MU-NLPC/Calc-aqua_rat huggingface dataset:
If m/21 is an integer, then each of the following must be an integer EXCEPT  Choose the most appropriate option.
A) 5/2  B) 4  C) 3  D) 2  E) 1

Solution: Now plug m =21 into the answer choices:   A. (21- 28)/7 = -1. This is an integer   B. (21+ 21)/7 = 6. This is an integer   C. 14(21)/98 = 3. This is an integer   D. (21^2 - 49)/49 = 8. This is an integer   E. (21+ 14)/14 = 5/2. This is NOT an integer   5/2nswer: 5/2
Answer: A
Find out the wrong term in the series 5, 10, 50, 500, 25000, 3000000  Pick:
A) 15,000,000	B) 12,500,000	C) 9,000,000	D) 3,00,000	E) 60,000

Solution: Explanation:   Each number with in the series is the product of the two numbers that proceed it.   So, if (5 * 10 = 50) , then (500 * 25000 = 12,500,000). 12,500,000 should replace 3000000.   Answer: 12,500,000) 12,500,000
Answer: B
The mean of 50 observations was 36. It was found later that an observation 48 was wrongly taken as 23. The corrected new mean is:	Choose the correct option
A) 36.5 B) 35 C) 34 D) 33 E) 32.5

Solution: Correct sum = (36 * 50 + 48 - 23)= 
(36 * 50 + 48 - 23) = 1_825
1825.   Correct mean= 1825/50= 
1825/50 = 73/2 = around 36.5
36.5   36.5NSWER 36.5
Answer: A
The larger of two negative consecutive even integers 2t and 2(t-1) is multiplied by 7 and then added to the smaller of the two original integers. Which of the following represents this operation?
Choose the most appropriate option:
A) 16t-2
B) 8t-2
C) -2
D) 3
E) -2-4t^2

Solution: larger of 2t-2, 2t (when they are negative) is 2t. the smallest of 2t and 2t-2 when they are positive is 2t-2.   therefore 7* 2t + 2t-2 = 16t-2.   option 16t-2.
Answer: A
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 40 white marbles. How many red marbles could be in bag A?  Pick:
A) 8
B) 3
C) 4
D) 6
E) 8

Solution: 6 is the answer.   Bag 8-   R:W:B = 2:6:9   Let W in bag 8 be 6K   Bab B -   R:W = 1:3   Let W in bag B be 4k   W = 30 = 6K+4k=> k =40/10= 
40/10 = 4
4   Total Red's in bag 8 will be 2K= 8   8
Answer: A
Arun got 30% of the maximum marks in an examination and failed by 10 marks. However, Sujith who took the same examination got 40% of the total marks and got 15 marks more than the passing marks. What were the passing marks in the examination? Options:
A) 90
B) 250
C) 85
D) 75
E) 65

Solution: Explanation:   Let x is the maximum marks of the examination   Marks that Arun got = 30 % of x = 30x/100   Given that Arun failed by 10 marks   ⇒Minimum Pass Mark = 30x/100 + 10......(Equation 1)   Marks that Sujith got = 40 % of x = 40x/100   Given that Sujith got 15 marks more than the passing marks   ⇒40x100=Minimum Pass Mark +15   ⇒Minimum Pass Mark =40 x100 −15......(Equation 2)   From equations 1 and 2, we have   30 x 100 + 10 = 40x/100 − 15   ⇒10x/100 = 10 + 15= 
10 + 15 = 25
25   ⇒x/10= 25   ⇒ x = 10 × 25 = 250   ⇒Maximum marks of the examination = x = 250   Substituting the value of x in Equation 1, we have   Minimum Pass Mark = 30x/100 + 10 = 30 × 250/100 + 10 = 75 + 10= 
75 + 10 = 85
85   Answer: Option 85
Answer: C
We had $350 left after spending 30% of the money that we took for shopping. How much money did we start with?
Choose the correct option.
A) $440	B) $460	C) $480	D) $500	E) $520

