MU-NLPC/Calc-aqua_rat huggingface dataset:
A can lay railway track between two given stations in 16 days and B can do the same job in 12 days. With help of C, they did the job in 4 days only. Then, C alone can do the job in:	Choose one.
A) 9 1/5 days	B) 9 3/5 days	C) 9 2/5 days	D) 10 days	E) 10 1/5 days

Solution: (A + B + C)'s 1 day's work =1/4   A's 1 day's work =1/16   B's 1 day's work =1/12   Therefore C's 1 day's work =1/4-(1/16+1/12)=(1/4-7/48)=5/48	.   So, C alone can do the work in	48/5= 9 3/5days.   Option 9 3/5 days
Answer: B
A cube of side 5 cm is painted on all its side. If it is sliced into 1 cubic centimer cubes, how many 1 cubic centimeter cubes will have exactly one of their sides painted?  Options:	A) 9	B) 61	C) 98	D) 54	E) 64

Solution: Explanatory Answer   When a 5 cc cube is sliced into 1 cc cubes, we will get  5 * 5 * 5= 
 5 * 5 * 5 = 125
125 cubes of 1 cubic centimeter.   In each side of the larger cube, the smaller cubes on the edges will have more than one of their sides painted.   Therefore, the cubes which are not on the edge of the larger cube and that lie on the facing sides of the larger cube will have exactly one side painted.   In each face of the larger cube, there will be 5 * 5= 
5 * 5 = 25
25 cubes.   Of these, the cubes on the outer rows will be on the edge. 16 such cubes exist on each face.   If we count out the two outer rows on either side of a face of the cube, we will be left with  3 * 3= 
 3 * 3 = 9
9 cubes which are not on the edge in each face of the cube.   Therefore, there will be 9 cubes of 1-cc volume per face that will have exactly one of their sides painted.   In total, there will be 9 * 6= 
9 * 6 = 54
54 such cubes.   Choice 54 is the correct answer.
Answer: D
How many 3-digit numbers are completely divisible 6 ?  Choose one:
A) 150
B) 166
C) 138
D) 182
E) 172

Solution: A   150   3-digit number divisible by 6 are: 102, 108, 114,... , 996   This is an A.P. in which a = 102, d = 6 and l = 996   Let the number of terms be n. Then tn = 996.   a + (n - 1)d = 996   102 + (n - 1) x 6 = 996   6 x (n - 1) = 894   (n - 1) = 149   n = 150   Number of terms = 150.
Answer: A
workers in a factory store products inside two different sized boxes. The bigger of the boxes can store 50 products while the smaller box can store 40 products. If a fresh batch of products numbering 212 in total were to be stored, what is the least number of products that will not be boxed?  Pick
A) 23
B) 11
C) 2
D) 10
E) 12

Solution: Total products to be stored 212   The big box can store 50   small box can store 40   storing 212 products in big box 212/50 =4 r 12   least number of toys that will be left unboxed=12   Answer: 12
Answer: E
In 1937, the ship of the great sailor SINBAD left an Egyptian port heading Ivory coast at Q mile/month .
One month later another ship of the greatest pirate ever CHENG I SAO was 5000 miles due south of the same Egyptian port and heading due north at Y miles/month. Six months later after the leaving of Sinbad’s ship from Egyptian port, how far apart were the ships? [Ivory coast is in the west of Egypt]	Choose the correct choice
A) { (6Q)^2 + (5000-5y)^2 }^1/2  B) { (36x)^2 + (5000-7y)^2 }^1/2  C) { (16x)^2 + (5000-7y)^2 }^1/2  D) { (7x)^2 + (5200-7y)^2 }^1/2  E) { (2x)^2 + (300-7y)^2 }^1/2

Solution: The chinese ship sailed for 5 months i.e. 5Y miles @Y miles/month, therefore distance from Egyptian port is 5000-5Y. Since { (6Q)^2 + (5000-5y)^2 }^1/2 is the only option with this value ...therefore { (6Q)^2 + (5000-5y)^2 }^1/2 is the answer
Answer: A
In a consumer survey, 85% of those surveyed liked at least one of three products: 1, 2, and 3. 50% of those asked liked product 1, 30% liked product 2, and 20% liked product 3. If 6% of the people in the survey liked all three of the products, what percentage of the survey participants liked more than one of the three products?	Choices:
A) 5
B) 9
C) 15
D) 20
E) 25

