MU-NLPC/Calc-aqua_rat huggingface dataset:
If P is a prime number greater than 3, find the remainder when P^2 + 16 is divided by 12.	Choose the correct answer.
A) 5 B) 1 C) 0 D) 8 E) 7

Solution: Every prime number greater than 3 can be written 6N+1 or 6N-1.   If P = 6N+1, then P^2 + 16 = 36N^2 + 12N + 1 + 16 = 36N^2 + 12N + 12 + 5   If P = 6N-1, then P^2 + 16 = 36N^2 - 12N + 1 + 16 = 36N^2 - 12N + 12 + 5   When divided by 12, it must leave a remainder of 5.   The answer is 5.
Answer: A
A meal cost $ 32.50 and there was no tax. If the tip was more than 10 pc but less than 15pc of the price, then the total amount paid should be:  Choose the correct choice from the following options.
A) 40-42
B) 39-41
C) 38-40
D) 37-39
E) 36-37

Solution: 10%(32.5) = 3.25   15%(32.5) =4.875   total amount could have been 32.5+3.25 and 32.5+4.875   => could have been between 35.75 and 37.375   => approximately between 36 and 37   Answer is 36-37.
Answer: E
x and y are integers. a+ b< 11 , and a> 6. What is the smallest possible value of a- b?
Select
A) 1	B) 2	C) 4	D) -2	E) -4

Solution: Focus on the transition points and plug in the values.   a> 6 so a could be 7, 8, 9, 10, 11 etc   Look at a= 7   7 + b< 11   b< 4   b could be 3, 2, 1, 0, -1 etc   When b is 3, we get a- b= 4   This must be the smallest value because as a increases, b reduces so a- b increases.   Take another example. a= 11 so b< 0.   a- b will give a value greater than 11.   Answer (4).
Answer: C
Today Joelle opened an interest-bearing savings account and deposited $5,000. If the annual interest rate is 5 percent compounded interest, and she neither deposits nor withdraws money for exactly 2 years, how much money will she have in the account?	Answers.
A) $6512.50
B) $7512.50
C) $5512.50
D) $4512.50
E) $5250.00

Solution: Interest for 1st year = 5000*5/100= 
5000*5/100 = 250
250   Interest for 2nd year= 5250 *5/100= 
5250 *5/100 = 525/2 = around 262.5
262.50   Total=5000+250+262.50= 
5000+250+262.50 = 5_512.5
5512.50   Answer : $5512.50
Answer: C
One train is traveling 36 kmph and other is at 15 meters a second. Ratio of the speed of the two trains is?
Choose the correct option.
A) 5:4  B) 5:6  C) 5:0  D) 2:3  E) 5:1

Solution: 36 * 5/18 = 15   10:15 => 2:3   Answer: 2:3
Answer: D
How many pairs (r, r+1) have one or more prime factors common, where r is an integer and 2 ≤ r ≤9 ?	Pick.
A) 0	B) 1	C) 2	D) 3	E) 4

Solution: r and r+1 are consecutive integers.   Two consecutive integers are co-prime, which means that they don't share ANY common factor but 1. For example 20 and 21 are consecutive integers, thus only common factor they share is 1.   0nswer: 0.
Answer: A
A juice manufacturer organized taste-testing sessions featuring four brands of orange juice, A, B, C and D. All customers who participated told the organizer which variety they thought was the most similar to freshly-squeezed orange juice. 61% preferred brand A and exactly half as many preferred brand B. Only 60 chose brand C. Which of the following could be the number of customers who preferred brand D? Pick one:
A) 1 B) 8 C) 18 D) 20 E) 27

Solution: I get D, but I'm not sure that my method is sound.   You have A + B + C + D = total testers. Stating the variety they think is most similar to freshly squeezed orange juice means each person should get 1 vote.   x = total number of testers   A + B + C + D   .61x + (.5)(.61x) + 65 + D = x   .61x + .305x + 65 + D = x   I took total testers = 1000 because that gives me nice numbers to deal with. Also, if I use 200 total testers, that gives me A = 122, B = 61, C = 65...that's over 200 without considering D.   x = 400   A = 244, B = 122, C = 65..also over 400   x = 600   A = 366, B = 183 C = 65....also over 600   x = 800   A = 488, B = 244, C = 65...D = 3...not an option on the list.   x = 1000   A = 610 B = 305 C = 65 D = 18....the first time I get an answer that is an option in the question.   18
Answer: C
The perimeter of one square is 48 cm and that of another is 20 cm. Find the perimeter and the diagonal of a square which is equal in area to these two combined?	Select
A) 13√6
B) 13√2
C) 13√9
D) 13√1
E) 13√5

