MU-NLPC/Calc-aqua_rat huggingface dataset:
Which of the following equations has real roots ?  Choose the correct choice.
A) 3x2 + 4x + 5 = 0  B) x2 + x + 4 = 0  C) (x - 1)(2x - 5) = 0  D) 2x2 - 3x + 4 = 0  E) None of these

Solution: Sol.(c) Roots of a quadratic equation   ax2 + bx + c = 0 are real if b2 - 4ac ≥ 0   Let us work with options as follows.   Option (a) : 3x2 + 4x + 5 = 0   b2 - 4ac = 42 - 4(3)(5) = -44 < 0.   Thus, roots are not real.   (b) : x2 + x + 4 = 0   b2 - 4ac = 12 - 4(1)(4) = 1 - 16 = -15 < 0. Thus, roots are not real. (c) :(x –1) (2x – 5) = 0 => 22 - 7x + 5 = 0   b2 - 4ac = (-7)2 - 4(2)(5) = 49 - 40= 
49 - 40 = 9
9 > 0.   Thus roots are real.   or x= 1 and x = 5/2 > 0; Thus, equation has real roots.   (d) : 2x2 - 3x + 4 = 0   b2 - 4ac = (-3)2 - 4(2)(4) = 9 - 32 = -23 < 0.   Thus, roots are not real. Hence, option (c) is correct.   Answer (x - 1)(2x - 5) = 0
Answer: C
The length of a rectangular plot is thrice its breadth. If the area of the rectangular plot is 867 sq m, then what is the breadth of the rectangular plot?  Choices:
A) 12	B) 17	C) 10	D) 12	E) 19

Solution: Let the breadth of the plot be b m.   Length of the plot = 3 b m   (3b)(b) = 867   3b2 = 867   b2 = 289 = 172 (b > 0)   b = 17 m.   Answer:17
Answer: B
If the numerator of a fraction R is tripled, and the denominator of a fraction is doubled, the resulting fraction will reflect an increase of what percent?
Choose the correct choice from the following answers: A) 16 1⁄6% B) 25% C) 33 1⁄3% D) 50% E) 66 2⁄3%

Solution: This question can be dealt with conceptually or by TESTing VALUES.   We're told that the numerator of a fraction R is tripled and the denominator of that same fraction is doubled. We're asked for the resulting increase, in percentage terms, of that fraction.   Let's TEST 2/1   If we triple the numerator and double the denominator, we end up with....   (2x3)/(1x2) = 6/2= 
6/2 = 3
3   Since we're increasing 2 to 3, we're increasing that fraction by (3-2)/2= 1/2 of itself = 50%   50%
Answer: D
Mangala completes a piece of work in 30 days, Raju completes the same work in 40 days. If both of them work together, then the number of days required to complete the work is  Choose the correct choice
A) 4 days	B) 6 days	C) 8 days	D) 17.14 days	E) 11 days

Solution: If A can complete a work in x days and B can complete the same work in y days, then, both   of them together can complete the work in x y/ x+ y days.   That is, the required No. of days = 30 × 40/70 = 17.14 days.   Answer : 17.14 days
Answer: D
There are 2 printers installed to print some pages. If you have to find out how many pages will the printers print at 35°C when one printer’s work is directly proportional and the others printer work is inversely proportional to the temperature and the total work done at 15°C is 20 pages and that done on 20°C is 25 pages?
Answers:
A) 40 pages  B) 41.2 pages  C) 40.7 pages  D) 43.2 pages  E) 39.7 pages

Solution: If 1st Printer works directly proportional to the temperature with constant K1 and   2nd printer works inversely proportional to the temperature with constant K2, then   Pages printed at particular temperature= T1*K1 + K2/T2 ----(i)   15K1+ (K2/15) = 20 ----(ii) &   20K1+ (K2/20) = 25 ----(iii)   On solving (ii) & (iii), K1=8/7 ,K2=300/7   From (i), Total pages printed at 35°C = (35*8/7) + [300/(7*35)] =40 + (60/49)= 41.22   ANSWER:41.2 pages
Answer: B
In what time a sum of money double itself at 3% per annum simple interest?	Choose the correct choice from the following choices.
A) 33 1/8%	B) 33 1/3%	C) 33 7/3%	D) 32 1/3%	E) 23 1/3%

