MU-NLPC/Calc-aqua_rat huggingface dataset:
Sony and Johnny caught 60 fishes. Sony caught four times as many as Johnny. How many fishes did Johnny catch?
Pick one:
A) 12
B) 16
C) 34
D) 38
E) 42

Solution: s+j=60   s=4*j   j=12   12NSWER:12
Answer: A
Set M contains number that satisfy the condition that, if integer x is in the set then x + 1 will also be in the set M. If -4 is one value in the set, which of the following values must also be present in the set M? I) -6 II) -2 III) 2	Choose the correct choice from the following answers:
A) I only  B) II only  C) I and II only  D) II and III only  E) I, II and III

Solution: Since -4 is in the set, then the set must also include -3, -2, -1, 0, 1, 2, 3, 4, etc...   Depending on whether -4 is the starting element in the set or not, we can have -6...or not.   The answer is II and III only.
Answer: D
3 candidates in an election and received 2136, 7636 and 11628 votes respectively. What % of the total votes did the winningcandidate got in that election?	Choose one:	A) 45%	B) 49%	C) 54%	D) 59%	E) 61%

Solution: Total number of votes polled = (2136 + 7636 + 11628) = 21260   So, Required percentage = 11628/21260 * 100 = 54%   54%
Answer: C
A train 240 m long passed a pole in 24 sec. How long will it take to pass a platform 650 m long?  Choose the correct choice from the following choices:	A) 11	B) 89	C) 77	D) 66	E) 22

Solution: Speed = 240/24= 
240/24 = 10
10 m/sec.   Required time= (240 + 650)/10= 
(240 + 650)/10 = 89
89 sec.   Answer:89
Answer: B
In one year, the population, of a village increased by 12% and in the next year, it decreased by 12%. If at the end of 2nd year, the population was 14784, what was it in the beginning?	Pick one.
A) 7787  B) 8000  C) 15000  D) 1277  E) 2081

Solution: x*112/100 * 88/100 = 14784   X*0.9856=14784   X=14784/0.9856= 
14784/0.9856 = 15_000
> 15000   Answer:15000
Answer: C
How much time will a train of length 200 m moving at a speed of 72 kmph take to cross another train of length 300 m, moving at 36 kmph in the same direction?	Pick:	A) 50 sec	B) 26 sec	C) 80 sec	D) 82 sec	E) 81 sec

Solution: The distance to be covered = Sum of their lengths = 200 + 300= 
200 + 300 = 500
500 m.   Relative speed= 72 -36= 
72 -36 = 36
36 kmph= 36 * 5/18= 
36 * 5/18 = 10
10 mps.   Time required= d/s = 500/10= 
500/10 = 50
50 sec.   50 secnswer: 50 sec
Answer: A
In a certain match all the teams were to play with each other. If there are 15 teams, how many matches will have to be played? Pick:	A) 120	B) 105	C) 110	D) 90	E) None of the above

Solution: 15c2   =105   ANSWER:105
Answer: B
The area of a circle is increased by 1500%. By what percent has the diameter of the circle increased?	Choose the correct choice from the following answers
A) 100% B) 500% C) 300% D) 600% E) 800%

Solution: The area of the circle is increased by 1500%, thus the area is increased 16 times.   The area of a circle it proportional to the square of the diameter (area=πd^2/4), therefore the diameter must increase 4 times (diameter increase 4 times = area increase 16 times), which is increase by 500%.   Answer: 500%.
Answer: B
If a and b are positive even integers, and the least common multiple of a and b is expressed as a*b/w, which of the following statements could be false?  Choose the correct choice from the following options:
A) n is a factor of both a and b	B) (a*b)/n < ab	C) ab is multiple of 2.	D) (a*b)/n is a multiple of 2.	E) w is a multiple of 4.