Solution: 4a = 48 4a = 20   a = 12 a = 5   a2 = 144 a2 = 25   Combined area = a2 = 169 => a = 13   d = 13√2   Answer: 13√2
Answer: B
The circumferences of two circles are 264 meters and 352 meters. Find the difference between the areas of the larger and the smaller circles?  Choose one:
A) 2898 sq m  B) 1788 sq m  C) 4312 sq m  D) 7656 sq m  E) 1786 sq m

Solution: Let the radii of the smaller and the larger circles be s m and l m respectively.   2∏s = 264 and 2∏l = 352   s = 264/2∏ and l = 352/2∏   Difference between the areas = ∏l2 - ∏s2   = ∏{1762/∏2 - 1322/∏2}   = 1762/∏ - 1322/∏   = (176 - 132)(176 + 132)/∏   = (44)(308)/(22/7) = (2)(308)(7)   = 4312 sq m   Answer:4312 sq m
Answer: C
P is 40% more efficient than Q. P can complete a work in 24 days. If P and Q work together, how many days will it take to complete the same work?	Choose the correct choice from the following answers
A) 8  B) 9  C) 11  D) 14  E) 15

Solution: The work done by P in 1 day = 1/24   Let work done by Q in 1 day = q   q × (140/100) = 1/24   q = 100/(24×140) = 10/(24×14)   The work done by P and Q in 1 day = 1/24 + 10/(24×14) = 24/(24×14)= 1/14   P and Q together can do the work in 14 days.   The answer is 14.
Answer: D
The average of five consecutive odd numbers A, B, C, D and E is 33. What percent of A is D ?
Choices:
A) 86.8
B) 88.6
C) 89.2
D) 90.1
E) 92.2

Solution: Explanation :   In such a case the middle number (C) is the average   ∴ C = 33 and A = 31 and D = 35   Required percentage = 31/35 x 100 = 88.6   Answer : Option 88.6
Answer: B
Three photographers, Lisa, Mike and Norm, take photos of a wedding. The total of Lisa and Mikes photos is 40 less than the sum of Mike's and Norms. If Norms photos number 10 more than twice the number of Lisa's photos, then how many photos did Norm Take?  Choose one:
A) 40	B) 50	C) 70	D) 80	E) 90

Solution: L+M=M+N-40 / N=2L+10   40=M+N-L-M   40=N-L   40=2L+10-L   30=L   2(30)+10=70   70
Answer: C
A is twice as good a workman as B and they took 7 days together to do the work B alone can do it in.	Choose the correct option.
A) 23 days B) 25 days C) 21 days D) 26 days E) 29 days

Solution: 21 days   21 days   W21 days = 2:1   2x + x = 1/7   x = 1/21 => 21 days
Answer: C
A pupil's marks were wrongly entered as 83 instead of 63. Due to that the average marks for the class got increased by half (1/2). The number of pupils in the class is:	Choose the correct choice from the following answers
A) 32
B) 50
C) 40
D) 20
E) 10

Solution: Let there be x pupils in the class.   Total increase in marks = x x 1/2 = x/2   x/2 = (83 - 63)   x/2	= 20   x= 40.   Answer: 40
Answer: C
Present ages of X and Y are in the ratio 5:6 respectively. Ten years hence this ratio will become 6:7 respectively. What is X's present age in years?
Choose the correct choice from the following.
A) 35 B) 36 C) 50 D) 39 E) 40

