MU-NLPC/Calc-aqua_rat huggingface dataset:
If n is a natural number, then (6n^2 + 6n) is always divisible by
Choose the correct choice from the following answers:	A) 6 only	B) 6 and 12 both	C) 12 only	D) 18 only	E) 12 and 18 both

Solution: (6n^2 + 6n) = 6n(n + 1), which is divisible by both 6 and 12, since n(n+1) is always even.   Answer 6 and 12 both.
Answer: B
If 5% more is gained by selling an article for Rs. 600 than by selling it for Rs. 580, the cost of the article is?
Choose the most appropriate option:
A) 127
B) 688
C) 400
D) 121
E) 123

Solution: Let C.P. be Rs. x.   Then, 5% of x = 600 - 580= 
600 - 580 = 20
20   x/20= 20 => x = 400   Answer: 400
Answer: C
The average of four positive integers is 69. The highest integer is 93 and the least integer is 39. The difference between the remaining two integers is 24. Which of the following integers is the higher of the remaining two integers?
Choose the correct choice from the following choices
A) 32	B) 86	C) 84	D) 22	E) 55

Solution: Let the four integers be A, B, C and D where A > B > C > D.   (A + B + C + D)/4 = 69 => A + B + C + D = 276 ---> (1)   A = 93, D = 39 and B - C = 24   (1) => B + C = 276 - (A + D) = 276 - 132= 
276 - 132 = 144
144.   B + B -24= 144   B = (144 + 24)/2= 
(144 + 24)/2 = 84
84   Answer:Option 84
Answer: C
A committee of two students has to be formed. There are five candidates: Jane, Joan, Paul, Stuart, and Jessica. If Paul and Stuart refuse to be in the committee together and Jane refuses to be in the committee without Paul, how many committees are possible?  Options:
A) 3	B) 4	C) 5	D) 6	E) 8

Solution: Let's try a different problem with your approach. There are five people: A, B, C, D, E. Need to chose 3 for a committee. A and B cannot be chosen together. B and C cannot be chosen together. How many options?   Your approach: total 10 options, 5c3.   Now, assume the wrong scenario where A and B are chosen together. There are three such scenarios. (A and B are chosen, just need one more person.) So we have to subtract the three wrong options. Similarly, there are three wrong scenarios where B and C are chosen together.   This gives us   10-3-3= 
  10-3-3 = 4
4 as the answer.   Yet this answer is wrong. There are five possibilities: ACD, ACE, ADE, 4DE   4
Answer: B
Two trains are running at 40 km/hr and 20 km/hr respectively in the same direction. Fast train completely passes a man sitting in the slower train in 8 seconds. What is the length of the fast train ? Choose the correct option.
A) 27 7/9 B) 44 4/9 C) 29 7/9 D) 30 7/9 E) None of these

Solution: Explanation:   As Trains are moving in same direction,   So, Relative Speed = 40-20= 
40-20 = 20
20 kmph= 20*(5/18) = 50/9 m/sec   Length of Train= Speed * Time   Length=50/9âˆ—8   =400/9   =44 4/9   Option 44 4/9
Answer: B
In 10 years, A will be twice as old as B was 10 years ago. If A is now 9 years older than B, the present age of B is  Choices:
A) 27	B) 66	C) 39	D) 28	E) 21

Solution: Let B's present age = x years. Then, A's present age = (x + 9) years.   (x + 9) + 10 = 2(x - 10)   => x + 19 = 2x - 20   => x =39.   Answer: 39
Answer: C
The average age of 36 students in a group is 14 years. When teacher's age is included to it, the average increases by one. What is the teacher's age in years ?
Choose the most appropriate option.
A) 35 years	B) 45 years	C) 51 years	D) 54 years	E) None of these

Solution: Explanation:   Age of the teacher = (37 * 15 - 36 * 14)= 
(37 * 15 - 36 * 14) = 51
51 years. Answer: 51 years
Answer: C
When positive integer A is divided by positive integer B, the result is 9.44. Which of the following could be the reminder when A is divided by B?
Choose the correct choice:
A) 11 B) 14 C) 15 D) 24 E) 19