Solution: If we divide bynand get a multiple ofaand ofb, then w must be a common factor. Answer A must be true.   Ifaandbare even integers, dividing by a factor (also an integer) results in something smaller than the productab. Answer B must be true.   If eitheraorbis even, then ab must be even. Answer C must be true.   If both are even, the smallest either number can be is 2. Thus, the smallest common factor must be 2. Answer D must be true.   Ifbis 6 andais 2,nwould be 6, which is not 4. w is a multiple of 4. can be false.
Answer: E
Solve the inequality
{(x^2)-7|x|+10}/{(x^2)-6x+9} Choose the correct choice:
A) -3  B) -5  C) 3  D) 5  E) 0

Solution: taking one time |x| as +ve we get x=5 while   taking |x| as -ve we get x= -5   ANSWER:-5
Answer: B
A's salary is 40% of B's salary which is 25% of C's salary. What percentage of C's salary is A's salary ?
Select:
A) 10
B) 93
C) 78
D) 76
E) 28

Solution: Explanation:   A's Salary = 40% of B = 40% of (25% of C) = % of C = 10% of C.   10nswer: 10) 10
Answer: A
There are 66 people in a certain community who belong to the local golf club, tennis club or both clubs. If twice as many people belong to the tennis club as belong to the golf club, what could be the number of people who belong to both clubs?	Pick one: A) 4 B) 31 C) 17 D) 21 E) 27

Solution: let's find the range of Both and hence the range of x.66 = x + 2xx = 22In this case Both = 0 Maximum value of Both: Say there is maximum overlap between the two sets. One set has x so it could be a subset of the set 2x.66 = 2xX=33 So Both lies between 0 and 33 Only option (B) satisfies this condition. ANSWER:31
Answer: B
In a class, there are 18 boys who are over 160 cm tall. If these constitute three-fourths of the boys and the total number of boys is two-thirds of the total number of students in the class, what is the number of girls in the class ?  Pick one:
A) 6	B) 12	C) 18	D) 24	E) 26

Solution: Explanation:   Let the number of boys be x. Then, (3/4)x = 18 or x = 18 x(4/3) = 24.   If total number of students is y, then (2/3) y = 24 or y = 24 x (3/2) = 36.   Therefore Number of girls in the class = (36 - 24)= 
(36 - 24) = 12
12.   Answer: 12
Answer: B
A train running at a speed of 36 kmph crosses an electric pole in 12 seconds. In how much time will it cross a 350 m long platform?  Answers
A) 18 min
B) 16 min
C) 19 min
D) 47 min
E) 12 min

Solution: Let the length of the train be x m.   When a train crosses an electric pole, the distance covered is its own length.   So, x = 12 * 36 * 5 /18= 
12 * 36 * 5 /18 = 120
120 m.   Time taken to cross the platform= (120 +350)/ 36 * 5/18 = 47 min.   Answer:47 min
Answer: D
Two brothers were expected to return here on the same day. Rajat returned 3 days earlier but Rohit returned 4 days later. If Rajat returned on Wednesday, what was the expected day when both the brothers were to return home and when did Rohit Return?  Choose the correct choice from the following answers:
A) Wednesday, Sunday  B) Thursday, Monday  C) Saturday, Wednesday  D) Monday, Friday  E) none

Solution: Rajat returned on Wednesday -i.e. 3 days earlier   so actual day to return home is Saturday.   Rohit returned after days so Wednesday.   ANSWER:Saturday, Wednesday
Answer: C
A is twice as good a work man as B and together they finish the work in 14 days. In how many days A alone can finish the work?
Options:	A) 12	B) 21	C) 77	D) 99	E) 22

Solution: WC = 2:1   2x + x = 1/14 => x = 1/42   2x = 1/21   A can do the work in 21 days.   Answer:21
Answer: B
Total value of the quantity sold for item C is what per cent of the total value of the quantity sold for Item E?	Choose the correct choice from the following choices:  A) 30  B) 60  C) 100  D) 80  E) 90