Solution: Let the present ages of X and Y be 5x and 6x years respectively.   Then, (5x + 10)/(6x + 10) = 6/7   7(5x +10) = 6(6x +10) => 35x+70= 36x+60 => x=10   X's present age = 5x = 5*10= 
5*10 = 50
50   ANSWER:50
Answer: C
A man on tour travels first 160 km at 64 km/hr and the next 160 km at 80 km/hr. The average speed for the first 250 km of the tour is:  Choose the correct choice from the following answers:	A) 55.55 km/hr	B) 35.55 km/hr	C) 71.11 km/hr	D) 36 km/hr	E) 71 km/hr

Solution: Total time taken = 160/64 + 160/80 = 9/2 hours   --> Average speed = 250 x 2/9 = 55.55 km/hr.   55.55 km/hrnswer : 55.55 km/hr.
Answer: A
A man rows his boat 75 km downstream and 45 km upstream, taking 2 1/2 hours each time. Find the speed of the stream?	Choose the correct choice from the following options.
A) 6 B) 7 C) 5 D) 8 E) 9

Solution: Speed downstream = d/t = 75/(2 1/2) = 30 kmph   Speed upstream = d/t = 45/(2 1/2) = 18 kmph   The speed of the stream = (30 - 18)/2= 
(30 - 18)/2 = 6
6 kmph   6nswer: 6
Answer: A
The average of six numbers is 3.85. The average of two of them is 3.4, while the average of the other two is 3.85. What is the average of the remaining two numbers ?	Choose one:
A) 4.3 B) 4.6 C) 4.2 D) 4.1 E) 4.9

Solution: Explanation:   Sum of the remaining two numbers = (3.85 * 6) - [(3.4 * 2) + (3.85 * 2)]   = 23.10 - (6.8 + 7.7) = 23.10 - 14.5 = 8.60.   Required average = (8.6 / 2) = 4.3.   4.3nswer: 4.3) 4.3
Answer: A
A small beaker is 1/2 filled with salt water. Another beaker, which has five times the capacity of the small beaker, is 1/4 filled with fresh water. After dumping all of the salt water from the small beaker into the large beaker, to what fraction of its capacity will the large beaker be filled?
Choose the correct answer
A) 7/20	B) 9/20	C) 11/20	D) 13/20	E) 17/20

Solution: 1/2 of the small beaker is 1/10 of the large beaker.   1/10 + 1/4 = 7/20   The answer is 7/20.
Answer: A
What will be remainder when (67^67 + 67) is divided by 68 ?	Options:
A) 5
B) 9
C) 87
D) 66
E) 12

Solution: Explanation:   (x^n + 1) will be divisible by (x + 1) only when n is odd.   (67^67 + 1) will be divisible by (67 + 1)   (67^67 + 1) + 66, when divided by 68 will give 66 as remainder.   66
Answer: D
In how many ways can the letters of the english alphabet be arranged so that there are seven letter between the letters A and B, and no letter is repeated
Select the correct option
A) 24P7 * 2 * 18!	B) 24P7 * 2 * 17!	C) 24P7 * 2 * 16!	D) 24P7 * 2 * 13!	E) 24P7 * 2 * 12!

Solution: We can fix A and B in two ways with 7 letters in between them. Now 7 letters can be selected and arranged in between A and B in 24P724P7 ways. Now Consider these 9 letters as a string. So now we have  26 - 9 + 1= 
 26 - 9 + 1 = 18
18 letters   These 18 letters are arranged in 18! ways. So Answer is 2 x 24P724P7 x 18!   Infact, 2 x 24P724P7 x 18!= 36 x 24!. So go for Option B as it was given as OA.   24P7 * 2 * 18!nswer:24P7 * 2 * 18!
Answer: A
A train 600 m long can cross an electric pole in 20 sec and then find the speed of the train? Choose the correct choice from the following answers.
A) 76 Kmph  B) 108 Kmph  C) 72 Kmph  D) 34 Kmph  E) 91 Kmph

Solution: Length = Speed * time   Speed = L/T   S = 600/20= 
600/20 = 30
30 M/Sec   Speed= 30*18/5 (To convert M/Sec in to Kmph multiply by 18/5)   Speed = 108 Kmph   Answer: 108 Kmph
Answer: B
The amount of principal Rs.8000 at compound interest at the ratio of 5% p.a. for 1 year is
Options:
A) s.9621
B) s.6921
C) s.8400
D) s.6261
E) s.6361