Solution: the remainder will be obtained from the decimal part when A is divided by B i.e. 0.44   0.44 = 44/100 = 11/25 so possible remainders are 11,22,33,44.   Only option 11-11 satisfies this   for remainder 11,   11ns - 11
Answer: A
Randy'sbar serves customers every weeknight from 5 pm to 2 am. In Randy's bar,Silvermoonbeer is sold at a constant rate except during happy hour, from 6:30 to 7:30 pm, when the rate triples.
If a keg of Silvermoon beer is half empty at 5pm on Monday, and two-thirds empty at the beginning of the happy hour, when will it be completely empty? Select
A) Monday, 7:30 pm  B) Monday, 9 pm  C) Monday, 7 pm  D) Monday, 7:45 pm  E) Monday, 9:30 pm

Solution: Let the keg be a 150 Litre keg   At 5 pm.. There are 75 litres   At 6:30 pm there are 50 litres.   So, consumption rate is 25 litres per 1.5 hours.   So it will take 3 hours to finish 50 litres at this rate.   During happy hour it sells 3 times faster. So, rate = 1 hour per 50 litres.   So, keg becomes empty at 6:30 + 1 hour = 7:45 pm   Answer is Monday, 7:45 pm
Answer: D
If a, b, and c are consecutive positive even integers and a > b > c, which of the following could be equal to a + b - c ? Choose the most appropriate option: A) 6 B) 2 C) -1 D) -3 E) -4

Solution: consectutive even , X , X + 2 , X + 4 where X = Even   now subtract X + (X+2) - (X+4)   doing this leaves us with X -2   what even number can we substitute in X to yield an answer choice   2 works 2 (plug in 4 for X)
Answer: B
The cost of producing x tools by a company is given by
C(x) = 600 x + 5500 (in $)
a) What is the cost of 100 tools?	Choose the correct choice from the following answers:  A) 65500 $  B) 125800 $  C) 125900 $  D) 6500 $  E) 122500 $

Solution: Solution   C(100) = 600*100 + 5500 = 125500 $   65500 $nswer 65500 $
Answer: A
Instead of multiplying a number by 3, the number is divided by 5. What is the percentage of error obtained ? Pick one
A) 92.33%  B) 91.33%  C) 95.33%  D) 93.33%  E) 94.33%

Solution: let the number be x   the right number is 3x   the wrong number is x/5   error is(3x-x/5)=14x/5   percentage of error is((14x/5)/3x)*100=93.33%   ANSWER:93.33%
Answer: D
Two workers A and B working together completed a job in 5 days. If A worked twice as efficiently as he actually did and B worked 1⁄3 as efficiently as he actually did, the work would have completed in 3 days. Find the time for A to complete the job alone.	Choices:
A) 6 1⁄4 days
B) 5 3⁄4 days
C) 5 days
D) 3 days
E) None of these

Solution: (A + B)’s one day’s work 1⁄5th work   Let A can do job in x days.   Then,A’s one day’s work = 1⁄x th work.   and B’s one day’s work = 1⁄5 - 1⁄x = x−5/5xth work.   Now, (2A)'s work + (1⁄3) B's work = 1⁄3 rd work.   ⇒ 2/x+1/3(x−5/5x)=1/3⇒ x = 25⁄4 = 61⁄4 days   6 1⁄4 daysnswer 6 1⁄4 days
Answer: A
4 liters of a 25 percent solution of alcohol in water are mixed with 3 liters of a 11 percent alcohol in water solution. What is the percentage of alcohol in the new solution?
Pick
A) 18.2%	B) 18.6%	C) 19.0%	D) 19.4%	E) 19.8%

Solution: The total amount of alcohol is 0.25(4) + 0.11(3) = 1.33 liters.   The percentage is 1.33 / 7 = 133 / 700 = 19 / 100 which is 19%   The answer is 19.0%.
Answer: C
{5, 6, 3, 8, 4}
If we want to get the median value of the set to be 10 which value should be inserted in the set of 5 values? Choose the correct answer:
A) 5  B) 7  C) 15  D) 12  E) 13

