MU-NLPC/Calc-aqua_rat huggingface dataset:
A rectangular block 6cm by 12cm by 15cm is cut into an exact number of equal cubes. Find the least possible number of cubes? Choose the correct choice from the following
A) 20  B) 25  C) 40  D) 50  E) 35

Solution: Volume of the block = 6*12*15= 
6*12*15 = 1_080
1080 cm^3   Side of the largest cube= H.40.F of 6,12,15 = 3cm   Volume of the cube = 3*3*3= 
3*3*3 = 27
27 cm^3   Number of cubes= 1080/27= 
1080/27 = 40
40   Answer is 40
Answer: C
If log 0.317 = 0.3332 and log 0.318 = 0.3364, then find log 0.319	Options:
A) 0.3396 B) 0.3496 C) 0.3596 D) 0.3696 E) 0.3796

Solution: log.318-log.317=.0032   log.318+log.oo1=log.319   .3364+.0032= 
.3364+.0032 = 0.3396
.3396   0.3396NSWER:0.3396
Answer: A
In a class of 120 students numbered 1 to 120, all even numbered students opt for Physics, whose numbers are divisible by 5 opt for Chemistry and those whose numbers are divisible by 7 opt for Math. How many opt for none of the three subjects? Pick:
A) 19
B) 41
C) 21
D) 26
E) 34

Solution: Explanatory Answer   We need to find out the number of students who took at least one of the three subjects and subtract that number from the overall 120 to get the number of students who did not opt for any of the three subjects.   Number of students who took at least one of the three subjects can be found by finding out A U B U C, where A is the set of those who took Physics, B the set of those who took Chemistry and C the set of those who opted for Math.   Now, AUBUC = A + B + C - (A n B + B n C + C n A) + (A n B n C)   A is the set of those who opted for Physics = 120/2= 
120/2 = 60
60 students   B is the set of those who opted for Chemistry= 120/5= 
120/5 = 24
24   C is the set of those who opted for Math= 120/7 = 17.   The 10th, 20th, 30th…… numbered students would have opted for both Physics and Chemistry.   Therefore, A n B = 120/10= 
120/10 = 12
12   The 14th, 28th, 42nd…. Numbered students would have opted for Physics and Math.   Therefore, C n A= 120/14 = 8   The 35th, 70th …. Numbered students would have opted for Chemistry and Math.   Therefore, A n B = 120/35 = 3   And the 70th numbered student would have opted for all three subjects.   Therefore, AUBUC = 60 + 24 + 17 - (12 + 8 + 3) + 1= 
60 + 24 + 17 - (12 + 8 + 3) + 1 = 79
79.   Number of students who opted for none of the three subjects= 120 - 79= 
120 - 79 = 41
41.   Answer 41
Answer: B
Find the area of a triangle whose sides are 41 cm, 28 cm, 15 cm. Also, find the length of the altitude corresponding to the largest side of the triangle.  Choose one
A) 4.1 cm	B) 5.1 cm	C) 6.1 cm	D) 7.1 cm	E) 8.1 cm

Solution: Semi-perimeter of the triangle = (a + b + c)/2   = (41 + 28 + 15)/2   = 84/2= 
84/2 = 42
42 cm   Therefore, area of the triangle= √(s(s - a) (s - b) (s - c))   = √(42 (42 - 41) (42 - 28) (42 - 15)) cm²   = √(42 × 1 × 27 × 14) cm²   = √(3 × 3 × 3 × 3 × 2 × 2 × 7 × 7) cm²   = 3 × 3 × 2 × 7 cm²   = 126 cm²   Now, area of triangle = 1/2 × b × h   Therefore, h = 2A/b   = (2 × 126)/41   = 252/41   = 6.1 cm   ANSWER : OPTION 6.1 cm
Answer: C
What is the greatest prime factor of 4^6 - 1?	Choices:
A) 13
B) 17
C) 19
D) 23
E) 29

