 1   thus smallest number will be 7(1)+1 = 8   now,   next number will be = 8+ lcm of 37   i.e 29   now we will find number of all such values less than 500 by using the formula for last term of an a.p   8+(n-1)21=400   n=23.42   or n= 23   Answer:- 23
Answer: C
Robert's salary was decreased by 50% and subsequently increased by 50%. how much percentage does he lose?
Choose the correct choice from the following answers:
A) 10%
B) 20%
C) 25%
D) 30%
E) 50%

Solution: let original salary be $100   new final salary = 150% of (50% of $100) = (150/100)*(50/100)*100= 
(150/100)*(50/100)*100 = 75
$75   decrease= 25%   correct option is 25%
Answer: C
A scuba diver descends at a rate of 40 feet per minute. a diver dive from a ship to search for a lost ship at the depth of 3000feet below the sea level..how long will he take to reach the ship?	Choose the correct choice from the following answers:
A) 70 minutes
B) 72 minutes
C) 75 minutes
D) 76 minutes
E) 77 minutes

Solution: Time taken to reach = 3000/40= 
3000/40 = 75
75 minutes   ANSWER:75 minutes
Answer: C
The positive difference between Sam and Lucy’s ages is b, and the sum of their ages is x. If Lucy is older than Sam, then which of the following represents Lucy’s age?  Pick:  A) (x-b)/2  B) b - x/2  C) 2b+ x  D) (x + b)/2  E) (b - x)/2

Solution: let Lucy's age be L and sam's age be S   as given,   L-S=b-- 1   L+S=x --2   adding both the equations 2L=a+z   L= (b+x)/2 answer is (x + b)/2
Answer: D
If K is the sum of reciprocals of the consecutive integers from 33 to 38, inclusive, then K is closest in value to which of the following?  Choose one: A) 1/12 B) 1/10 C) 1/8 D) 1/7 E) 1/4

Solution: 1/33 , 1/34 , 1/35 , 1/36 , 1/37 , 1/38   Hypothetically , assume all 6 Numbers to be 1/33   Hence sum of it would result in = 6/33 ( almost equals 1/6 , or slightly more than 1/6 - )   If all 6 nos were to be 1/38 ... Sum of which would result in 6/38 = 3/19 .   Hence answer should lie between 1/6 and 1/7 (3/21)   1/7 i.e 1/7
Answer: D
In an election, candidate A got 55% of the total valid votes. If 15% of the total votes were declared invalid and the total numbers of votes is 560000, find the number of valid vote polled in favor of candidate?	Answers
A) 261800
B) 355800
C) 356500
D) 356800
E) 357000

Solution: Total number of invalid votes = 15 % of 560000   = 15/100 × 560000   = 8400000/100= 
8400000/100 = 84_000
84000   Total number of valid votes 560000 – 84000= 476000   Percentage of votes polled in favour of candidate 261800 = 55 %   Therefore, the number of valid votes polled in favour of candidate 261800 = 55 % of 476000   = 55/100 × 476000   = 26180000/100= 
26180000/100 = 261_800
261800   261800)
Answer: A
Mike earns $17.5per hour and Phil earns $10.5 per hour. Approximately how much less, as a percentage, does Phil earn than Mike per hour?  Choose the correct choice from the following choices:
A) 25% B) 32.5% C) 37% D) 37.5% E) 40%

Solution: What % less of 17.5 is 10.5   let it be x % less ,then   =17.5(1-x/100)=10.5   1-x/100=10.5/17.5   x=200/5= 
200/5 = 40
40%   Ans 40%
Answer: E
Two trains are moving at 60 kmph and 70 kmph in opposite directions. Their lengths are 150 m and 100 m respectively. The time they will take to pass each other completely is?
Choose the correct choice from the following choices
A) 6 12/13 sec	B) 7 1/7 sec	C) 7 2/2 sec	D) 8 1/2 sec	E) 7 1/9 sec

Solution: 70 + 60= 
70 + 60 = 130
130 * 5/18= 325/9 mps   D = 150 + 100= 
150 + 100 = 250
250 m   T= 250 * 9/325 = 90/13 = 6 12/13 sec   6 12/13 secnswer: 6 12/13 sec
Answer: A
Which of the following is a prime number ?  Pick
A) 72
B) 86
C) 88
D) 97
E) 98

Solution: Clearly, 97 is a prime number.   Option 97
Answer: D
Ratio of Ravi's and Ashok's present ages is 4:5 After 6 years it will be 5:6. What is Ravi's present age?
Choose the correct choice from the following choices:
A) 16 Years	B) 15 Years	C) 20 Years	D) 24 Years	E) 25 Years

Solution: Let present ages are 4x and 5x   After 6 years hence   4x+6/5x+6=5/6   After solving above eqn   X=6   So ravis present age become  4*6= 
 4*6 = 24
24   ANSWER:24 Years
Answer: D
What is the remainder when 46*49 is divided by 8?	Select the correct option.
A) 1  B) 3  C) 4  D) 6  E) 7