Solution: c.i=p(1+r/100)^n   =8000(1+5/100)   =Rs8400   ANSWER:s.8400
Answer: C
The equation (M )/42 = (p – 7)/21 relates two temperature scales, where M is the number of degrees on one scale and P is the number of degrees on the other scale. Which of the following equations can be used to convert temperatures from the P scale to the M scale?
Choose the correct choice from the following choices.
A) P	B) P-7	C) (P-7)*2	D) (P-7)62	E) P-5

Solution: M/42 =(P-7)/21   M = (P-7)*42/21   =(P-7)*2   (P-7)*2
Answer: C
If 2^5, 4^3, and 13^2 are all factors of the product of 936 and w where w is a positive integer, what is the smallest possible value of w?	Choose one.
A) 26
B) 39
C) 42
D) 208
E) 156

Solution: Here 156 has three two's   two three's   and one 13   rest of them must be in w   so w= 13*4*4= 
13*4*4 = 208
208   Smash 208
Answer: D
A man is 24 years older than his son. In two years, his age will be twice the age of his son. The present age of the son is? Choose the correct choice from the following options
A) 11  B) 25  C) 27  D) 22  E) 91

Solution: Let the son's present age be x years.   Then, man's present age = (x + 24) years.   (x + 24) + 2 = 2(x + 2) x + 26 = 2x + 4 => x = 22.   Answer: 22
Answer: D
If 9/(5 + 3/x) = 1, then x =  Choices
A) 3  B) 1  C) 3/4  D) -1/3  E) -3

Solution: The expression 9/(5 + 3/x) = 1 should have been equal to something .   If 9/(5 + 3/x) = 1   => 9x/(5x+3)= 1   => 9x= 5x + 3   =>4x = 3   =>x = 3/4   3/4orrect Option : 3/4
Answer: C
In how many ways can the integer 15 be expressed as a product of two different positive integers?  Choose the correct choice from the following.
A) 10 B) 8 C) 5 D) 4 E) 2

Solution: 15=3*5   Since 15 is not a perfect square, no of ways=2   Answer 2
Answer: E
The average amount with a group of seven numbers is Rs. 20. If the newly joined member has Rs. 62 with him, what was the average amount with the group before his joining the group?
Choose the correct choice from the following answers:
A) s.13	B) s.12	C) s.15	D) s.22	E) s.14

Solution: Total members in the group = 7   Average amount = Rs. 20   Total amount with them = 7 * 20 = Rs. 140   One number has Rs. 62. So, the amount with remaining 6 people = 140 - 62 = Rs. 78   The average amount with them = 78/6 = Rs.13.   s.13nswer:s.13
Answer: A
A train , 800 meter long is running with a speed of 78 km/hr. It crosses a tunnel in 1 minute. What is the length of the tunnel (in meters)? Choose the correct option
A) 440 m	B) 500 m	C) 260 m	D) 430 m	E) 450 m

Solution: Explanation:   Distance = 800+x meter where x is the length of the tunnel   Time = 1 minute = 60 seconds   Speed = 78 km/hr = 78×10/36 m/s = 130/6 = 65/3 m/s   Distance/time = speed   (800+x)/60 = 65/3   => 800+x = 20×65 = 1300   => x = 1300 - 800= 
1300 - 800 = 500
500 meter   Answer: Option 500 m
Answer: B
The diagonals of two squares are in the ratio of 3:7 then find the ratio of its areas?
Choose the correct option
A) 7:37
B) 6:46
C) 9:49
D) 8:68
E) 6:61

Solution: Let the diagonals of the squares be 3x and 7x   Ratio of their areas = 1/2 (3x)^2 : 1/2 (7x)^2 = 9x^2 : 49x^2 = 9:49   Answer is 9:49
Answer: C
The volume of a cube is 2197 cc. Find its surface.
Choose the correct answer.
A) 864 B) 1014 C) 1299 D) 1268 E) 1191

Solution: a3 = 2197 => a = 136a2 = 6 * 13 * 13= 
6 * 13 * 13 = 1_014
1014Answer: 1014
Answer: B
2, 4, 3, 6, ?, ?, 9, 18, ?, ?, 33.
Options:	A) 16,31	B) 16,32	C) 15,30	D) 15,32	E) 15,31