Solution: Let x be the amount of money we started with.   0.7x = 350   x = 500   The answer is $500.
Answer: D
The cost price of 13 articles is equal to the selling price of 11 articles. Find the profit percent? Options.
A) 18 2/18%
B) 18 2/11%
C) 18 2/31%
D) 18 4/11%
E) 16 2/11%

Solution: 13 CP = 11 SP   11 --- 2 CP   100 --- ? =>18 2/11%   Answer: 18 2/11%
Answer: B
If n = 3p, where p is a prime number greater than 2, how many different positiveevendivisors does n have, including n ?  Pick one.
A) Two
B) Three
C) Four
D) Six
E) Eight

Solution: This is an interesting question because we are immediately given the option to insert any prime number we wish for p. Since this is a problem-solving question, and there can only be one correct answer, we can select any value for p, as long as it is a prime number greater than 2. We always want to work with small numbers, so we should select 3 for p. Thus, we have:   n = 4 x 3   n = 12   Next we have to determine all the factors, or divisors, of P. Remember the term factor is synonymous with the term divisor.   1, 12, 6, 2, 4, 3   From this we see that we have 4 even divisors: 12, 6, 2, and 4.   If you are concerned that trying just one value of p might not substantiate the answer, try another value for p. Let’s say p = 5, so   n = 4 x 5   n = 20   The divisors of 20 are: 1, 20, 2, 10, 4, 5. Of these, 4 are even: 20, 2, 10 and 4. As we can see, again we have 4 even divisors.   No matter what the value of p, as long as it is a prime number greater than 2, n will always have 4 even divisors.   The answer is Three.
Answer: B
If P= {multiplies of 3 between 1 and 20}, Q = {even natural number upto 15} , find the intersection of the two given set P and Q.	Choose the correct answer:
A) P∪Q= {6,12}  B) P∩Q= {6,12}  C) P∩Q= {10,12}  D) P∪Q= {10,12}  E) P∪Q= {8,10}

Solution: P= {3,6,9,12,15,18}, Q= {2,4,6,8,10,12,14}   Intersection of P and Q is the largest set containing only those elements which are common to both the given sets P and Q. correct answer : (P∩Q= {6,12}) P∩Q= {6,12}
Answer: B
46080, 3840, 384, 48, 8, 2, ?
Select:	A) 1	B) 1⁄64	C) 1⁄8	D) None of these	E) 1/32

Solution: Explanation :   46080 ÷ 12 = 3840   3840 ÷ 10 = 384   384 ÷ 8 = 48   48 ÷ 6 = 8   8 ÷ 4 = 2   2 ÷ 2 = 1   1nswer : Option 1
Answer: A
A, B and C rents a pasture for Rs.950. A put in 12 horses for 8 months, B 16 horses for 9 months and 18 horses for 6 months. How much should C pay?	Select the correct option: A) 295 B) 199 C) 676 D) 156 E) 122

Solution: 12*8 :16*9 = 18*6   8: 12: 9   9/29 * 950= 295   295nswer: 295
Answer: A
In a group of ducks and cows, the total number of legs are 28 more than twice the number of heads. Find the total number of cows.
Answers.
A) 12
B) 14
C) 16
D) 18
E) 20

Solution: Let the number of ducks be d   and number of cows be c   Then, total number of legs = 2d + 4c = 2(d + 2c)   total number of heads = c + d   Given that total number of legs are 28 more than twice the number of heads   => 2(d + 2c) = 28 + 2(c + d)   => d + 2c = 14 + c + d   => 2c = 14 + c   => c = 14   i.e., total number of cows = 14   Answer is 14.
Answer: B
A box contains 2 white balls and 4 red ball. in how many ways can 3 balls be drawn from the box , if at least one black ball is to be included i the draw ? Pick.
A) 32 B) 48 C) 64 D) 96 E) None

Solution: Solution   We have many (1 black and 2 non-black) or (2 black and 1 non-black) or (3 black).   So, Required number of ways = (3 C 1 × 6 C 2) + (3 C 2 × 6 C 1) + (3 C 3)   = ( 3x 6x 5/2x1) + ( 3x 2/2x1x 6) + 1 = (45 + 18 + 1)= 
(45 + 18 + 1) = 64
64.   Answer 64
Answer: C
If the height of a cone is increased by 120% then its volume is increased by? Choose the correct choice from the following answers.
A) 100	B) 777	C) 998	D) 729	E) 120