Solution: P = (P*3*R)/100   R = 33 1/3%   Answer: 33 1/3%
Answer: B
In a contest, a bowl contains 16 keys, only one of which will open a treasure chest. If a contestant selects the key that opens the treasure chest, she wins the contents of that chest. If Anna is allowed to draw two keys, simultaneously and at random, from the bowl as the first contestant, what is the probability that she wins the prize?	Choices: A) 15/256 B) 3/32 C) 1/16 D) 1/8 E) 1/32

Solution: P(not winning) = 15/16*14/15 = 7/8   P(winning) = 1 - 7/8 = 1/8   The answer is 1/8.
Answer: D
The sum of two numbers is 35. Their difference is 5. The bigger number is
Pick one:
A) 20  B) 25  C) 30  D) 35  E) 45

Solution: X + Y = 35   X - Y = 5   20dding 2X = 40 ==> X = 20 and Y = 35 - 20= 
35 - 20 = 15
15   Bigger number is X= 20   20nswer 20.
Answer: A
Population of a city in 20004 was 1000000. If in 2005 there isan increment of 15% , in 2006 there is a decrements of 35 % and in 2007 there is an increment of 45%, then find the population of city atthe end of the year 2007 Choices.
A) 976374
B) 979923
C) 980241
D) 2356677
E) 1083875

Solution: Required population = P (1 + R1/100)(1 - R2/100)(1 + R3/100)   = P (1 + 15/100)(1 - 35/100)(1 + 45/100)   = 1083875   1083875
Answer: E
x = 13.165
y = 7.586
z = 11.545
The number A is obtained by first rounding the values of x, y, and z to the hundredths place and then adding the resulting values. The number B is obtained by first adding the values of x, y, and z and then rounding the sum to the hundredths place. What is the value of A – B? Pick:  A) 0.01  B) 0.02  C) 0.03  D) 0.1  E) 0.2

Solution: Rounding off the values:   x = 13.17   y = 7.59   z = 11.55   A = 13.17 + 7.59 + 11.55= 
13.17 + 7.59 + 11.55 = 32.31
32.31   x + y + z= 13.165 + 7.586 + 11.545 = 32.206   B = 32.21   A - B = 0.1   Option 0.1
Answer: D
The length of a rectangular garden is three times its width. If the area of the rectangular garden is 675 square meters, then what is the width of the rectangular garden?
Choose the correct choice from the following choices:
A) 14	B) 15	C) 16	D) 17	E) 18

Solution: Let x be the width of the garden.   3x^2 = 675   x^2 = 225   x = 15   The answer is 15.
Answer: B
Chris age after 15years will be 5 times his age 5years back. what is the present age of Chris?	Choose the correct answer
A) 20
B) 25
C) 15
D) 22
E) 10

Solution: Chris present age= x   after 15years = x+15   5years back = x-5   x+15= 5(x-5)   x=10   Answer is 10
Answer: E
A and B can do a piece of work in 6 days. With the help of C they finish the work in 4 days. C alone can do that piece of work in?
Choose the most appropriate option:	A) 10 DAYS	B) 20 DAYS	C) 25 DAYS	D) 15 DAYS	E) 45 DAYS

Solution: C = 1/5 – 1/6 = 1/30 => 30 days   Answer:20 DAYS
Answer: B
It is required to fix a pipe such that water flowing through it at a speed of 7 metres per minute fills a tank of capacity 880 cubic metres in 10 minutes. The inner radius of the pipe should be :  Answers
A) √2 m
B) 2 m
C) 1⁄2 m
D) 1⁄√2 m
E) None of these

Solution: Let inner radius of the pipe be r.   Then, 880 = 22⁄7 × r2 × 7 × 10   or r2=880/22×10=4   or r = √4=2 m   Answer 2 m
Answer: B
If x and y are positive integers, and x^3*y^4 = 2,000, which of the following is the value of xy? Choose the correct choice:
A) 2	B) 4	C) 8	D) 10	E) 20