Solution: 2, 4, 3, 6, ?, ?, 9, 18, ?, ?, 33.   ans: 2, 4, 3, 6, 4, 8, 9, 18, 16, 32, 33.   ANSWER:16,32
Answer: B
An error 4% in excess is made while measuring the side of a square. The percentage of error in the calculated area of the square is:	Choose the correct answer: A) 4.16 B) 5.16 C) 7.16 D) 8.16 E) 9.16

Solution: Explanation:   100 cm is read as 104 cm.   A1 =(100 × 100)cm2 = 10000   and A2= (104 × 104)cm2= 10816   (A2 - A1) = 10816-10000= 
10816-10000 = 816
816=> 816/10000*100= 
816/10000*100 = 204/25 = around 8.16
8.16   Answer : 8.16
Answer: D
If k^3 is divisible by 1620, what is the least possible value of integer k?  Select
A) 12
B) 30
C) 60
D) 90
E) 120

Solution: 1620 = 2^2*3^4*5   Therefore k must include at least 2 * 3^2 * 5 = 90.   The answer is 90.
Answer: D
What is the sum of the greatest common factor and the lowest common multiple of 48 and 72?
Choose the correct choice from the following answers.
A) 192	B) 120	C) 168	D) 160	E) 184

Solution: Prime factorization of the given numbers   72= 2^3 * 3^2   48= 2^4 *3   Greatest common factor = 2^3*3 = 24   Lowest common multiple = 2^4*3^2 =144   Sum = 24+ 144= 
24+ 144 = 168
168   Answer 168
Answer: C
40 % of 2 is equal to	Choose the correct option.
A) 0.2	B) 0.8	C) 0.6	D) 0.7	E) 0.9

Solution: 40 % of 2 = (40 / 100) * 2= 
(40 / 100) * 2 = 4/5 = around 0.8
0.8   Answer: Option 0.8
Answer: B
What will come in place of the x in the following Number series? 73205, 6655, 605, 55, x	Choices:	A) 67900	B) 73205	C) 73789	D) 87654	E) 98555

Solution: (73205)   5 x 11 = 55, 55 x 11 = 605, 605 x 11 = 6655, 6655 x 11 = 73205
Answer: B
In a class, there are 24 boys whose ages is decreased by 4 months, when one boy aged 20 years is replaced by a new boy. Find the age of the new boy. Pick one: A) 9 YEARS B) 10 YEARS C) 12 YEARS D) 14 YEARS E) 15 YEARS

Solution: Let age of the new boy was X.   Age decreased = 4 months = 4/12 = 1/3 years   Now, we have formula for this type of questions,   Number of members in the Group * age decreased = difference in ages of boy in and boy out.   24 * (1/3) = 20 -X   X = 12 years.   ANSWER : OPTION 12 YEARS
Answer: C
Acording to a military code, SYSTEM is SYSMET and NEARER is AENRER. What is the code for FRACTION ?  Options.
A) CARFTINO	B) CARFTION	C) ARFCNOIT	D) CARFNOIT	E) SUIIQQWE

Solution: Explanation:   The letter is the first half and the letter half of the word are separately reversed to obtain the code.   Answer: CARFNOIT
Answer: D
The price of pulses has fallen by 30%. How many quintals can be bought for the same amount which was sufficient to buy 12 quintals at the higher price?
Answers.
A) 20 B) 22.5 C) 17 D) 30 E) 32.5

Solution: 80% of original price can buy = 12 quintals.   Therefore, he can buy ( 12 x 100 )/ 70 = 17 quintals at the lower price.   ANSWER:17
Answer: C
A dog takes 3 leaps for every 7 leaps of a hare. If one leap of the dog is equal to 3 leaps of the hare, the ratio of the speed of the dog to that of the hare is :	Options.
A) 9:7
B) 9:9
C) 9:6
D) 9:1
E) 9:2