Solution: 90   90   Total value of the quantity sold for item C = Rs(45 × 7.5 × 100)   = Rs 33750   Total value of the quantity sold for item 90 = Rs(15 × 25 × 100) = Rs 37500   ∴ Required percentage = 33750/37500X 100 = 90
Answer: E
P can do a work in 12 days. Q can do the same work in 9 days and R can do the same in 12 days. Q and R start the work and leave after 3 days. P finishes the remaining work in --- days.	Choose the correct answer
A) 5 B) 8 C) 9 D) 10 E) 11

Solution: Work done by P in 1 day = 1/24   Work done by Q in 1 day = 1/9   Work done by R in 1 day = 1/12   Work done by Q and R in 1 day = 1/9 + 1/12 = 7/36   Work done by Q and R in 3 days = 3Ã—7/36 = 7/12   Remaining work = 1 â€“ 7/12 = 5/12   Number of days in which P can finish the remaining work = (5/12) / (1/12)= 
(5/12) / (1/12) = 5
5   Option 5
Answer: A
A man can row downstream at 28 kmph and upstream at 10 kmph. Find the speed of the man in still water and the speed of stream respectively?
Choices
A) 2, 9
B) 4, 9
C) 8, 9
D) 19, 9
E) 7, 9

Solution: Let the speed of the man in still water and speed of stream be x kmph and y kmph respectively.   Given x + y = 28 --- (1)   and x - y = 10 --- (2)   From (1) & (2) 2x = 38 => x = 19, y = 9.   Answer:19, 9
Answer: D
Find the area of trapezium whose parallel sides are 20 cm and 18 cm long, and the distance between them is 15 cm?  Answers:
A) 272 cm
B) 786 cm
C) 285 cm
D) 186 cm
E) 179 cm

Solution: Area of a trapezium   = 1/2 (sum of parallel sides) * (perpendicular distance between them)   = 1/2 (20 + 18) * (15)   = 285 cm   Answer: 285 cm
Answer: C
A man has Rs. 640 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 ?  Choose the correct choice from the following answers.
A) 33 B) 38 C) 37 D) 120 E) 28

Solution: Let number of notes of each denomination be x.   Then x + 5x + 10x = 640   ⇒ 16x = 640   ∴ x = 40.   Hence, total number of notes = 3x = 120   Answer:120
Answer: D
The owner of a furniture shop charges his customer 25% more than the cost price. If a customer paid Rs. 4800 for a computer table, then what was the cost price of the computer table?
Pick one: A) Rs. 3840 B) Rs. 5270 C) Rs. 6275 D) Rs. 6720 E) None of these

Solution: CP = SP * (100/(100 + profit%))   = 4800(100/125) = Rs. 3840.   Rs. 3840NSWER:Rs. 3840
Answer: A
M is the sum of the reciprocals of the consecutive integers from 501 to 600, inclusive. Which of the following is true?	Answers.
A) 1/3 < M < 1/2 B) 1/5 < M < 1/3 C) 1/7 < M < 1/5 D) 1/6 < M < 1/6 E) 1/12 < M < 1/9

Solution: M = 1/501 + 1/502 + 1/503 + ...... + 1/600   If we replace the first 99 terms by 1/600, then we get a sum = 100/600 = 1/6. Since the actual terms are larger than 1/600, the sum is larger than 1/6.   If we replace the all the 100 terms by 1/500, we get a sum = 100/500 = 1/5. Since the actual terms are smaller than 1/500, the sum is less than 1/5.   Therefore 1/6 < M < 1/5   Choice 1/6 < M < 1/6
Answer: D
A train 200 m long passed a pole in 20 sec. How long will it take to pass a platform 610 m long?  Choose the correct choice from the following answers:
A) 46
B) 54
C) 92
D) 76
E) 81

Solution: Speed = 200/20= 
200/20 = 10
10 m/sec.   Required time= (200 + 610)/10= 
(200 + 610)/10 = 81
81 sec.   Answer: 81
Answer: E
A bag contains 6 black and 6 white balls. One ball is drawn at random. What is the probability that the ball drawn is white?
Choose the correct choice from the following answers.
A) 3/4  B) 1/2  C) 1/7  D) 1/8  E) 4/3