Solution: Median is the middle number of a sorted distribution. In case of even number of items, Median will be the average of middle two values.   The question asks fora new number that will cause the median of new set at 10.   Mentionable that given set is already sorted and number of items of new set will be 5+1= 
5+1 = 6
6.   To get median 10,the sum of 3th4th Term should be 20 i.e. 3+7.   So to keep the median 10,the new item should be >=7   Answer is 7
Answer: B
In the standard formulation of a flavored drink the ratio by volume of flavoring to corn syrup to water is 1 : 12 : 30. In the "sport" formulation, the ratio of flavoring to corn syrup is three times as great as in the standard formulation, and the ratio of flavoring to water is half that of the standard formulation. If a large bottle of the "sport" formulation contains 3 ounces of corn syrup, how many ounces of water does it contain?
Select
A) 45 B) 50 C) 55 D) 60 E) 63

Solution: F:C:W   1:12:30   Sport version:   F:C   3:12   F:W   1:60   OR 3:180   So C:F:W = 12:3:180   C/W = 12/180 = 3 ounces/x ounces   x = 3*180/12= 
3*180/12 = 45
45 ounces of water   45NSWER:45
Answer: A
A car takes 6 hours to cover a distance of 450 Km. how much should the speed in Kmph be maintained to cover the same direction in 3/2th of the previous time?  Choose the correct choice from the following options.
A) 48 Kmph
B) 50 Kmph
C) 52 Kmph
D) 56 Kmph
E) 60 Kmph

Solution: Time = 6   Distence = 450   3/2 of 6 hours = 6 * 3/2= 
6 * 3/2 = 9
9 Hours   Required speed= 450/9= 
450/9 = 50
50 Kmph   50 Kmph
Answer: B
If radius of a circle is diminished by 10% then its area is diminished by	Select
A) 22  B) 19  C) 877  D) 26  E) 271

Solution: Explanation:   Let old radius = 10 units.   New radius is diminshed by 10%. So new radius = 90% (10) = 9 units.   Old area = π × r2 = 100π   New area = π × 92 = 81π   Change = 19π/100π ×100 = 19%   Answer: 19
Answer: B
From a group of boys and girls, 15 girls leave. They are then left 2 boys for each girl. After this, 45 boys leave. There are then 5 girls for each boy. Find the number of girls in the beginning Choices
A) 20 B) 10 C) 30 D) 50 E) 40

Solution: Assume the number of boys at present = x   Then, the number of girls at present = 5x   Before the boys left, the number of boys were (x+45) and number of girls were 5x   Hence, 2(5x) = x + 45   => 10x = x + 45   => x = 5   Number of girls in the beginning = (5x + 15) = (5×5 + 15) = 40   Answer is 40.
Answer: E
You collect baseball cards. Suppose you start out with 16. Since you're nice, you give John 7 baseball cards. How many baseball cards do you have at the end?  Pick one.
A) 11	B) 12	C) 13	D) 9	E) 15

Solution: Solution   Start with 16 baseball cards.   John takes 7 baseball cards from you:   16 - 7= 
  16 - 7 = 9
9 baseball cards.   So you have 9 at the end.   Correct answer : 9
Answer: D
The current birth rate per Two thousand is 52, whereas corresponding death rate is 21 per two thousand. The net growth rate in terms of population increase in percent is given by
Choose the correct choice from the following answers:	A) 1.80%	B) 1.45%	C) 1.25%	D) 1.35%	E) 2.10%

Solution: Sol.   Net growth on 1000 = (52 - 21)= 
(52 - 21) = 31
31.   Net growth on 100= (27/2000 Ã— 100)% = 1.35%.   Answer 1.35%
Answer: D
A circular rim 28 inches in a diameter rotates the same number of inches per second as a circular rim 35 inches in diameter. If the smaller rim makes D revilutions per second, how many revilutions per minute does the larger rim makes in terms of D?
Choose the correct choice from the following answers.
A) a) 48pi/D B) b) 75m C) c) 48D D) d) 24D E) e) D/75