Solution: Explanation:   Dog : Hare = (3*3) leaps of hare : 7 leaps of hare = 9 : 7.   9:7nswer: 9:7) 9:7
Answer: A
Vijay lent out an amount Rs. 10000 into two parts, one at 8% p.a. and the remaining at 10% p.a. both on simple interest. At the end of the year he received Rs. 890 as total interest. What was the amount he lent out at 8% pa.a?
Choose the correct choice from the following.
A) 5529	B) 5500	C) 5520	D) 5521	E) 5192

Solution: Let the amount lent out at 8% p.a. be Rs. A   => (A * 8)/100 + [(10000 - A) * 10]/100   = 890   => A = Rs.5500.   Answer:5500
Answer: B
A juice manufacturer organized taste-testing sessions featuring four brands of orange juice, A, B, C and D. All customers who participated told the organizer which variety they thought was the most similar to freshly-squeezed orange juice. 61% preferred brand A and exactly half as many preferred brand B. Only 45 chose brand C. Which of the following could be the number of customers who preferred brand D? Choices
A) 1 B) 8 C) 14 D) 20 E) 27

Solution: I get D, but I'm not sure that my method is sound.   You have A + B + C + D = total testers. Stating the variety they think is most similar to freshly squeezed orange juice means each person should get 1 vote.   x = total number of testers   A + B + C + D   .61x + (.5)(.61x) + 65 + D = x   .61x + .305x + 65 + D = x   I took total testers = 1000 because that gives me nice numbers to deal with. Also, if I use 200 total testers, that gives me A = 122, B = 61, C = 65...that's over 200 without considering D.   x = 400   A = 244, B = 122, C = 65..also over 400   x = 600   A = 366, B = 183 C = 65....also over 600   x = 800   A = 488, B = 244, C = 65...D = 3...not an option on the list.   x = 1000   A = 610 B = 305 C = 65 D = 14....the first time I get an answer that is an option in the question.   14
Answer: C
If John has earned 350 dollars by working 2 hrs/day a week at a constant daily rate for 5 weeks, which of the following represents his daily wage? Select the correct option.
A) 1	B) 2	C) 5	D) 4	E) 3

Solution: John total earning = 350   No days he worked = 2 * 7= 
2 * 7 = 14
14   Rate= 5 week   Daily wage = total / (Rate * days)   = 350/(5*7*2)= 
350/(5*7*2) = 5
5   5 is correct answer...
Answer: C
In an increasing sequence of 10 consecutive integers, the sum of the first 5 integers is 545. What is the sum of the last 5 integers in the sequence?  Choose the correct choice from the following answers
A) 585  B) 580  C) 575  D) 570  E) 565

Solution: All 5 integers are 5 numbers larger than in the first sum (eg. 1 becomes 6, 2 7...). 5*5=25+545= 
25+545 = 570
570   570
Answer: D
In the xy-plane the point (-2 -3) is the centre of a circle, the point (-2, 3) lies inside the circle and the point (6,-3) lies outside the circle. If the radius r of the circle r is an integer then r=
Select:
A) 6
B) 5
C) 4
D) 7
E) 2

Solution: Can be solved without much calculations.   You are given that (-2,-3) is the center of the circle. Point (6,-3) lies inside the circle ---> the radius is lesser than distance of (-2,-3) from (6,-3) ---> lesser than 8 units but the radius will also be greater than the distance of (-2,-3) from (-2,3) ----> greater than 6 units.   Thus the radius is >6 but <8and as it is an integer, the only possible value of radius = 7 units.   7 is the correct answer.
Answer: D
If the sides of a triangle are 4 cm, 9 cm and 13 cm, what is its area?	Choose the correct choice from the following choices.
A) 18  B) 20  C) 22  D) 26  E) 28

Solution: The triangle with sides 4 cm, 9 cm and 13 cm is right angled, where the hypotenuse is 13 cm.   18rea of the triangle = 1/2 * 4 * 9= 
1/2 * 4 * 9 = 18
18 cm2   18nswer: Option 18
Answer: A
A cube has five of its faces painted half red and half white. The other face is completely painted white. What is the ratio between the red painted areas and the white painted areas of the cube?
Answers:
A) 6:11
B) 2:5
C) 3:4
D) 5:7
E) 2:3