Solution: x^3y^4 = (xy)^3 * y = 2000   a. if xy = 2 => 2^3 = 8, can't find y   b. xy = 4 (same as above)   c. xy = 8, 8^3 = 512; 2000/512 is not integer   d. xy = 10, 10^3 = 1000, y = 2000/1000= 
2000/1000 = 2
2   e. xy= 20, 20^3 = 8000 > 2000   so the answer is 10
Answer: D
If the ratio of a to b is 8 to 3 and the ratio of b to c is 1 to 5, what is the ratio of a to c?
Choose one
A) 8/15
B) 1/3
C) 2/5
D) 4/5
E) 7/6

Solution: a:b =8:3 -- 1   b:c = 1:5   =>b:c = 3 :15 --2   From 1 and 2 , we get   a:c = 8:15   8/15nswer 8/15
Answer: A
150 men consume 1050 kg of rice in 30 days. In how many days will 70 men consume 980 kg of rice?  Choose the correct choice from the following choices:
A) 77 days
B) 60 days
C) 16 days
D) 97 days
E) 17 days

Solution: Rate of consumption of each man = 1050/(150 * 30) = 7/30 kg/day   Let us say 70 men take x days to consume 150 kg.   Quantity consumed by each item in x days = (7x/30) kg   Quantity consumed by 70 men in x days = (7/30 x)(70) kg   = (7/30 x) * (70) = 960   x = 60 days.   Answer: 60 days
Answer: B
From 7 positive numbers and 7 negative numbers, how many groups of 4 numbers, yielding a positive product, can be formed? Answers: A) 720 B) 625 C) 327 D) 960 E) 511

Solution: The number of ways to choose 4 positive numbers is 7C4 = 35.   The number of ways to choose 4 negative numbers is 7C4 = 35.   The number of ways to choose 2 positive and 2 negative is 7C2*7C2 = 21*21= 
21*21 = 441
441.   The total number of groups is 35+35+441= 
35+35+441 = 511
511.   The answer is 511.
Answer: E
If (10^4 * 3.456789)^12 is written as a single term, how many digits would be to the right of the decimal place?	Choose the correct choice from the following answers.
A) 16 B) 20 C) 24 D) 28 E) 32

Solution: 3.456789^12 has   6*12= 
  6*12 = 72
72 decimal places.   10^48 moves the decimal place to the right 48 places.   (10^4 * 3.456789)^12 has   72-48= 
  72-48 = 24
24 digits after the decimal point.   The answer is 24.
Answer: C
The cost of diamond varies directly as the square of its weight. Once, this diamond broke into four pieces with weights in the ratio 1 : 2 : 3 : 4. When the pieces were sold, the merchant got Rs. 70,000 less.
Find the original price of the diamond.  Select:
A) Rs. 1.4 lakh	B) Rs. 2 lakh	C) Rs. 1.4 lakh	D) Rs. 1 lakh	E) None of these

Solution: Explanation :   If we assume weight of diamond 10x. Well I came up with 10x because the ratio   Given 1 : 2 : 3 : 4 adds upto 10.   So, individual weights of diamonds will be x, 2x, 3x and 4x   Original price = k(10x)2   Price for pieces = k(x2 + 4x2 + 9x2 + 16x2) = k30x2   Thus change in price we see is 100kx2 - 30kx2 = 70kx2 which is given as 70,000.   Thus the original price 100kx2 will be 1,00,000.   Answer : Rs. 1 lakh
Answer: D
The Shopkeeper increased the price of a product by 25% so that customer finds it difficult to purchase the required amount. But somehow the customer managed to purchase only 70% of the required amount. What is the net difference in the expenditure on that product? Choose the correct choice from the following answers:
A) 10% B) 11% C) 12.5% D) 13% E) 13.5%