Solution: distance covered by a circular wheel per sec* = 2*pi* r * n   where n is number of revolution   So we know the smaller rim makes D rev per sec so the inches coverd SR per sec = 28 * pi* D   the problem the say SR rotates the same number of inches as the LR.   The inches covered by the LR per sec = 35 * pi*Y   So equate both u will get Y = 4/5 D   Theis is in sec we need the answer in min so 48 D   answer is c) 48D
Answer: C
In Rwanda, the chance for rain on any given day is 1/2. What is the probability that it rains on 4 out of 9 consecutive days in Rwanda?	Choices
A) 4/7	B) 3/7	C) 63/256	D) 4/28	E) 28/135

Solution: using Binomial. theorem   n63/256r (p)^r (q)^n-r   963/2564 (1/2)^4 (1/2)^r   which is 63/256   Answer is 63/256.
Answer: C
A person can walk at a constant rate of 8mph and can bike at a rate of 24mph. If he wants to travel 80 miles in 8 hours using bike and walking at their constant rates, how much distance would he require to walk?	Choose one:
A) 20	B) 30	C) 56	D) 60	E) 72

Solution: Total distance = 80   Distance = Speed * Time   Walking speed = s1 = 8   Walking time = t1   Bike speed = s2 = 24   Time traveled in bike = t2   d1 + d2 = 80   s1t1 + s2t2 = 80   8*t1 + 24*t2 = 80   t1 + 3*t2 = 10 ----- (1)   Given: t1 + t2 = 8 ----- (2)   (1) - (2) --> 2t2 = 2 , t2=1and t1 = 8 - 1= 
8 - 1 = 7
7   Walking distance= s1*t1 = 8*7= 
8*7 = 56
56   Answer: 56
Answer: C
A can give B 100 meters start and C 200 meters start in a kilometer race. How much start can B give C in a kilometer race?
Select the correct option:	A) 110.12 meters	B) 111.12 meters	C) 112.12 meters	D) 113.12 meters	E) None of these

Solution: Explanation:   A runs 1000 meters while B runs 900 meters and C runs 800 meters.   Therefore, B runs 900 meters while C runs 800 meters.   So, the number of meters that C runs when 111.12 meters runs 1000 meters = (1000 x 800)/900 = 8000/9 = 888.88 meters   Thus, 111.12 meters can give C  (1000 - 888.88)= 
 (1000 - 888.88) = 111.12
111.12 meters start   Answer: 111.12 meters
Answer: B
The cash realised on selling a 14% stock is Rs.120.50, brokerage being 1/4% is Choices
A) 120.25
B) 120.35
C) 106.5
D) 156
E) 240

Solution: Explanation:   Cash realised= Rs. (120.50 - 0.25)   = Rs. 120.25.   120.25nswer: 120.25
Answer: A
In how many ways the letters of the word RAIXBON be arranged?  Choose the correct choice from the following options.
A) 2476 B) 4432 C) 3532 D) 5040 E) 7349

Solution: Total ways of arranging the letters = 7! = 5040 ways.   5040)
Answer: D
In a kilometer race, A beats B by 51 meters or 11 seconds. What time does A take to complete the race?
Pick one.
A) 22  B) 190  C) 277  D) 204  E) 208

Solution: Time taken by B run 1000 meters = (1000 * 11)/51 = 215 sec.   Time taken by A = 215 - 11= 
215 - 11 = 204
204 sec.Answer:204
Answer: D
If 75 percent of 600 is 50 percent of x, then x=? Select the correct option
A) 800	B) 900	C) 1000	D) 1100	E) 1200

Solution: 0.75 * 600 = 0.5 * x   x = 7.5/5 * 600= 
7.5/5 * 600 = 900
900
Answer: B
How many integers are divisible by 9 between 10! and 10! + 100 inclusive?	Choose the most appropriate option.
A) 6	B) 7	C) 8	D) 9	E) 10