Solution: we can make use of the rule :   Remainder of { (a * b)/n}} = Remainder of (a/n) * Remainder of (b/n)   Here   Remainder of { 46 * 49)/8}} = Remainder of (46/8) * Remainder of (49/8) = 6 * 1= 
6 * 1 = 6
6   Answer :6
Answer: D
Nick's average (arithmetic mean) test score on 4 tests is 78. What must be the student's score on a 5th test for the Nick's average score on the 5 tests to be 80? Choose the correct choice from the following answers:
A) 80
B) 82
C) 84
D) 86
E) 88

Solution: E. 88   Nick must score at least an 80 for sure. If he scores an 8, then he will need to score 2 pots for each of the 4 other tests tomake upthe difference. They each were at 78 (at least the average is, but this is a small point and doesn't matter to the answer). So 4 tests that were each 2 points short of the 80 average that is desired means the next test must be 8 points higher than the desired average, so  80+8= 
 80+8 = 88
88.
Answer: E
Guadalupe owns 2 rectangular tracts of land. One is 300 m by 500 m and the other is 250 m by 630 m. The combined area of these 2 tracts is how many square meters?	Choose the correct option:
A) 3,360
B) 307,500
C) 621,500
D) 704,000
E) 2,816,000

Solution: One is 300 m by 500 m and the other is 250 m by 630 m :   (300*500)+(250*630) = 150000+157500   307500   ANSWER:307,500
Answer: B
What is the ratio between perimeters of two squares one having 3 times the diagonal then the other? Options
A) 3:5	B) 3:3	C) 3:9	D) 3:1	E) 3:2

Solution: d = 3d d = d   a√2 = 3d a√2 = d   a = 3d/√2 a = d/√2   =>3:1   Answer: 3:1
Answer: D
Sound is said to travel in air at about 1100 feet per second. A man hears the axe striking the tree, 11/5 seconds after he sees it strike the tree. How far is the man from the wood chopper?
Options
A) 3449  B) 3777  C) 2998  D) 2420  E) 2778

Solution: Speed of the sound = 1100 ft/s   Time = 11/5 second   2420istance = Speed × Time = 1100 ×115=220×11=2420 ft   Answer : 2420
Answer: D
Which of the following is closest to 10^150 – 10^30 ?	Choices:	A) 10^210	B) 10^180	C) 10^150	D) 10^90	E) 10^6

Solution: 10^150 – 10^30   10^30 * (10^120 – 1)   as we know 10^2 - 1 means 100-1 and we get 99, which is approximately 100. hence (10^120 – 1) would remain as 10^120.   and 10^30 * 10^120 = 10^150. Answer is 10^150.
Answer: C
If two numbers are in the ratio 6:7. If 10 is Reduced to both of the numbers then the ratio becomes 5:6 then find the smallest number?	Choose the correct option:
A) 50	B) 30	C) 60	D) 70	E) 80

Solution: Explanation:   6:7   6x - 10 : 7x - 10 = 5 : 6   6[6x - 10] = 5[7x - 10]   36x - 60 = 35x - 50   36x - 35x = 60 - 50= 
60 - 50 = 10
10   the small number is= 6   6x = 60 (Answer = 60)   Short cut method:   a:b = 6:7   c:d = 5:6   1.Cross multiplication with both ratios   a * d ~ b * c = 6 * 6 ~ 7 * 5 = 36 ~ 35 = 1   2. If 10 is reduced both the number means  10 * 5= 
 10 * 5 = 50
50 and   10 * 6= 
  10 * 6 = 60
60,   Then 50 ~ 60= 10   ===> 1 -----> 10   ===> 6 -----> 60 (Answer is = 60)   Answer: Option 60
Answer: C
In some quantity of ghee, 60% of pure ghee and 40% of is vanaspati. If 10kg of pure ghee is added, then the strength of vanaspati ghee becomes 20%. The original quantity was?
Select:
A) 5kg
B) 10kg
C) 15kg
D) 20kg
E) 25kg

Solution: Let the original quantity be x kg   vanaspati ghee in x kg = 40/100 *x = 2x/5 kg   (2x/5)/(x+10) = 20/100   2x/(5x+50) = 1/5   5x = 50   x = 10kg   Answer is 10kg
Answer: B
There are 20 balls in a jar. You take out 2 blue balls without putting them back inside, and now the probability of pulling out a blue ball is 1/5. How many blue balls were there in the beginning?  Choose the correct choice from the following.
A) 12.  B) 9.  C) 8.  D) 7.  E) 6.

Solution: 12 = 3 blue balls + 18 / 2   12.nswer: 12.
Answer: A
The present population of a town is 3600. Population increase rate is 20% p.a. Find the population of town before 2 years?
Choose the correct choice from the following choices: A) 2500 B) 2100 C) 3500 D) 3600 E) 2050

Solution: P = 3600   R = 20%   Required population of town = P/(1 + R/100)^T   = 3600/(1 + 20/100)^2   = 3600/(6/5)^2   = 2500(approximately)   2500nswer is 2500
Answer: A