Solution: Quantity X Rate = Price   1 x 1 = 1   0.7 x 1.25 = 0.875   Decrease in price = (0.125/1) × 100 = 12.5%   12.5%
Answer: C
In a railway compartment, there are 2 rows of seats facing each other with accommodation for 5 in each, 4 wish to sit facing forward and 3 facing towards the rear while 3 others are indifferent. In how many ways can the 10 passengers be seated?
.	Choose the correct answer: A) 172000 B) 12600 C) 45920 D) 43200 E) 54200

Solution: Start with the 4 people who want to face forward - for the first one, there are 5 options, for next one, 4 options and so on till we get 5*4*3*2.   Next, go on to 3 people who want to face back - for the first one, there are 5 options, for the next one, 4 options and so on till we get 5*4*3.   Now, we have 3 seats leftover and 3 indifferent people who can be arranged in 3*2*1 ways.   All in all, we can arrange 10 people in 5*4*3*2*5*4*3*3*2*1 = 14400 * 3= 
14400 * 3 = 43_200
43200   Answer (43200)
Answer: D
If the arithmetic mean of x,y and z is 6 times the arithmetic mean of w, x and y. What is the value of the expression (x+y)?
Choose the most appropriate option.
A) (z-5w)/6	B) (z+6w)/5	C) (-z-5w)/6	D) (z-6w)/5	E) (z-6w)/6

Solution: Arithmetic Mean 1 = (x+y+z)/3   Arithmetic Mean 2 = (w+x+y)/3   Arithmetic Mean 1=6*Arithmetic Mean 2   (x+y+z)/3=6*(w+x+y)/3   x+y+z=6w+6x+6y   x+y=(z-6w)/5   Hence, the correct answer is (z-6w)/5
Answer: D
How many seconds will a 800 metre long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr?	Choose the most appropriate option
A) 25  B) 30  C) 40  D) 48  E) 50

Solution: Relative speed of the train=63-3= 
63-3 = 60
60kmph=60*5/18=50/3 m/sec   t=800*3/50= 
800*3/50 = 48
48sec   ANSWER:48
Answer: D
A clock is observed by someone.
The hour hand is exactly at a minute mark, and the minute hand is six minutes ahead of it in the first glance.
When the clock is looked at again, the hour hand is exactly on a different minute mark, and the minute hand is seven minutes ahead of it this time.
Can you find out the time that has elapsed between the first and the second observation?	Select the correct option: A) 2 hours and 12 minutes B) 3 hours and 12 minutes C) 4 hours and 12 minutes D) 5 hours and 12 minutes E) 6 hours and 12 minutes

Solution: Solution:   In the first observation, the time was 1:12. In the second observation, the time was 3:24.   Therefore, 2 hours and 12 minutes have elapsed   2 hours and 12 minutesnswer 2 hours and 12 minutes
Answer: A
Walking 3/2 of his usual rate, a boy reaches his school 4 min early. Find his usual time to reach the school? Select
A) 12 B) 99 C) 27 D) 28 E) 20

Solution: Speed Ratio = 1:3/2 = 2:3   Time Ratio = 3:2   1 -------- 3   4 --------- ? 12 m.12nswer:12
Answer: A
In a class there are 20 boys and 25 girls. In how many ways can a boy and a girl be selected?
Choices.
A) 657 ways
B) 500 ways
C) 576 ways
D) 545 ways
E) 552 ways

Solution: We can select one boy from 20 boys in 20 ways.   We select one girl from 25 girls in 25 ways   We select a boy and girl in 20 * 25 ways i.e., = 500 ways.   Answer: 500 ways
Answer: B
A team of 8 persons joins in a shooting competition. The best marksman scored 85 points. If he had scored 92 points, the average score for the team would have been 84. The number of points, the team scored was  Select the correct option:
A) 665
B) 127
C) 272
D) 287
E) 227

Solution: Let the total score be x.   (x + 92 - 85) / 8 = 84.   So, x + 7 = 672 => x = 665.   665nswer: 665
Answer: A
There is enough provisions for 600 men in an army camp for 35 days. If there were 300 men less, how long will the provision last?	Choose the correct choice from the following options
A) 40days  B) 50days  C) 60days  D) 70days  E) 80days