Solution: 4^6-1 = (4^3-1)(4^3+1) = 63*65 = 7*9*5*13   The answer is 13.
Answer: A
The H.C.F. of two numbers is 10 and the other two factors of their L.C.M. are 13 and 14. The larger of the two numbers is:
Choose one
A) 100  B) 120  C) 180  D) 140  E) 60

Solution: Clearly, the numbers are (10 x 13) and (10 x 14).   Larger number = (10 x 14) = 140. Answer: Option 140
Answer: D
7% of the total quantity of rice is lost in grinding when a country has to import 6 million tonnes, but when only 7 3/4% is lost, it can import 3 million tonnes. Find the quantity of rice grown in the country.  Choose the most appropriate option.
A) 200  B) 300  C) 400  D) 450  E) 560

Solution: Let x be the total grown quantity of wheat. According to the question   (7%of x)+ 64 31 %of x)+3 7x 31x => 100+ 6 = 400 + 3 1200 x = — 400 million tonnes rice grown   400
Answer: C
How long does a train 110 m long running at the speed of 72 km/hr takes to cross a bridge 132 m length?
Pick:
A) 9.8 sec	B) 12.1 sec	C) 12.42 sec	D) 14.3 sec	E) 15.3 sec

Solution: Speed = 72 * 5/18= 
72 * 5/18 = 20
20 m/sec   Total distance covered= 110 + 132= 
110 + 132 = 242
242 m.   Required time= 242/20= 
242/20 = 121/10 = around 12.1
12.1 sec.   ANSWER:12.1 sec
Answer: B
Rahul went to a shop and bought things worth Rs. 25, out of which 30 paise went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items? Answers
A) Rs. 15	B) Rs. 17	C) Rs. 19.7	D) Rs. 21	E) Rs. 22

Solution: Total cost of the items he purchased = Rs.25   Total tax incurred = 30 paise = Rs.   30   100   30100   Let the cost of the tax free items   =   x   =x   Given that tax rate = 6%   ∴   (   25   −   30   100   −   x   )   6   100   =   30   100   ⇒   6   (   25   −   0.3   −   x   )   =   30   ⇒   (   25   −   0.3   −   x   )   =   5   ⇒   x   =   25   −   0.3   −   5   =   19.7   Option Rs. 19.7
Answer: C
A Train requires 8 seconds to pass a pole while it requires 18 seconds to cross a stationary train which is 400 mtrs long. Find the speed of the train.  Choose the correct choice from the following answers
A) 144 kmph B) 124 kmph C) 134 kmph D) 150 kmph E) 160 kmph

Solution: In 8s the train crosses the pole and in 18 sec the train crosses one more stationary train   In 10 sec the train travels a distance of 400 mtrs   Speed = 400/10= 
400/10 = 40
40 m/s= 40 (3600/1000) = 40 * 18/5= 
40 * 18/5 = 144
144 kmph   144 kmphnswer: 144 kmph
Answer: A
Which of the following points falls outside of the region defined by 2y≤4x−12?	Select:
A) (5, 1)
B) (3, -8)
C) (2, 0)
D) (1, -2)
E) (0, -14)

Solution: Equation given is 2y<=4x-12   Simplifying this; y<=2x-6   Plug in the values provided in the options,   A. 1<=4   B. -8<=0   C. 0<=-2   D.-2<=-2   E. -14<=-12   Option (2, 0) is the answer.
Answer: C
Day after tomorrow is my birthday. On the same day next week falls 'Holi'. Today is Monday. What will be the day after 'Holi'?	Choose the most appropriate option.
A) Wednesday  B) Thursday  C) Friday  D) Saturday  E) None of these

Solution: next week is WEDNESDAY   ThursdayUT THEY ASKED   What will be the day after 'Holi'?   SO THURSDAY   ANSWER:Thursday
Answer: B
Three candidates contested in an election and received 5136, 7636, 11628 votes respectively. What is the percentage of the total votes did the winning candidate get?	Choose the correct choice from the following answers:
A) 45%
B) 48%
C) 57%
D) 51%
E) 62%