Solution: 120%   Answer:120
Answer: E
Find the average of all prime numbers between 60 and 90  Choose one
A) 45
B) 55
C) 69
D) 65
E) 77

Solution: Prime numbers between 60 and 90 are 67, 71, 73, 79, 83, 89   Required average = (67+ 71+ 73+ 79+ 83+ 89)/6 = 462/6= 
462/6 = 77
77   Answer is 77
Answer: E
An egg seller sells his eggs only in the packs of 3 eggs, 6 eggs, 9 eggs, 12 eggs etc., but the rate is not necessarily uniform. One day Raju (which is not the same egg seller) purchased at the rate of 3 eggs for a rupee and the next hour he purchased equal number of eggs at the rate of 6 eggs for a rupee. Next day he sold all the eggs at the rate of 9 eggs for Rs. 2. What is his percentage profit or loss?
Pick one
A) 10% loss
B) 11.11% loss
C) 3% loss
D) 2.5 % profit
E) None of These

Solution: Solution: CP of one egg in first case = 1/3 = 33.33 paise   CP of one egg in second case = 1/6 = 16.66 paise   Average CP = (33.33 +16.66)/2 = 25 paise   Selling price of 9 eggs = Rs. 2   SP of one egg = 200/9   Profit or loss = [(25 - (200/9))*100]/25   Profit or loss = -11.11. (loss)   Answer: Option 11.11% loss
Answer: B
Two trains of equal are running on parallel lines in the same direction at 46 km/hr and 36 km/hr. The faster train passes the slower train in 36 sec. The length of each train is? Options
A) 50
B) 77
C) 55
D) 43
E) 12

Solution: Let the length of each train be x m.   Then, distance covered = 2x m.   Relative speed = 46 - 36= 
46 - 36 = 10
10 km/hr.= 10 * 5/18 = 25/9 m/sec.   2x/36 = 25/9 => x = 50.   50nswer: 50
Answer: A
A is twice efficient than B. A and B can both work together to complete a work in 7 days. Then find in how many days A alone can complete the work?	Choose the correct choice from the following answers:
A) 10.9	B) 10.5	C) 10.8	D) 10.1	E) 80.1

Solution: Ans: Let us assume A can do 2 units of work each day, then B can do only 1 unit a day. If both can complete the work in 7 days, total work done by these two togeter = (2 + 1 ) x 7 = 21 units   If these 21 units to be done by A alone, then he will take  21 / 2= 
 21 / 2 = 21/2 = around 10.5
10.5 days.   \Answer:10.5
Answer: B
In a public show 50 % of the seats were filled. If there were 600 seats in the hall, how many seats were vacant?	Pick one:  A) 100  B) 110  C) 120  D) 300  E) 150

Solution: 50 % of 600   = 50/100 × 600   = 300   Therefore, the number of vacant seats = 600 - 300= 
600 - 300 = 300
300.   Answer:300
Answer: D
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? Select the correct option:  A) 230 m  B) 245 m  C) 260 m  D) 275 m  E) 295 m

Solution: Relative speed = (120 + 80) km/hr   = 200 x 5/18   = 500/9 m/sec   Then, (x+270)/9 = 500/9   --> x + 270 = 500   --> x = 230.   230 mnswer : 230 m.
Answer: A
{130, 280, 250, n}
Which of the following could be the median of the 4 integers listed above?
I. 160
II. 210
III. 250	Select the correct option.
A) I only  B) II only  C) I and II only  D) II and III only  E) I, II, and III

Solution: If 160 is the median, (n+250) / 2 = 160. Then n = 70. But n < 130, so 160 can not be the median.   If 210 is the median, (n+250) / 2 = 210. Then n = 170. Thus 210 can be the median.   If 250 is the median, (n+250) / 2 = 250. Then n = 250. Thus 250 can be the median.   The answer is II and III only.
Answer: D
What will be the acute angle between hands of a clock at 2 : 30?
Choose the correct choice from the following options
A) 105° B) 115° C) 95° D) 135° E) None of these