Solution: Let number of balls = (6 + 6)= 
(6 + 6) = 12
12.   Number of white balls= 6.   P (drawing a white ball) =6/12=1/2.   Option 1/2.
Answer: B
Two trains are moving in the same direction at 162 kmph and 18 kmph. The faster train crosses a man in the slower train in 33 seconds. Find the length of the faster train?	Choose one:	A) 1300	B) 1310	C) 1320	D) 1330	E) 1340

Solution: Relative speed = (162 - 18) * 5/18 = 8 * 5= 
8 * 5 = 40
40 mps.   Distance covered in 33 sec= 33 * 40= 
33 * 40 = 1_320
1320 m.   The length of the faster train= 1320 m.   Answer:1320
Answer: C
A man standing at a point P is watching the top of a tower, which makes an angle of elevation of 30° with the man’s eye. The man walks some distance towards the tower to watch its top and the angle of the elevation becomes 60°. What is the distance between the base of the tower and the point P?
Choose the correct choice from the following options:
A) 4√3 units	B) 8 units	C) 12 units	D) Data inadequate	E) None

Solution: Solution   One of AB, AD and CD must have been given.So, the data is inadequate.   Answer Data inadequate
Answer: D
By mixing two brands of coffee and selling the mixture at the rate of $177 per kg. a shopkeeper makes a profit of 18%. If to every 2 kg of one brand costing $200 per kg, 3 kg of the other brand is added, then how much per kg does the other brand cost?
Choose the correct answer:
A) $110.66	B) $132.66	C) $116.66	D) $126.66	E) $118.66

Solution: C   $116.66   Let the cost of the brand be $X per kg.   C.P. of 5 kg = (2 * 200 + 3 * x) = $(400 + 3x)   S.P of 5 kg = $(5 * 177)= 
(5 * 177) = 885
$885   [885 - (400 + 3x)]/(400 + 3x) * 100= 18   24250 - 150x = 3600 + 27x   177x = 20650 => x = 116 2/3   So, cost of the other brand = $116.66.
Answer: C
6 men and 12 boys finish a job in 12 days, 12 men and 12 boys finish it in 10 days. 10 men and 10 boys shall finish it in how many days?  Options:
A) 12 days  B) 11 days  C) 14 days  D) 16 days  E) 18 days

Solution: 6M + 12B ----- 12 days   12M + 12B ------- 10 days   10M + 10B -------?   72M + 144B = 120M +120B   24B = 48M => 2M = B   3B + 12B = 15B ---- 12 days   5B + 10B 3  + 12= 
3  + 12 = 15
15B ---- 12 days   5B + 10B = 15B -----?   5  + 10= 
  5  + 10 = 15
15B -----?=> 12 days   12 daysNSWER:12 days
Answer: A
A 260 metres long train runs at a speed of 55 Kmph.How much time will it take to cross a Platform 290 meters long?	Choose the correct choice from the following answers
A) 36 seconds
B) 18 seconds
C) 60 seconds
D) 20 seconds
E) None of these

Solution: total distance =260m+290m=550m   speed260 +290= 
260 +290 = 550
550m   speed=55*5/18=275/18   therefore time taken=(550/275)*18= 
(550/275)*18 = 36
36 sec   36 secondsNSWER:36 seconds
Answer: A
For every positive integer n, the nth term of a sequence is the total sum of three consecutive integers starting at n. What is the total sum of terms 1 through 70 of this series?  Answers
A) 6845 B) 7225 C) 7665 D) 8025 E) 8485