Solution: Total number of votes polled = 5136+7636+11628= 
5136+7636+11628 = 24_400
24400   Required percentage= 11628*100/24400 = 48%   Answer is 48%
Answer: B
A Father told his son, " I was as old as you are at present, at the time of your birth," if the father is 38 years old now, then what was the son age five years back?
Choose the correct choice from the following choices:
A) 14 years
B) 19 years
C) 38 years
D) 33 years
E) 37 years

Solution: Let the present age of the son be x years, then   x = 38 - x   x = 19 years.   Five years back, son’s age = x - 5 = 19 - 5= 
19 - 5 = 14
14 years   14 yearsNSWER:14 years
Answer: A
The H.C.F. of two numbers is 30 and the other two factors of their L.C.M. are 13 and 14. The larger of the two numbers is:
Select:
A) 276	B) 299	C) 420	D) 345	E) 365

Solution: Clearly, the numbers are (30 x 13) and (30 x 14).   Larger number = (30 x 14) = 420. Answer: Option 420
Answer: C
Denise is trying to open a safe whose combination she does not know. IF the safe has 4000 possible combinations,and she can try 150 different possibilities,what is the probability that she does not pick the one correct combination.
Select the correct option: A) 0.9625 B) 159/160 C) 157/160 D) 3/160 E) 0.8625

Solution: If Denise does not pick the correct combination in first 150 try, then the correct combination is one of remaining 3850. So Probability = 3850/4000= 
3850/4000 = 77/80 = around 0.9625
0.9625   answer is 0.9625
Answer: A
A man misses a bus by 40 minutes if he travels at 30 kmph. If he travels at 40 kmph, then also he misses the bus by 10 minutes. What is the minimum speed required to catch the bus on time?  Choices:
A) 49 kmph
B) 45 kmph
C) 95 kmph
D) 75 kmph
E) 46 kmph

Solution: Let the distance to be travelled to catch the bus be x km   x/30 - x/40 = 30/60 => (4x - 3x)/120 = 1/2 => x = 60 km   By traavelling 30 kmph time taken = 60/30= 
60/30 = 2
2 hours   By taking 2 hours, he is late by 40 min. So, he has to cover 60 km in at most speed= 60/(4/3)= 
60/(4/3) = 45
45 kmph.   Answer: 45 kmph
Answer: B
(935421 x 625) = ?  Choose one.
A) 584638125
B) 584638150
C) 584638180
D) 584638220
E) 584638225

Solution: 935421 x 625 = 935421 x 54 = 935421 x 10 4   2   =	935421 x 104	=	9354210000   24	16   = 584638125   584638125)
Answer: A
How long will a boy take to run round a square field of side 50 meters, if he runs at the rate of 9km/hr? Choose the correct choice from the following options
A) 80sec
B) 45sec
C) 1min
D) 32sec
E) 25sec

Solution: Speed = 9 km/hr = 9*5/18 = 5/2 m/sec   Distance = 50*4= 
50*4 = 200
200m   Time taken= 200*2/5= 
200*2/5 = 80
80sec   80secnswer is 80sec
Answer: A
How many three letter words are formed using the letters of the word POLICE?
Choices.
A) 22  B) 120  C) 140  D) 24  E) 91

Solution: Explanation:   The number of letters in the given word is six.   The number of three letter words that can be formed using these four letters is Ã¢Â´PÃ¢â€šÆ’ = 6*5*4= 
6*5*4 = 120
120.   Answer: 120
Answer: B
A shop owner professes to sell his articles at certain cost price but he uses false weights with which he cheats by 10% while buying and by 10% while selling. What is his percentage profit?
Choose one.
A) 10.22%
B) 20.22%
C) 21.22%
D) 22.22%
E) Can't be calculated