Solution: At 2'O Clock, Minute Hand will be 10 × 6 = 60°   behind the Hour Hand.   In 30 minutes, Minute Hand will gain (51⁄2)° × 30   = 150 + 15= 
150 + 15 = 165
165°   ∴ 105°ngle between Hour Hand and Minute Hand= 165 – 60 = 105°   105°nswer 105°
Answer: A
A box contains SEVEN bulbs out of which 4 are defective. If THREE bulbs are chosen at random, find the probability that atleast one bulb is good Options:	A) 5/38	B) 4/39	C) 4/31	D) 4/35	E) 6/35

Solution: Required probability = 1-4C3/7C3=1 - 4/35 = 31/35.Answer:4/35
Answer: D
The ages of 2 persons differ by 38 years. If 12 years ago the elder one be 6 times as old as the younger one, find the present age of elder person.	Choose the correct choice from the following choices
A) 30.5 B) 48.5 C) 50.4 D) 62.6 E) 57.6

Solution: age of the younger person = x   age of the elder person = x+38   6(x-12) = x+38-12   x= 19.6   age of elder person = 19.6+38= 
19.6+38 = 57.6
57.6   Answer is 57.6
Answer: E
A boat travels 72 km downstream in 8 hours and 84 km upstream in 12 hours. Find the speed of the boat in still water and the speed of the water current.  Choose the correct option
A) 8 km/hr, 1 km/hr  B) 5 km/hr, 4 km/hr  C) 1 km/hr, 6 km/hr  D) 2 km/hr, 1 km/hr  E) 4 km/hr, 1 km/hr

Solution: Downstream speed=72km/8hrs   =9kmph   upstream speed72  /8= 
72  /8 = 9
9kmph   upstream speed=84km/12hrs   =7kmph   speed of boat84  /12= 
84  /12 = 7
7kmph   speed of boat=avg of downstream and upstream speeds   speed of boat=(9+7)/2= 
(9+7)/2 = 8
8kmph.   current speed=half of the difference of downstream and upstream speeds   currend speed=(9-7)/2= 
(9-7)/2 = 1
1kmph   ans is 8km/hr,1km/hr   8 km/hr, 1 km/hrNSWER:8 km/hr, 1 km/hr
Answer: A
A and B began business with Rs.3000 and Rs.4000 after 8 months, A withdraws Rs.1000 and B advances Rs.1000 more. At the end of the year, their profits amounted to Rs.630 find the share of A	Select
A) Rs.300  B) Rs.56  C) Rs.100  D) Rs. 240  E) Rs.90

Solution: Explanation:   (3*8 + 2*4):(4*8 + 5*4)   8:13   8/21 * 630 =Rs. 240   ANSWER:Rs. 240
Answer: D
A sum of money invested at compound interest to Rs. 800 in 3 years and to Rs 880 in 4 years. The
rate on interest per annum is.  Pick one:	A) 4%	B) 5%	C) 6%	D) 7%	E) 10%

Solution: Explanation:   S.I. on Rs 800 for 1 year = 80   Rate = (100*80)/(800*1)= 
(100*80)/(800*1) = 10
10%   Answer: 10%
Answer: E
A worker is paid a regular rate of $0.10 for completing a survey. The worker completes 50 surveys per week. For any survey involving the use of her cellphone, she is paid at a rate of that is 30% higher than her regular rate. If she completed 35 surveys involving the use of her cellphone, how much did she get that week?
Choose the correct option.
A) $13
B) $9
C) $10.50
D) $1.50
E) $12

Solution: $10(0.3)=$0.30 per each survey involving the use of her cell phone   $30(35)=$10.50 for completing surveys involving the cell phone   $0.10(50-35)=$0.10(15)=$1.50   Total $1.50+$10.50=$12   Answer $12 12. 1.50+ 10.50= 
 1.50+ 10.50 = 12
$12   Answer $12 12.
Answer: E
For any non-zero a and b that satisfy |ab| = ab and |b| = -b
|b - 4| + |ab - b| = ?
Select the correct option:	A) a) ab - 4	B) b) 2b - ab - 4	C) c) ab + 4	D) d) ab - 2b	E) e) ab - 2b + 4