Solution: Let x be the area of each face of the cube.   The area painted red is 5(x/2) = 5x/2   The area painted white is 5(x/2) + x = 7x/2x   The ratio of red to white is 5x/2:7x/2 which is 5:7.   The answer is 5:7.
Answer: D
The smallest value of n, for which n+2 is not a prime number, is	Choose the most appropriate option:
A) 1,2
B) 4,6
C) 2,4
D) 8,12
E) 9,6

Solution: (1 + 2)= 
(1 + 2) = 3
3.   (2 + 2)= 
(2 + 2) = 4
4.   (3 + 2)= 
(3 + 2) = 5
5.   (4 + 2)= 
(4 + 2) = 6
6.   which is not prime , n=2,4.   ANSWER:2,4
Answer: C
The average age of 40 students in a class is 10years. If teacher's age is also included then average increases 1year then find the teacher's age?	Choose one
A) 59	B) 55	C) 61	D) 51	E) 36

Solution: Total age of 50 students = 40*10= 
40*10 = 400
400   Total age of 51 persons= 41*11= 
41*11 = 451
451   Age of teacher= 451-400= 
451-400 = 51
51years   Answer is 51
Answer: D
Sequence Q consists of 16 consecutive integers. If -6 is the least integer in sequence Q, what is the range of the positive integers in sequence Q?	Choose the correct choice from the following:
A) 16	B) 15	C) 9	D) 8	E) 7

Solution: Since set Q consists of 16 consecutive integers and -6 is the least integer then set Q is consecutive integers from -6 to 9, inclusive: 9-(-6)+1= 
9-(-6)+1 = 16
16.   The range of positive integers in sequence Q is 9-1= 
9-1 = 8
8.   Answer: 8.
Answer: D
Robert is travelling on his cycle and has calculated to reach point A at 2 P.M. if he travels at 10 kmph, he will reach there at 12 noon if he travels at 15 kmph. At what speed must he travel to reach A at 1 P.M.?
Choose the correct answer:	A) 8	B) 12	C) 11	D) 16	E) 18

Solution: Explanation :   Let the distance travelled by x km.   Then,   => (x/10) - (x/15) = 2   => 3x - 2x =60   => x = 60   => Time taken to travel 60 km at 10 km/hr = 60/10= 
60/10 = 6
6 hours.=> So, Robert started 6 hours before 2 P.M. i.e., at 8 A.M.   Therefore ,   Speed required = (60/5) km/hr   = 12 km/hr   Answer : 12
Answer: B
How many digits 2^400 has?
Choices:
A) 31  B) 35  C) 50  D) 99  E) 121

Solution: 2^10 = 1.024 * 10^3 => 2^100 = (1.024)^10 * 10^120   therefore 121 digits would be my best guess   121
Answer: E
The reciprocal of the hcf and lcm of two are 1/14 and 1/312 .if one of the number is 24 then other no. is  Choose the correct choice from the following choices:
A) 126  B) 136  C) 146  D) 156  E) 182

Solution: reciprocal of the hcf and lcm of two are 1/14 and 1/312   so, HCF = 14 , LCM = 312   LCM * HCF = product of two numbers = a*b => b = LCM * HCF / a   so, other = 14*312 / 24= 
14*312 / 24 = 182
182   ANSW182R:182
Answer: E
On a test consisting of 30 questions. No. of wrong answers is 50% less than number of right answers. Each answer was either right or wrong. What is the ratio of right answers to wrong answers?
Choose one
A) 1 : 5  B) 2 : 6  C) 2 : 1  D) 3 : 7  E) 4 : 9

Solution: Sol. Let the number of wrong answer - x and number of right answer = 30-x x = 50/100 of (30-x) x = 10   Required ratio = 20 : 10 = 2 : 1   2 : 1
Answer: C
A does a work in 10 days and B does the same work in 15 days. In how many days they together will
do the same work ?
Choose the correct choice from the following: A) 5 days B) 6 days C) 7 days D) 8 days E) None of these

Solution: Explanation:   Firstly we will find 1 day work of both A and B, then by adding we can get collective days for them,   So,   A's 1 day work = 1/10   B's 1 day work = 1/15   (A+B)'s 1 day work =   (110+115)=(3+230)=16   So together they can complete work in 6 days.   Answer: 6 days
Answer: B