Solution: The owner buys 100 kg but actually gets 110kg;   The owner sells 100 kg but actually gives 90kg;   Profit: (110-90)/90*100=~22.22%   Answer: 22.22%.
Answer: D
In a certain game, each player scores either 2 points or 5 points. If n players score 2 points and m players score 5 points, and the total number of points scored is 50, what is the least possible positive R difference between n and m?  Choices
A) 1	B) 3	C) 5	D) 7	E) 9

Solution: We have equation 2n + 5m = 50   We have factor 2 in first number and we have factor 5 in second number.   LCM(2, 5) = 10   So we can try some numbers and we should start from 5 because it will be less list than for 2   2 * 5= 
2 * 5 = 10
10 and n should be equal 20   4 * 5= 
4 * 5 = 20
20 and n should be equal 15   6 * 5= 
6 * 5 = 30
30 and n should be equal 10   8 * 5= 
8 * 5 = 40
40 and n should be equal 5   10 * 5= 
10 * 5 = 50
50 and n should be equal 0   third variant give us the mininal difference   n - m= 10 - 6= 
10 - 6 = 4
4   And there is some mistake in my way of thinking because we don't have such answer )   If we change the task and will seek for difference between m and n   than minimal result R will be 8 - 5= 
8 - 5 = 3
3   And answer 3
Answer: B
The cost of setting up a magazine is Rs. 2800. The cost of paper and ink etc is Rs. 80 per 100 copies and printing cost is Rs. 160 per 100 copies. In last month 2000 copies were printed but only 1500 copies could be sold at Rs. 5 each. Total 25% profit on the sale price was realized. There is one more resource of income from magazine which is advertising. What sum of money obtained from the advertising in magazine?
Pick.
A) Rs. 1750
B) Rs. 2350
C) Rs. 1150
D) Rs. 1975
E) None of these

Solution: Solution: Set up cost = Rs. 2800   Paper etc = Rs. 1600   Printing cost = Rs. 3200   Total cost = Rs. 7600   Total sale price = 1500*5= 
1500*5 = 7_500
7500   Let amount obtained from advertising be x then,   (7500+x)-7600= 25 % of 7500   x = 1975.   Answer: Option Rs. 1975
Answer: D
The arithmetic mean of a data set is 46 and the standard deviation of the set is 4. Which of the following contains the interval two standard deviations from the mean of the set?
Options:
A) 38 to 55
B) 38 to 54
C) 48 to 54
D) 80 to 54
E) 38 to 60

Solution: Arithmetic Mean = 46   SD = 4 (One Interval )   Two SD intervals means 38__42__46 __50__54   answer 38 to 54
Answer: B
Three friends are buying a gift for a friend. Declan contributes 4 dollars more than 1/4 the cost of the gift, Ed contributes 1 dollar less than 1/3 the cost of the gift, and Frank contributes the remaining 20 dollars. What is the cost of the gift?  Options: A) 48 B) 54 C) 60 D) 55.2 E) 72

Solution: 55.2eclan = 55.2, Ed = E, Frank = F   t = total   55.2 + E + F = t   (t/4 + 4) + (t/3 - 1) + 20 = t   t = 23 + (7t/12)   12t = 23(12) + 7t   5t = 23(12)   t = 55.2   The correct answer is 55.2.
Answer: D
A pharmaceutical company received $4 million in royalties on the first $24 million in sales of generic equivalent of one of its products and then $5 million in royalties on the next $60 million in sales. By approximately what percent did the ratio of royalties to sales decrease from the first $24 million in sales to the next $60 million in sales?	Options:  A) 10%  B) 20%  C) 25%  D) 30%  E) 35%

Solution: change in ratio of royalties to sales = 4/24 -5/60 = 1/12   % decrease = (1/12)/(4/24) *100 = 20%   Answer: 20%)
Answer: B
In how many ways can the letters in PRECISION be arranged? In how many of these arrangements do the vowels occupy even places ?
Choose one.
A) 1140
B) 1440
C) 1420
D) 1460
E) 1520