Solution: |a| = -a Suggests that 'a' is Negative   |ab| = ab Suggests that 'ab' is Positive   'ab' is Positive Suggests that 'a' and 'b' have same Sign i.e. either both positive or both negative   But since 'a' is Negative therefore 'b' is Negative too.   Since b is negative so |b - 4| = -b+4   Since ab is Positive and b is Negative so |ab - b| = ab - b   i.e. |b - 4| + |ab - b| = -b+4 + ab - b =ab - 2b + 4   Answer: Option e) ab - 2b + 4
Answer: E
One-sixth of the light switches produced by a certain factory are defective. Four-fifths of the defective switches are rejected and 1/20 of the non defective switches are rejected by mistake. If all the switches not rejected are sold, what percent of the switches sold by the factory are defective?
Pick one:	A) 4%	B) 5%	C) 6%	D) 11%	E) 16%

Solution: 1/6 of the switches are defective.   The defective switches that are not rejected are 1/5*1/6 = 1/30 = 4/120 of all switches.   The non defective switches that are sold are 5/6*19/20 = 95/120 of all switches.   The percent of switches sold that are defective is 4/99 which is about 4%.   The answer is 4%.
Answer: A
Which one the following fractions has the exact division of nine?
Pick one.
A) 47776/9 B) 37777/9 C) 87777/9 D) 57777/9 E) 67777/9

Solution: Numerator for all option is 9. If the numerator value digits are added together and forms the number equal to 9, then it is exact division of 9. So Option (C) 8+7+7+7+7 = 36= 3+6= 
3+6 = 9
9. Answer (87777/9).
Answer: C
The 5 th term and 21 st term of a series in A.P are 10 and 42 respectively. Find the 31 st term. Choose the correct choice from the following answers
A) 50  B) 55  C) 65  D) 62  E) 52

Solution: a + 4d = 10 ………….. (1)   a + 20d = 42 ………….. (2)   Eqn (2) – Eqn (1) gives 16d = 32 , d = 2   Substituting d =2 in either (1) or (2), a = 2.   31 st term = a + 30d = 2 + 30*2= 
2 + 30*2 = 62
62   ANSWER:62
Answer: D
. A man is 24 years older than his son. In two years, his age will be twice the age of his son. The present age of this son is Pick:
A) 21 years  B) 22 years  C) 23 years  D) 24 years  E) 25 years

Solution: Explanation:   Let's Son age is x, then Father age is x+24.   => 2(x+2) = (x+24+2)   => 2x+4 = x+26   => x = 22 years   Answer: Option 22 years
Answer: B
(xn - an) is completely divisible by (x - a), when Choose the correct choice from the following answers.
A) n is any natural number  B) n is an even natural number  C) n is and odd natural number  D) n is prime  E) None

Solution: For every natural number n, (xn - an) is completely divisible by (x - a).   n is any natural number)
Answer: A
How many kg of pure salt must be added to 100kg of 10% solution of salt and water to increase it to a 15% solution?	Choose the most appropriate option:
A) A)5.8	B) B)1.3	C) C)9.6	D) D)12.5	E) E)7.9

Solution: 5.8mount salt in 100kg solution = 10*100/100= 
10*100/100 = 10
10 kg   Let x kg of pure salt be added   then(10+x)/(100+x)=15/100   200+20x=300+3x   17x = 100   x = 5.8   5.8nswer is 5.8
Answer: A
Carol is four times Alice’s age but only twice as old as Betty. Alice is thirty-six years younger than Carol. How old is Betty?	Choose one:
A) 36  B) 39  C) 42  D) 48  E) 24