Solution: Exp: We have, M1D1 = M2D2   600*35= 300* D2   D2 = 600*35/300= 
600*35/300 = 70
70 days.   Answer: 70days
Answer: D
In a 4 person race, medals are awarded to the fastest 3 runners. The first-place runner receives a gold medal, the second-place runner receives a silver medal, and the third-place runner receives a bronze medal. In the event of a tie, the tied runners receive the same color medal. (For example, if there is a two-way tie for first-place, the top two runners receive gold medals, the next-fastest runner receives a silver medal, and no bronze medal is awarded). Assuming that exactly three medals are awarded, and that the three medal winners stand together with their medals to form a victory circle, how many different victory circles are possible? Pick.
A) 24	B) 52	C) 96	D) 144	E) 648

Solution: Gold can be awarded in 4 ways, then silver can be awarded in 3 ways and Bronze in 2 ways.   therefore the total number of ways are :   4*3*2= 
  4*3*2 = 24
24ways of awarding the medals and the same number of ways of forming the circle.   This is when there is no tie. And if there is tie, for example all three receive the GOLD or the Silver or the Bronze, then there are 4 more cases. which implies 24*4= 
24*4 = 96
96. ANS:96
Answer: C
An amount of Rs.20,000 is to be distributed amongst P, Q, R and S such that “P” gets twice as that of “Q” and “S” gets four times as that of “R”. If “Q” and “R” are to receive equal amount, what is the difference between the amounts received by S and P?
Choose the correct choice from the following choices.
A) 2378
B) 2697
C) 2697
D) 5000
E) 6971

Solution: Explanation:   We have, P = 2Q & S = 4R   Further Q = R & P + Q + R + S = 20,000   Thus we get, 2Q + Q + Q + 4Q = 20,000   8Q = 20,000 or Q = Rs. 2500   Thus, R = Rs. 2500, P = 5000 & S = Rs. 10000   Hence, the required difference = (S – P) = (10000 – 5000) = Rs. 5000   ANSWER:5000
Answer: D
By selling 45 lemons for Rs 40, a man loses 20 %. How many should he sell for Rs 24 to gain 20 % in the transaction ? Choose the correct option: A) 16 B) 18 C) 20% D) 22 E) 24

Solution: Explanation:   Let S.P. of 45 lemons be Rs. x.   Then, 80 : 40 = 120 : x or x = 40x120/80 = 60   For Rs.60, lemons sold = 45   For Rs.24, lemons sold =45/60x24= 18. Answer: 18
Answer: B
If Doug can mow the lawn in 3 hours, and Julie can mow the same lawn in 6 hours, how long will it take for both of them to mow the lawn together?
Choose the correct choice from the following answers:
A) 1 hr
B) 2 hr
C) 3 hr
D) 4 hr
E) 5 hr

Solution: If Doug can mow the lawn in 3 hours, then in 1 hour he can mow 1/3 of the lawn.   If Julie can mow the lawn in 6 hours, then in 1 hour she can mow 1/6 of the lawn.   Let x = number of hours it would take them together to mow the lawn so,   1/3 + 1/6 = 1/x   x=2 hours   Answer: 2 hr
Answer: B
60% of a number is added to 120, the result is the same number. Find the number?
Choose one:
A) 150	B) 200	C) 300	D) 150	E) 478

Solution: Explanation:   (60/100) * X + 120 = X   2X = 600   X = 300   300
Answer: C
A train 220 meters long is running with a speed of 60 kmph. In what time will it pass a man who is running at 6 kmph in the direction opposite to that in which the train is going? Choose the correct choice from the following answers:
A) 12
B) 6
C) 7
D) 8
E) 9

Solution: Speed of train relative to man = (60 + 6) km/hr = 66 km/hr   [66 * 5/18] m/sec = [55/3] m/sec.   Time taken to pass the man = [220 * 3/55= 
220 * 3/55 = 12
12 sec   12nswer: 12
Answer: A
The diameter of a cylindrical tin is 10 cm and height is 5 cm. Find the volume of the cylinder?	Choose the correct choice from the following options.
A) 125  B) 155  C) 130  D) 120  E) 100