Solution: 4 vowels out of which two are identical can be arranged in even places in 4!/2!=12 # of ways.   Remaining 5 letters can be arranged in 5!=120 # of ways.   Total 12*120= 
12*120 = 1_440
1440.   ans:1440
Answer: B
If the personal income tax rate is lowered from 42% to 28%, what is the differential savings for a tax payer having an annual income before tax to the tune of $34500?  Choose the correct choice from the following answers:  A) $3500  B) $5000  C) $4830  D) $7000  E) $10000

Solution: Saving = (42-28)% of 34500 = 4830.   Answer:$4830
Answer: C
What will come in place of the x in the following Number series? 5,28,57,88,125
Choose one:  A) 123  B) 155  C) 166  D) 178  E) 190

Solution: 28=23+5   57=29+28   88=31+57   125=37+88   166=41+125= 
41+125 = 166
166   166
Answer: C
The average salary of all the workers in a workshop is Rs. 8000. The average salary of 7 technicians is Rs. 12000 and the average salary of the rest is Rs. 6000. The total number of workers in the workshop is:  Choose the correct choice from the following answers.
A) 21
B) 20
C) 22
D) 25
E) 40

Solution: Let the total number of workers be x. Then,   8000x = (12000 * 7) + 6000(x - 7)   = 2000x = 42000   = x = 21.   21NSWER 21
Answer: A
When n is divided by 24, the remainder is 4. What is the remainder when 3n is divided by 8?
Choose the correct answer:  A) 3  B) 4  C) 5  D) 6  E) 7

Solution: Let n=4 (leaves a remainder of 4 when divided by 24)   3n = 3(4) =12, which leaves a remainder of 4 when divided by 8.   Answer 4
Answer: B
Let D represent a set of four distinct prime numbers. If the sum of the numbers in D is even and x is a member of D, then what is the least possible value that x can be? Choices
A) 1
B) 2
C) 3
D) 5
E) 7

Solution: We are told that D is a set of four distinct prime numbers, and the sum of the numbers in D is even. Since the question involves odds, evens and the smallest possible prime, you should immediately think of 2, the smallest prime number and the only even prime number.   If 2 were a member of the set, then we would have one even number and three odd numbers. Since such sum would always be odd, 2 cannot be a member of the set. Thus, all the members of D must be odd to yield an even sum.   Since all the members of the set must be odd prime numbers, the answer is the smallest odd prime number, which is 3.   The correct answer is choice (C).   Note:1 is not a prime number.
Answer: C
A man, a woman and a boy can complete a job in 3, 4 and 12 days respectively. How many boys must assist 1 man and 1 woman to complete the job in 1/4 of a day? Choose the most appropriate option:
A) 41	B) 43	C) 31	D) 84	E) 81

Solution: (1 man + 1 woman)’s 1 day work = 1/3 + 1/4 = 7/12   Work done by 1 man and 1 women in 1/4 day = ((7/12) x (1/4)) = 7/48   Remaining work = 1 - 7/48 = 41/48   Work done by 1 boy in 1/4 day = ((1/12) x (1/4)) = 1/48   Therefore, Number of boys required = ((41/48) x 48) = 41   41NSWER:41
Answer: A
Find the area between two concentric circles defined by
x2 + y2 -2x + 4y + 1 = 0
x2 + y2 -2x + 4y - 11 = 0  Choose the most appropriate option:
A) 11 Pi	B) 12 Pi	C) 13 Pi	D) 14 Pi	E) 15 Pi

Solution: Rewrite equations of circles in standard form. Hence equation x2 + y2 -2x + 4y + 1 = 0 may be written as   (x - 1)2 + (y + 2) 2 = 4 = 22   and equation x2 + y2 -2x + 4y - 11 = 0 as   (x - 1)2 + (y + 2) 2 = 16 = 42   Knowing the radii, the area of the ring is Pi (4)2 - Pi (2)2 = 12 Pi   correct answer is 12 Pi) 12 Pi
Answer: B
In how many different number of ways 5 men and 2 women can sit on a shopa which can accommodate persons?	Choose the correct option
A) 210  B) 220  C) 230  D) 240  E) 250