Solution: Each term of the series has the form (n+n+1+n+2) = 3n+3   Since the series goes from 1 to 70, the sum of the series is:   3(1+2+...+70) + 70(3) ( + +1+ +2)= 
( + +1+ +2) = 3
3n+3   Since the series goes from 1 to 70, the sum of the series is:   3(1+2+...+70) + 70(3)=   3(70)(71)/2 + 70(3) =   105*71 + 210= 
105*71 + 210 = 7_665
7665   The answer is 7665.
Answer: C
A rectangular circuit board is designed to have width w inches, perimeter p inches, and area r square inches. Which of the following equations must be true?  Pick one
A) w^2 + pw + r = 0	B) w^2 - pw + 2r = 0	C) 2w^2 + pw + 2r = 0	D) 2w^2 - pw - 2r = 0	E) 2w^2 - pw + 2r = 0

Solution: Notice that we can discard options A, and C right away. The sum of 3 positive values Cannot be 0.   Now, assume:   Width =w = 1 inchand length = 1 inch;   Perimeter =p = 4 inches;   Area =r = 1 square inches.   Plug the values of w, p, and r into the answer choices: only for E 2w^2 - pw  + 2= 
 + 2 = 2
2 - 4 + 2= 
2 - 4 + 2 = 0
0.   Answer: 2w^2 - pw + 2r= 0.
Answer: E
The length of a rectangular floor is more thanits breadth by 200%. If Rs.324 is requiredto paint the floor at the rate of Rs.3/sq m, what would be the length of the floor?	Choose the correct answer:
A) 12
B) 18
C) 19
D) 20
E) 21

Solution: Let the length and the breadth of the floor be l m and b m respectively.   l = b + 200% of b = l + 2b = 3b   Area of the floor = 324/3= 
324/3 = 108
108 sq m   l b= 108 i.e., l * l/3 = 108   l2 = 324 => l = 18.   18
Answer: B
A man invested Rs. 14,400 in Rs. 100 shares of a company at 20% premium. If his company declares 5% dividend at the end of the year, then how much does he get? Choose the most appropriate option:
A) 234
B) 600
C) 388
D) 278
E) 129

Solution: Explanation:   Number of shares = =120.   Face value = Rs.(100 x 120) = Rs.12000.   Annual income = = Rs. 600   Answer: 600) Rs.600
Answer: B
The greatest common factor of 16 and the positive integer n is 4, and the greatest common factor of n and 45 is 3. Which of the following could be the greatest common factor of n and 90?
Pick one: A) 3 B) 14 C) 30 D) 42 E) 70

Solution: Greatest common factor n and 16 is 4 = 2*2 * 2*2   Greatest common factor n and 45 is 3 = 3*3 *5   Greatest common factor n and 90 is = 2*3*5= 
2*3*5 = 30
30   30
Answer: C
Count the numbers between 10 - 99 which yield a remainder of 3 when divided by 9 and also yield a remainder of 2 when divided by 5?	Choose the correct choice from the following choices:
A) Two
B) Five
C) Six
D) Four
E) One

Solution: Twonswer = Two) Two   Numbers between 10 - 99 giving remainder 3 when divided by 9 = 12, 21, 30, 39, 48, 57, 66, 75, 84, 93   The Numbers giving remainder 2 when divided by 5 = 12, 57 = 2
Answer: A
Steve gets on the elevator at the 11th floor of a building and rides up at a rate of 87 floors per minute. At the same time Joyce gets on an elevator on the 71st floor of the same building and rides down at a rate of 93 floors per minute. If they continue traveling at these rates, at which floor will their paths cross?	Choose the correct choice from the following answers:
A) 19  B) 28  C) 40  D) 32  E) 44

Solution: Steve gets on the elevator at the 11th floor of a building and rides up at a rate of 87 floors per minute. At the same time Joyce gets on an elevator on the 71st floor of the same building and rides down at a rate of 93 floors per minute. If they continue traveling at these rates, at which floor will their paths cross?   60 floors/180 floors per minute=1/3 minutes     11+87/3= 
  11+87/3 = 40
40   71-93/3= 
71-93/3 = 40
40   Answer : 40
Answer: C
Suppose the operation * is dened on the set of integers by a*b = a+2b.
Then for every two integers a and b, the value of a*(b*a) is the same
as	Pick
A) a*b	B) b*a	C) (3a)*b	D) b*(4a)	E) (5a)*b