Solution: r = 5 h = 5   π * 5 * 5 * 5 = 125 π cc   125nswer:125
Answer: A
A person walks from one end to the other of a 100-meter long moving walkway at a constant rate in 25 seconds, assisted by the walkway. When this person reaches the end, they reverse direction and continue walking with the same speed, but this time it takes 150 seconds because the person is traveling against the direction of the moving walkway. If the walkway were to stop moving, how many seconds would it take this person to walk from one end of the walkway to the other?	Choose the correct choice:
A) 37  B) 39  C) 41  D) 43  E) 45

Solution: Let v be the speed of the person and let x be the speed of the walkway.   25(v+x)=100 then 150(v+x)=600   150(v-x)=100   When we add the two equations:   300v=700   v=7/3   time = 100 / (7/3) = (300 / 7) seconds which is about 43 seconds   The answer is 43.
Answer: D
log base 10 root of 10 root of 10 root of 10..........infinity?	Select the correct option
A) 0	B) 1	C) 2	D) 3	E) 4

Solution: root 10 of 10 of 10 ............infinity=10   so log base 10 of 10=1   ANSWER:1
Answer: B
A 160 meter long train crosses a man standing on the platform in 6 sec. What is the speed of the train?	Choose the correct option
A) 96 kmph
B) 94 kmph
C) 92 kmph
D) 86 kmph
E) 76 kmph

Solution: S = 160/6 * 18/5= 
160/6 * 18/5 = 96
96 kmph   96 kmphNSWER:96 kmph
Answer: A
If f(x)=x^3 and x is a natural number what CANNOT be a solution to f(x)? Pick:
A) 1	B) 8	C) 27	D) 36	E) 64

Solution: 36 is not a perfect cube. The answer is 36.
Answer: D
A person lent a certain sum of money at 4% per annum at simple interest and in 8 years the interest amounted to Rs.170 less than the sum lent. What was the sum lent?  Choose the correct choice:  A) 228  B) 278  C) 250  D) 500  E) 821

Solution: P - 170 = (P*4*8)/100   P = 250   Answer: 250
Answer: C
The number of new words that can be formed by rearranging the letters of the word 'ALIVE' is ?
Pick:
A) 287  B) 266  C) 119  D) 166  E) 266

Solution: Number of words which can be formed = 5! - 1   = 120 - 1= 
120 - 1 = 119
119.   Answer:119
Answer: C
Angelina walked 720 meters from her home to the grocery at a constant speed. She then walked 480 meters to the gym at double the speed. She spent 40 seconds less on her way from the grocery to the gym than on her way from home to the grocery. What was Angelina's speed, in meters per second, from the grocery to the gym? Pick one:
A) 2
B) 3
C) 4
D) 6
E) 24

Solution: let the speed be X...   so time taken from home to grocery= 720/x..   the speed to gym = 2x..   so time taken = 480/2= 
480/2 = 240
240/x..   its given 720/x-240/x=40..   480/x=40..   x=12m/secs..   so grocery to gym=2*12= 
2*12 = 24
24m/s...   24
Answer: E
A merchant marks his goods up by 50% and then offers a discount of 20% on the marked price. What % profit does the merchant make after the discount?
Select the correct option:  A) 20%  B) 25%  C) 69%  D) 31%  E) 19%

Solution: Let the price be 100.   The price becomes 150 after a 50% markup.   Now a discount of 20% on 150.   Profit=120-100   20%   answer 20%
Answer: A
A rectangular field is 25 yards long and 12 yards wide. A fence is needed for the perimeter of the
field. Fencing is also needed to divide the field into three square sections. How many feet of fencing
are needed? (It is a good idea to make a drawing for this one.)  Pick
A) 320 ft	B) 273 ft	C) 294 ft	D) 330 ft	E) 230 ft