Solution: Beyond the obvious Algebra approach to this question, it can also be solved by TESTing THE ANSWERS.   We're told 3 facts about the relative ages of 3 people:   1) Carol's age is 4 times Alice's age   2) Carol's age is 2 times Betty's age   3) Carol is 36 years older than Alice   We're asked for BETTY'S age.   Since Carol is TWICE Betty's age, Betty is clearly younger than Carol, so we'll TEST smaller answer first.   IF....   Betty = 24   Then Carol = 2(24) = 48   Then Alice = 48 - 36= 
48 - 36 = 12
12 AND   48/4= 
  48/4 = 12
12   All of these values mesh perfectly with the facts and with one another, so Betty MUST be 24   24
Answer: E
If a coin is tossed 6 times what is the probability that it will land either heads 6 times or tails 6 times? Choices:
A) 1/4
B) 1/8
C) 1/16
D) 1/32
E) 1/64

Solution: The probability of 6 heads is (1/2)^6 = 1/64   The probability of 6 tails is (1/2)^6 = 1/64   The probability of 6 heads or 6 tails is 1/64 + 1/64 = 1/32   The answer is 1/32.
Answer: D
The ages of two persons differ by 16 years. 7 years ago, the elder one was 3 times as old as the younger
one. What are their present ages of the elder person  Choose the correct choice from the following options.
A) 15	B) 31	C) 25	D) 30	E) 35

Solution: Explanation:   Let's take the present age of the elder person = x   and the present age of the younger person = x � 16   (x � 7) = 3 (x-16-7)   => x � 7 = 3x � 69   => 2x = 62   => x = 62/2= 
62/2 = 31
31   Answer: Option 31
Answer: B
The perimeter of a square is equal to the radius of a circle having area 39424 sq cm, what is the area of square?	Pick:
A) 1225 sq cm	B) 441 sq cm	C) 784 sq cm	D) Can’t say	E) None of these

Solution: Let the side of square =a cm and radius of circle=r cm   Given, 4a= r   Also Area of square= Pi*r^2= 39424, r^2=12544 or r=112   So a= r/4= 112/4= 
112/4 = 28
28   Hence Area of square=a^2=28^2=784 cm^2   ANSWER:784 sq cm
Answer: C
The sum of 11 hours 45 minutes and 2 hours 15 minutes is approximately what percent of a day?  Choose the correct choice from the following answers.
A) approx 54% B) approx 58% C) approx 74% D) 28% E) 72%

Solution: Since the question is asking for an approximate percentage   11:45+2:15 ~ 14 hours   % of day = 14*100/24 ~ 58%   Answer is approx 58%.
Answer: B
How much time will take for an amount of Rs. 450 to yield Rs. 78 as interest at 4.5% per annum of simple interest?
Choose the correct choice from the following:
A) 8 years
B) 3 years 10 months
C) 3 years
D) 9 years
E) 5 years

Solution: Time = (100 * 78) / (450 * 4.5)   = 3 years 10 months   Answer: 3 years 10 months
Answer: B
The average weight of 36 men is 50 kg. It was found later that the figure of 37 kg was misread as 73 kg. What is the correct average?
Options
A) 49 kg B) 51 kg C) 50.5 kg D) 51.5 kg E) None of these

Solution: Correct average = [( 50 x 36) - 73 + 37 )]/36 = 1764/36= 
1764/36 = 49
49 kg.   49 kgNSWER:49 kg
Answer: A
A snooker tournament charges $45.00 for VIP seats and $15.00 for general admission (“regular” seats). On a certain night, a total of 300 tickets were sold, for a total cost of $7,500. How many fewer tickets were sold that night for VIP seats than for general admission seats?
Options
A) 212 B) 240 C) 220 D) 230 E) 225

Solution: let no of sits in vip enclosure is x then x*45 +15( 300-x) =7500 or 30x = 7500 -4500 , x = 3000/30= 
3000/30 = 100
100   vip=100 general 220   220
Answer: C
Adam borrowed some money at the rate of 6% p.a. for the first two years , at the rate of 9% p.a. for the next three years , and at the rate of 14% p.a. for the period beyond five years. 1£ he pays a total interest of Rs. 11,400 at the end of nine years how much money did he borrow?	Answers.
A) Rs.8,000 B) Rs.09,000 C) Rs.11,000 D) Rs.10,000 E) Rs.12,000