Solution: E - 7   10! is divisible by 9   There are 11 numbers between 10! and 10!+ 100 that are divisible by 9.   Hence 10
Answer: E
A is a working partner and B is a sleeping partner in the business. A puts in Rs.15000 and B Rs.25000, A receives 10% of the profit for managing the business the rest being divided in proportion of their capitals. Out of a total profit of Rs.9600, money received by A is? Choose the correct choice from the following.
A) 4229 B) 4220 C) 4211 D) 4200 E) 4212

Solution: 15:25 => 3:5   9600*10/100= 
9600*10/100 = 960
960   9600 - 960= 
9600 - 960 = 8_640
8640   8640*3/8= 
8640*3/8 = 3_240
3240 + 960= 
3240 + 960 = 4_200
4200   Answer:4200
Answer: D
A customer purchased a package of ground beef at a cost of $1.95 per pound. For the same amount of money, the customer could have purchased a piece of steak that weighed 35 percent less than the package of ground beef. What was the cost per pound of the steak?
Select the correct option
A) $2.50
B) $2.75
C) $3.00
D) $3.25
E) $3.50

Solution: For simplicity, let's assume the customer bought 1 pound of ground beef for $1.95.   Let x be the price per pound for the steak.   Then 0.65x = 195   x = 195/0.65 = $3.00   The answer is $3.00.
Answer: C
In a single throw of a die, what is probability of getting a number greater than 4? Choose the most appropriate option:
A) 1/3
B) 2/3
C) 4/6
D) 1/6
E) 5/6

Solution: E= {5,6}   n(E)=2   P(S)=n(E)/n(S)   =2/6   =1/3   1/3NSWER 1/3 1/3
Answer: A
What is the average of 1/2, 3/5 and 3/10? Choices
A) 7/15  B) 3/10  C) 2/5  D) 1/2  E) 6/5

Solution: Sum of 1/2,3/5,3/10 =14/10   7/15verage = 14/10*1/3 =7/15   7/15nswer 7/15 7/15
Answer: A
A, B and C completed a piece of work, A worked for 6 days, B for 9 days and C for 4 days. Their daily wages were in the ratio of 3:4:5. Find the daily wages of C, if their total earning was Rs.1480? Choose the correct option:
A) 170Rs
B) 108Rs
C) 100Rs
D) 160Rs
E) 103Rs

Solution: 3x 4x 5x   6 9 4   18x + 36x + 20x = 1480   74x = 1480 => x = 20   5x =100Rs.   Answer:100Rs
Answer: C
During a Pizza buffet where A eats more times 5 than B, and B eats 7 times less than C.find the least number of times all the three has to eat
Pick:
A) 35
B) 45
C) 25
D) 28
E) 42

Solution: A eats more than B if B eats 1 times than the ratio of A and B is A:B is 5:1 and as B eat 7 times less the C the the ratio of B : C is 1:7 the the least number of times all three has eat is the LCM of A,B,C that is 35 ..   35NSWER:35
Answer: A
A certain factory produces buttons and buckles at a uniform weight. If the total weight of 2 buttons and 2 buckles is one third of 11 buckles and 3 buttons, then the weight of 3 buttons and 1 buckles is how many times that of 5 buckles and 6 buttons?  Choose the correct answer:	A) 7/15.	B) 2/5.	C) 6/11.	D) 5/9.	E) 8/15.

Solution: 2buttons + 2buckles = 1/3(11buckles + 3buttons)   6buttons + 6buckles = 11buckles + 3buttons   3buttons = 5buckles   Weight of 3buttons and 1buckles = 5buckles + 1buckles = 6buckles   Weight of 6buttons and 5buckles = 10buckles + 5buckles = 15buckles   (3buttons and 2buckles) = x * (6buttons and 5buckles)   6 = x*15   x = 6/15=2/5   Answer: 2/5.
Answer: B
The average of the first five multiples of 9 is:  Pick
A) 20	B) 27	C) 28	D) 30	E) None of these