Solution: 7p3 = 7 × 6 × 5 = 210   210)
Answer: A
A gardener wants to plant trees in his garden in such a way that the number of trees in each row should be the same. If there are 2 rows or 7 rows or 9 rows, then no tree will be left. Find the least number of trees required	Choose the correct choice from the following options:
A) 22  B) 60  C) 126  D) 76  E) 21

Solution: Explanation:   The least number of trees that are required = L126M(2, 7, 9) = 126   Answer: 126
Answer: C
What will be the remainder of the following division:
(1234567....141516...20212223....404142)/43?  Choose the correct choice from the following.
A) 0
B) 1
C) 2
D) 3
E) 4

Solution: first add the digits   1+2+3+.........+42   =>903   then 903 divided by 43   because it is the rule of division by 43( a prime number)   so 903%43=0   % is modulo operator it returns the remainder part   0NSWER:0
Answer: A
It takes 6 tons of copper ore and 15 tons of iron ore to make one ton of alloy A. How many tons of alloy A can be made from 60 tons of copper ore and 90 tons of iron ore? Select.
A) 4  B) 5  C) 6  D) 7  E) 8

Solution: Yes, you need copper ore:iron ore in the ratio 6:15. Total 21 tons of the mix in this ratio will give 1 ton of alloy A.   If you have 60 tons of copper ore, it is enough for 60/6= 
60/6 = 10
10 tons of alloy A.   If you have 90 tons of iron ore, it is enough for 90/15= 
90/15 = 6
6 tons of alloy A.   Since iron ore is available for only 6 tons of alloy A, you can make only 6 tons of alloy A.   The leftover copper ore alone cannot make any alloy A and hence will be leftover only.   Answer must be 6.   (6)
Answer: C
Two trains running opposite to each other with a speed of 60kph and 55kph having lengths of 180m and 200m respectively. How long it will take the trains to completely pass each other(in seconds)?  Select the correct option:  A) 9.89  B) 10.21  C) 11.89  D) 14.22  E) 19.13

Solution: Speed of the train relative to each other=60+55= 
60+55 = 115
115kph=31.94m/s   Distance need to be covered=180+200= 
180+200 = 380
380m   Time taken by the trains to pass each other=380/31.94=11.89s   Answer: 11.89
Answer: C
Two cars started from the same point, at 5 am, traveling in opposite directions at 40 and 50 mph respectively. At what time will they be 450 miles apart?  Select:  A) 8am  B) 10am  C) 11am  D) 12am  E) 14am

Solution: After t hours the distances D1 and D2, in miles per hour, traveled by the two cars are given by   D1 = 40 t and D2 = 50 t   After t hours the distance D separating the two cars is given by   D = D1 + D2 = 40 t + 50 t = 90 t   Distance D will be equal to 450 miles when   D = 90 t = 450 miles   t = 5 hours.   5 am + 5 hours = 10 am   Answer:10am
Answer: B
Which of the following options is equal to 2.71 x 10(power 7)? Choose the correct choice:  A) 27100000  B) 27500000  C) 27200000  D) 21100000  E) 17100000

Solution: = 2.71 x 10(power 7)   = 2.71 x 10000000   = 27100000.   27100000nswer is 27100000.
Answer: A
IF x is an integer greater than 6, then all the following must be divisible by 3 EXCEPT
Choose the correct choice from the following answers:
A) 3x^3
B) 9x/3
C) 9x^2
D) x(x+1)(x+2)
E) x-3