Solution: Let the sum borrowed be x. Then,   (x*2*6)/100 + (x*9*3)/100 + (x*14*4)/100 = 11400   (3x/25 + 27x/100 + 14x / 25) = 11400   95x/100 = 11400   x = (11400*100)/95= 
(11400*100)/95 = 12_000
12000.   Hence , sum borrowed= Rs.12,000   Answer is Rs.12,000.
Answer: E
In a village of 100 households, 80 have at least one DVD player, 90 have at least one cell phone, and 65 have at least one MP3 player. If x and y are respectively the greatest and lowest possible number of households that have all three of these devices, x – y is:
Choose the correct option: A) 65 B) 55 C) 45 D) 30 E) 20

Solution: Am I missing something here??? it seems straightforward......   The obvious maximum that have all 3 is 65, because you are limited by the SMALLEST number.   The minimum is simply the sum of the max of each people who DONT have the product, so:    100-90= 
 100-90 = 10
10 don't have Cell    100-80= 
 100-80 = 20
20 don't have DVD   and  100-65= 
 100-65 = 35
35 don't have MP3   SO a total of   10+20+35= 
  10+20+35 = 65
65 combined who might NOT have SOME combination of the 3 products. So subtract that from 100, to give you the minimum of the people who COULD have all 3 and you get  100-65= 
 100-65 = 35
35.   65-35= 
65-35 = 30
30   30
Answer: D
2 trains starting at the same time from 2 stations 200 km apart and going in opposite direction cross each other at a distance of 110 km from one of the stations. What is the ratio of their speeds Choose the correct option.
A) 11:9
B) 13:9
C) 17:9
D) 21:9
E) None of these

Solution: Explanation:   We know total distance is 200 Km   If both trains crossed each other at a distance of 110 km then one train covered 110 km and other 90 km [  110+90= 
  110+90 = 200
200km]   So ratio of their speed= 110:90 = 11:9   Option 11:9
Answer: A
If 2 persons can do 2 times of a particular work in 2 days, then, 7 persons can do 7 times of that work in?  Choose the correct choice from the following answers:
A) 2 days	B) 4 days	C) 6 days	D) 7 days	E) 8 days

Solution: That is, 1 person can do one time of the work in 2 days.   Therefore, 7 persons can do 7 times work in the same 2 days itself   2 days)
Answer: A
The rate of a certain chemical reaction is directly proportional to the square of the concentration of chemical A present and inversely proportional to the concentration of chemical B present. If the concentration of chemical B present is increased by 100 percent, which of the following is closest to the percent change in the the concentration of chemical A required to keep the reaction rate unchanged.
Choose the correct choice from the following options:
A) 100 % decrease	B) 50% decrease	C) 40% decrease	D) 40% increase	E) 50% increase

Solution: r = k A^2 / B for some constant k<>0   (Question should also give B<>0)   So we have   r1 = k A1^2 / B1   r2 = k A2^2 / B2   r1 = r2   B2 = (1+100%)B1 = 2B1   k A1^2 / B1 = k A2^2 / B2   A1^2 / B1 = A2^2 / 2B1   2A1^2 = A2^2   (sqrt(2)A1)^2 = A2^2   A1,A2>0   A2 = sqrt(2) * A1   A2 = (1 + 41.4%) * A1   About 40% increase   ANSWER:40% decrease
Answer: C
in how many can the letters of the word COLLEGE be arranged,such that its vowels do not come together?  Choose the correct choice from the following answers:
A) 980  B) 920  C) 1020  D) 1060  E) 1080

Solution: COLLEGE   C=1,O=1,G=1, L=2,E=2   vowels = O E E   total no. of words formed = 7!/(2!*2!) = 7!/4 = 1260   no. of words when vowels come together = CLLG(OEE) => 5!/2! * 3!/2! = 180   no. of words having vowels not together = 1260 - 180= 
1260 - 180 = 1_080
1080   ANSW1080R:1080
Answer: E