Solution: 25 + 12 + 25 +12= 
25 + 12 + 25 +12 = 74
74 yds. for   outside of field.   12 + 12= 
12 + 12 = 24
24 yds. for dividing sections    74 + 24= 
 74 + 24 = 98
98 yds. of fencing   98 x 3= 294 ft. of fencing   correct answer 294 ft
Answer: C
How many 4-letter words with or without meaning, can be formed out of the letters of the word, 'LOGARITHMS', if repetition of letters is not allowed?	Choose the most appropriate option.
A) 40	B) 400	C) 5040	D) 5400	E) 5800

Solution: 'LOGARITHMS' contains 10 different letters.   Required number of words	= Number of arrangements of 10 letters, taking 4 at a time.   = 10P4   = (10 x 9 x 8 x 7)   = 5040.   Answer: Option 5040
Answer: C
In a certain store, the profit is 320% of the cost. If the cost increases by 25% but the selling price remains constant, approximately what percentage of the selling price is the profit?	Choices:
A) 60%
B) 70%
C) 80%
D) 90%
E) 100%

Solution: Let C.P.= Rs. 100. Then, Profit = Rs. 320, S.P. = Rs. 420.   New C.P. = 125% of Rs. 100 = Rs. 125   New S.P. = Rs. 420.   Profit = Rs. (420 - 125) = Rs. 295.   Required percentage = 295/420	x 100	%	=	1475/21	% = 70% (approximately).   70%)
Answer: B
The radius of a cylindrical vessel is 8cm and height is 3cm. Find the whole surface of the cylinder?  Choose the correct choice from the following answers.
A) 308 sq cm  B) 220 sq cm  C) 440 sq cm  D) 553.1 sq cm  E) 138 sq cm

Solution: r = 8 h = 3   2πr(h + r) = 2 * 22/7 * 8(11) = 553.1   ANSWER:553.1 sq cm
Answer: D
If the space diagonal of cube C is 5 inches long, what is the length, in inches, of the diagonal of the base of cube C?
Choose the correct choice:
A) 5/(√6)
B) 5·√(2/3)
C) 5·√(3/2)
D) 5·√3
E) 5·√6

Solution: n cube C, let's say that each side has side length x   So, the diagonal = √(x² + x² + x²) = √(3x²)   Here, we're told that the diagonal has length 5, so we can write:   5 = √(3x²)   Square both sides to get: 25 = 3x²   Divide both sides by 3 to get: 25/3 = x²   Square root both sides: √(25/3) = x   Or.... (√25)/(√3) = x   Simplify: 5/(√3) = x   ANSWER:5·√(2/3)
Answer: B
The number of stamps that Kaye and Alberto had were in the ration of 5:3 respectively. After Kaye gave Alberto 15 of her stamps, the ration of the number of Kaye had to the number of Alberto had was 4:3. As a result of the gift, Kaye had how many more stamps than Alberto?
Choose the correct choice from the following options:
A) 20
B) 30
C) 70
D) 60
E) 90

Solution: 70   K1 = 5x   A1 = 3x   K2 = 5x - 15   A2 = 3x + 15   K2/A2 = 7/5   (5x-15)/(3x+15) = 4/3   3*(5x-15) = 4*(3x+15)   15x - 45 = 12x + 60   3x = 105   x = 35   K2 = 5*35 - 15= 
5*35 - 15 = 160
160   A2= 3*35 + 15 = 90   K2 - A2 = 70   Answer : 70
Answer: C
The sum of four consecutive even numbers is 292. What would be the smallest number?  Choose the correct choice from the following choices:  A) 74  B) 76  C) 70  D) 68  E) 65

Solution: Let the four consecutive even numbers be 2(x - 2), 2(x - 1), 2x, 2(x + 1)   Their sum = 8x - 4 = 292 => x = 37   Smallest number is: 2(x - 2) = 70.   ANSWER:70
Answer: C
A 1200 m long train crosses a tree in 120 sec, how much time will I take to pass a platform 700 m long?  Options:
A) 287 Sec	B) 190 Sec	C) 187 Sec	D) 286 Sec	E) 276 Sec

Solution: L = S*T   S= 1200/120= 
1200/120 = 10
10 m/Sec.   Total length (D)= 1900 m   T = D/S   T = 1900/10= 
1900/10 = 190
190 Sec   Answer: 190 Sec
Answer: B