Solution: Solution: Required average = (total sum of multiple of 9)/5   = (9+18+27+36+45)/5= 
(9+18+27+36+45)/5 = 27
27   Note that, average of 9 and 45 is also 27.   And average of 18 and 36 is also 27.   Answer: Option 27
Answer: B
Find the ratio in which wheat of inferior quality (Rs.14/kg) be mixed with wheat of superior quality (Rs.28/kg) so that the shopkeeper gains Rs.2 by selling the resulting mixture at Rs.20/kg.
Choose the correct option:
A) 5 : 2
B) 5 : 9
C) 5 : 3
D) 5 : 1
E) 5 : 8

Solution: Explanation:   Let the resulting mixture be 1 kg, and x kg be the amount of wheat of inferior quality.   Therefore, (1-x)kg is the amount of wheat of superior quality.   5 : 2s the shopkeeper gains Rs.2, the cost of the mixture is Rs.18   14*x + 28*(1-x) = 18   14x - 28x + 28 = 18   14x = 10   x = 5/7   (1 – x) = 2/7   x : (1-x) = 5/7 : 2/7   = 5 : 2   5 : 2NSWER: 5 : 2
Answer: A
A can complete a project in 20 days and B can complete the same project in 30 days. If A and B start working on the project together and B quits 10 days before the project is completed, in how many days total will the project be completed?	Pick one
A) 18  B) 27  C) 26  D) 16  E) 12

Solution: A's rate is 1/20 of the project per day.   B's rate is 1/30 of the project per day.   The combined rate is 1/12 of the project per day.   In the last 10 days, A can do 1/2 of the project.   Thus A and B must complete 1/2 of the project, which takes 6 days.   The total number of days is  6 + 10= 
 6 + 10 = 16
16.   The answer is 16.
Answer: D
In a certain parking lot, 3% of the cars are towed for parking illegally. However 80% of the cars which are parked illegally are not towed. What % of cars in the parking lot are parked illegally.'  Choose the correct choice from the following.
A) 11  B) 13  C) 15  D) 60  E) 75

Solution: So Total no. of cars parked illegally: 300   Total no. of cars: 2000   300/2000*100, So 15%   ANSWER:15
Answer: C
What is the sum of the first 21 natural numbers (starting from 1)?	Choose the most appropriate option
A) 191  B) 201  C) 211  D) 221  E) 231

Solution: The sum of n natural numbers = n*(n+1) / 2 = 21*22/2= 
21*22/2 = 231
231   The answer is 231.
Answer: E
If the perimeter of a square and a rectangle is equal to one another, find out the ratio of the area of both these shapes in case the sides of the rectangle are in the
ratio of 2 :5. Choose the correct choice from the following answers:
A) 40 : 49 B) 24 : 25 C) 4 : 5 D) 5 : 6 E) 4 : 9

Solution: Let side of square=a   length of rectangle=l   breadth of rectangle=b   l/b=2/5------->l=2b/5-----(1)   given 4a=2(l+b)-------->4a=2(2b/5+b)   a=7b/10------(2)   we have to find l*b/a^2   substituting from (1) &(2)   (b*2b/5)/49b^2/100------40/49   40 : 49nswer: 40 : 49
Answer: A
If, when the two parties of knights encounter one another after a month, exactly one knight changes from one travelling party to the other travelling party, that knight must be  Choose the correct choice from the following answers:	A) P	B) Q	C) R	D) S	E) T

Solution: Q because Q always have to travel in northern route   ANSWER:Q
Answer: B
By selling an article at Rs.400, a profit of 25% is made. Find its cost price?
Choose the most appropriate option:  A) 228  B) 320  C) 287  D) 480  E) 811

Solution: SP = 400   CP = (SP)*[100/(100+P)]   = 400 * [100/(100+25)]   = 400 * [100/125] = Rs.320   Answer: 320
Answer: B
The price of an article has been reduced by 35%. In order to restore the original price the new price must be increased by ? Choose the correct answer.
A) 51.8 % B) B) 49.25 % C) 47.2 % D) 53.84 % E) None of these