Solution: One checks which of the choices is the same as a(ba) = a(b+2a) = a+2(b+2a) =   a +2b +4a = 5a + 2b. Since (5a) b = 5a + 2b, the answer is (e).   correct answer (5a)*b
Answer: E
What will come in place of the x in the following Number series? 11, 14, 19, 22, 27, 30, 35, 38, 43 , 46 x Answers
A) 23	B) 51	C) 36	D) 35	E) 45

Solution: (51)   The pattern is + 3, + 5, + 3, + 5, …………   So the missing term is = 46 + 5= 
46 + 5 = 51
51.
Answer: B
Heena covers a distance in 40 min , if she drives at a speed of 60 km/h on an average. Find the speed at which she must drive at to reduce the time of the journey by 60%. Choose the correct choice
A) 60 km/h	B) 140.48km/h	C) 100 km/h	D) 148.14 km/h	E) 85 km/h

Solution: Given Speed = 60 Kmph.   It means Heena covered 60 km in 60 min (1 hour). So, in 40 min he will cover 40 km.   60% time reduced = 40 - 60% of 40 = 16min.   Thus, Heena needs to cover 40 km in 16 min (0.27 hour).   Speed * Time = Distance.   Speed * 0.27 = 40   Speed = 148.14 kmph.   ANSWER : OPTION 148.14 km/h
Answer: D
If a and b are consecutive integers (b>a), which of the following statements could be false? 1. a^4+b is always even number. 2. a^2*b is always even number 3. (a + b) is always an odd number. Pick
A) III only B) II only C) I,II only D) I,III only E) I only

Solution: 2^4+3 =16+3= 
16+3 = 19
19 Option I false   2^2 * 3= 4+3= 
4+3 = 7
7 (odd number). Option II is false   odd + even= odd. Option III is true   Answer : I,II only
Answer: C
a,b,c,d, sitting in a row what is the probability that a & b sitting adjacent. Pick one
A) 9/2	B) 1/2	C) 3/2	D) 5/2	E) 7/2

Solution: total number of arrangement is= 4!= 24   Favorable event i.e a and b can be arranged in 2! and the remaining can be arranged in 3! since ab can be in any of the four positions.   so2!*3!/4! = 1/2   ANSWER:1/2
Answer: B
A classroom has equal number of boys and girls. SEVEN girls left to play kho-kho, leaving twice as many boys as girls in the classroom. What was the total number of girls and boys present initially?	Choose one
A) 16 B) 24 C) 32 D) 28 E) 54

Solution: after 7 girls left remaining 7 girls   now boys 14 are twice as many as remaining girls.   initially boys=14 and girls=14.   ANSWER:28
Answer: D
A cistern is fille in 8 hours and it takes 12 hours when there is a leak in its bottom. If the cistern is full, in what time shall the leak empty it?
Choose the correct choice from the following options:	A) 22 hours	B) 21 hours	C) 24 hours	D) 23 hours	E) 25 days

Solution: Explanation:   work done by 1 hour by filling pipe = 1/8   work done by 1 hour by the leak and the filling pipe =1/12   work done by 1 hour by the leak = 1/8 – 1/12 =1/24   Hence the leak can empty it in 24 hours.   Answer: Option 24 hours
Answer: C
A cube is divided into 343 identical cubelets. Each cut is made parallel to some surface of the cube. But before doing that, the cube is painted with green on one set of opposite faces, red on another set of opposite faces, and blue on the third set of opposite faces. How many cubelets are painted with exactly one colour? Options:  A) 125  B) 150  C) 175  D) 200  E) 225

Solution: Each side of the cube has 7 x 7 = 49 cubelets.   Only the interior cubelets are painted one colour.   On each side, 5 x 5 = 25 cubelets are painted one colour.   Since the cube has six sides, the number of cubes with one colour is  6*25= 
 6*25 = 150
150   The answer is 150.
Answer: B
The average (arithmetic mean) of the integers from 25 to 225, inclusive, is how much lower than the average of the integers from 50 to 1050 inclusive? Choose the most appropriate option.
A) 450 B) 375 C) 500 D) 425 E) 400