Solution: *any number multiplied by 3, will be divided by 3   for option x-3 if we put value x=10, 10-3=7 is not divisible by 3   Answer : x-3
Answer: E
X, Y, W and Z are intezers and the expressing X - Y - Z is even and Y - W - Z is odd. If X is even then which of	Choose the correct option:
A) W must be odd  B) J must be odd  C) Y must be odd  D) Z must be odd  E) F must be odd

Solution: Ans. If X is even and X - Y - Z is even then Y and Z both should be odd or both should be even.   If Y - W - Z is odd, and Y and Z are also odd W should be odd   If Y - W - Z is even, and Y and Z are even then W should be odd.   W must be ODD   W must be oddnswer:W must be odd
Answer: A
10 distinct integers are arranged in ascending order. The range of the first 7 is 25 and that of last 7 is 30. What is the maximum range R of the 10 numbers? Select
A) 25  B) 27  C) 30  D) 52  E) 55

Solution: Positions: 1 2 3 4 5 6 7 8 9 10   Given: 1st position = x; 4th position = a; 7th position = y; 10th position = b   y - x = 25   Let x be 0 and y = 25. We are asked to maximize the range and the integers are distinct.   b - a = 30 --> b = 30 + a   In order to increase the range, we have to maximize the value of 'b'.   'b' can be maximized by taking the max value of 'a'.   From the assumed values, maximum value of 'a' can be 22.   Therefore, b = 30 + 22= 
30 + 22 = 52
52   Range R= 52 - 0= 
52 - 0 = 52
52   Answer: 52
Answer: D
The average age of a class of 14 students is 10 yrs. if the teacher's age is also included, the average increases by one year. Find the age of the teacher Select the correct option
A) 30 Years B) 31 Years C) 32 Years D) 34 Years E) 25 Years

Solution: Total age of students is 14X10 = 140 Years   Total age inclusive of teacher = 15X (10+1) = 165   So, Teacher's age is 165-140= 
165-140 = 25
25 Yrs   There is a shortcut for these type of problems   Teacher's age is 10+(15X1)= 25 Years   25 Years
Answer: E
A starts business with a capital of Rs.1200 B and C join with some investments after 3 and 6 months respectively. If the end of a year, the profit is divided in the ratio 2:3:5 respectively. What is B's investment in the business?
Choose the correct choice:
A) 2400 B) 2888 C) 2766 D) 91987 E) 2121

Solution: 1200 * 12: x * 9 = 2:3   x = 2400   2400nswer: 2400
Answer: A
A man want to buy 2 cars. If there are 10 cars that satisfy the man's criteria,in how many different ways can the man select the 2 cars if the order of selection doesn't matter.
Pick one
A) 54
B) 120
C) 32
D) 210
E) 45

Solution: The number of ways of choosing 2 cars out of 10 are counted by = 10C2 ways = 45   Answer: Option 45
Answer: E
In the youth summer village there are 200 people, 100 of them are not working,75 of them have families and 125 of them like to sing in the shower. What is the largest possible number of people in the village, which are working, that don't have families and that are singing in the shower?	Choices
A) 125
B) 150
C) 100
D) 130
E) 140

Solution: total =200   not working =100   having family=75   like to sing in shower = 125   working=200-100= 
200-100 = 100
100   not having family= 200-75= 
200-75 = 125
125   like to sing in shower= 125   largest possible number is the lowest possible among the above   Thus 100   100
Answer: C
There are nine leopards and one sheep.
Leopard can eat sheep but since as the land is magical, the leopards who eats the sheep , turns into sheep and then can be eaten by the remaining leopard(s).
If we leave them for some time then how many sheep and leopard will be there , when we come back ?
Choose the correct choice from the following options.
A) 7 leopard and 3 sheep  B) 8 leopard and 1 sheep  C) 6 leopard and 4 sheep  D) 5 leopard and 1 sheep  E) 2 leopard and 5 sheep

Solution: 8 leopard and 1 sheep   8 leopard and 1 sheep   since all animal are rational , once 1st leopard eats the sheep all the rest of leopard would know about this.
Answer: B