Solution: Explanation:   100   65   -------   65 ------- 35   100 ------ ? => 53.84 %   ANSWER IS 53.84 %
Answer: D
which of the following inequalities indicates the set of all values of d for which the lengths Q of the three sides of a triangle can be 3,4, and d? Choose the correct choice from the following
A) 0<d<1 B) 0<d<5 C) 0<d<7 D) 1<d<5 E) 1<d<7

Solution: This question is a good way to apply one of the most basic relation between the 3 sides of a triangle. In a triangle (ANY TRIANGLE), any side MUST be greater than the positive difference of the other two sides and less than than the sum of the other 2 sides. Let the sides of a triangle be a,b,c .   Thus,   |a-b| < c < a+b   |b-c| < a < b+c   |c-a| < b < a+c   Thus, if the sides of the triangle are 3,4 and d,   4-3<d<4+3 ---=""> 1<d<7. Thus 1<d<7 is the correct answer.</d<4+3>
Answer: E
Joe’s average (arithmetic mean) test score across 4 equally weighted tests was 35. He was allowed to drop his lowest score. After doing so, his average test score improved to 40. What is the lowest test score that was dropped?
Choose the correct choice from the following
A) 20 B) 25 C) 55 D) 65 E) 80

Solution: The arithmetic mean of 4 equally weighted tests was 35. So what we can assume is that we have 4 test scores, each 35.   He dropped his lowest score and the avg went to 40. This means that the lowest score was not 35 and other three scores had given the lowest score 5 each to make it up to 35 too. When the lowest score was removed, the other 3 scores got their 5 back. So the lowest score was  3 *5= 
 3 *5 = 15
15 less than 35.   So the lowest score=35 - 15= 
35 - 15 = 20
20   20nswer (20)
Answer: A
When Rajeev was born, his father was 32 years older than his brother and his mother was 25 years older than his sister. If Rajeev's brother is 6 years older than Rajeev and his mother is 3 years younger than his father, how old was Rajeev's sister when Rajeev was born? Select:
A) 10 years
B) 11 years
C) 12 years
D) 13 years
E) 14 years

Solution: his brother is x years old   thn his father is 6+32= 
6+32 = 38
38 when rajeev was born   and his mother is 3 years yonger thn hi father so his mother was 35 years old whn rajeev was born   and his sister is 25 year younger thn his mother   so rajeev's sister was 10 years old when rajeev was born.   10 yearsNSWER:10 years
Answer: A
If (x^2 + 1)y=4, which of the following is not a possible value for y? Choose the correct answer: A) 3/2 B) 2 C) 4/3 D) 4 E) 9/2

Solution: Its simple   equation is (x^2 +1)y = 4 ===> x^2 = (4/y) - 1 . As , in LHS, it is x^2 the value has to be positive or zero in RHS.   Hence, (4/y) - 1>= 0 ===> y =< 4. Now only option E has greater value of 'y' than 4.   Thus, correct ans is 9/2
Answer: E
The ratio of the area of a square to that of the square drawn on its diagonal is?	Choose the correct choice from the following options.
A) 4/16	B) 4/13	C) 4/11	D) 4/19	E) 4/12

Solution: P(SᴜK)   = P(S) + P(K) - P(S∩K), where S denotes spade and K denotes king.   P(SᴜK)   = 13/52 + 4/52 - 1/52   = 4/13   Answer:4/13
Answer: B
Find the surface area of a 10 cm × 4 cm × 3 cm brick.  Choose the correct choice from the following:  A) 84 sq. cm  B) 124 sq. cm  C) 164 sq. cm  D) 180 sq. cm  E) None of these

Solution: Solution   Surface area = [2(10 × 4 + 4 × 3 + 10 × 3)] cm2 = (2 × 82)cm2 = 164 cm2   Answer 164 sq. cm
Answer: C
Find the length of the longest pole that can be placed in a room 12 m long 8m broad and 9m high.  Select.
A) 22m  B) 77m  C) 88m  D) 17m  E) 16m

Solution: Explanation:   Length of longest pole = Length of the diagonal of the room   \inline {\color{Black}\sqrt{12^2+8^2+9^2}=\sqrt{289}=17m}   Answer: 17m
Answer: D