Solution: For an AP the mean or average of series is average of first and last term.   So, average of numbers between 50 to 1050, inclusive = (50+1050)/2= 
(50+1050)/2 = 550
550   average of numbers between 25 to 225, inclusive= (25+225)/2= 
(25+225)/2 = 125
125   difference= 550 - 125= 
550 - 125 = 425
425   Answer is 425
Answer: D
If 10! × 10!/10^n is an integer, what is the largest possible value of n?
Select the correct option
A) 20 B) 16 C) 8 D) 4 E) 1

Solution: 10! × 10!/10^n is an integer.   Or 10! × 10!/(1^2n*5^n)   This means we need to find the power of 5 in the numerator. We can safely say that the number of powers of 5 will be lower than the number of powers of 4 in the numerator.   Largest power of 5 in 10! = [10/5] + [10/25] = 2   Since there are 2 20!'s, power of 2 in the numerator = 2*2= 
2*2 = 4
4   Hence the largest value of b for which 10! × 10!/10^n is integer= 4   Correct Option : 4
Answer: D
What least number mustbe subtracted from 427398 so that remaining no.is divisible by 15
Pick one:
A) 3
B) 5
C) 6
D) 8
E) 9

Solution: Explanation:   On dividing 427398 by 15 we get the remainder 3, so 3 should be subtracted   Option 3
Answer: A
The perimeter of a semi circle is 144 cm then the radius is?  Choices
A) 17  B) 28  C) 19  D) 11  E) 12

Solution: 36/7 r = 144 => r   = 28   Answer: 28
Answer: B
A glucose molecule contains 6 carbon, 12 hydrogen and 6 oxygen atoms. During photosynthesis, green plants create glucose daily. If, over a period of 12 days, an eucalyptus plant (a green plant) creates 12,000 molecules of glucose then approximately how many more atoms of hydrogen than carbon are created on average per day?
Pick
A) 60,000  B) 6,000  C) 2,500  D) 250  E) 0

Solution: Solution:   We know that 12,000 glucose molecules are created over a period of 12 days. Therefore 12,000/12 = 1,000 glucose molecules are created on average per day.   Each glucose molecule contains 6 carbon atoms and 12 hydrogen atoms. So 1,000 glucose molecules contain 6 × 1,000 = 6,000 carbon atoms and 12 × 1,000 = 12,000 hydrogen atoms. The difference is 12,000 – 6,000 = 6,000.   The correct answer is 6,000.
Answer: B
If (x^2 + 1)y=7, which of the following is not a possible value for y?
Choose the correct choice from the following answers:
A) 2  B) 2/3  C) 4/3  D) 4  E) 15/2

Solution: Its simple   equation is (x^2 +1)y = 7 ===> x^2 = (7/y) - 1 . As , in LHS, it is x^2 the value has to be positive or zero in RHS.   Hence, (7/y) - 1>= 0 ===> y =< 7. Now only option E has greater value of 'y' than 7.   Thus, correct ans is 15/2
Answer: E
Consider the sets Tn = {n, n + 1, n + 2, n + 3, n + 4}, where n = 1, 2, 3,...., 84. How many of these sets contain 6 or any integral multiple thereof (i.e., any one of the numbers 6, 12, 18, ...)? Choose the correct choice from the following choices.
A) (a) 80 B) (b) 81 C) (c) 82 D) (d) 83 E) (e) 70

Solution: T1: 1,2,3,4,5   T2: 2,3,4,5,6   T3: 3,4,5,6,7   etc.   means that every multiple of 6 will be involved in 5 sets. We have (84-6)/6+1= 
(84-6)/6+1 = 14
14 such multiples.   So, final number of sets is  14*5= 
 14*5 = 70
70   Answer: (e) 70
Answer: E