Solution: Use the forumla ;   Total = Group1 + Group2 + Group3 - (sum of 2-group overlaps) - 2*(all three) + Neither   100 = 50 + 30 + 20 - ( sum of 2) -2(6) +15   100 = 103-( sum of 2)   3 = sum of 2   so more than 1 = 9   9
Answer: B
Sara bought both German chocolate and Swiss chocolate for some cakes she was baking. The Swiss chocolate cost $3.5 per pound, and German chocolate cost $2.8 per pound. if the total the she spent on chocolate was $28 and both types of chocolate were purchased in whole number of pounds, how many total pounds of chocolate she purchased?  Choose the correct choice from the following options:
A) 9	B) 8	C) 10	D) 12	E) 15

Solution: If there were all the expensive ones,3.5....   There would be 28/3.5 or 8 of them but since 2.8$ ones are also there, answer has to be >8..   If all were 2.8$ ones, there will be 28/2.8 or 10...   So ONLY 9 is left   9nswer 9..
Answer: A
A School has 15 teaching staff and 10 non teaching staff. The 15 teaching staff have an average salary of $1000. The average salary of the 10 non teaching staff is $500. What is the average salary for the school?	Choose the correct choice from the following choices
A) $650  B) $800  C) $1300  D) $400  E) $900

Solution: The number of teaching staff are 15   Their average salary is $1000   The number of non teaching staff is 10   Their average salary is $500   The total amount of salary for teaching staff is 15*1000 is $15,000   The total amount of salary for non teaching staff is 10*500 is 5000   Total amount of salary for the school is 15,000+5000=20,000   Average salary for the school is 20,000/15+10=800   Answer is $800
Answer: B
In an increasing sequence of 8 consecutive even integers, the sum of the first 4 integers is 212. What is the sum of all the integers in the sequence?
Choices:
A) 252 B) 368 C) 456 D) 586 E) 590

Solution: let the first term of the sequence be x   since it is consecutive even integers the terms be we x, x+2,x+4...x+14 (up to 8 terms)   now,   sum of first 4 terms =212   or,   4x+12=212   x=200/4= 
200/4 = 50
50   Thus the answer can now be calculated by either summing up 50+52+54+... 8th term   or   s=n/2(2a+(n-1)d   =8/2(2*50+(7*2))   =4(100+14)=456   456
Answer: C
The ratio of two numbers is 3:4 and their sum is 28. The greater of the two numbers is?	Choose the correct choice from the following:  A) 8  B) 10  C) 12  D) 16  E) 18

Solution: 3:4   Total parts = 7   = 7 parts --> 28 (7 × 4 = 28)   = 1 part ---->4 (1 × 4 = 4)   = The greater of the two number is = 4   = 4 parts ----> 16 (4 × 4 = 16)   16)
Answer: D
A train running at 1/5 of its own speed reached a place in 10hours. How much time could be saved if the train would have run at its own speed?	Answers.
A) 8hrs  B) 10hrs  C) 12hrs  D) 15hrs  E) 6hrs

Solution: New speed = 1/5 of usual speed   New time = 5/1 of usual time   5/1 of usual time = 10 hrs   Usual time = 10*1/5= 
10*1/5 = 2
2 hrs   Time saved= 10-2= 
10-2 = 8
8 hrs   8hrsnswer is 8hrs
Answer: A
Calculate the number of bricks, each measuring 25 cm x 15 cm x 8 cm required to construct a wall of dimensions 10 m x 4 cm x 6 m when 10% of its volume is occupied by mortar ?  Choose the correct answer:  A) 720  B) 600  C) 660  D) 6000  E) 6500

Solution: Explanation:   Let the number of bricks be 'N'   10 x 4/100 x 6 x 90/100 = 25/100 x 15/100 x 8/100 x N   10 x 4 x 6 x 90 = 15 x 2 x N => N = 720.   720nswer IS 720
Answer: A
The parameter of a square is double the perimeter of a rectangle. The area of the rectangle is 480 sq cm. Find the area of the square?	Choose one:	A) 480	B) 997	C) 266	D) 288	E) 611

Solution: Let the side of the square be a cm. Let the length and the breadth of the rectangle be l cm and b cm respectively.   4a = 2(l + b)   2a = l + b   l . b = 480   We cannot find ( l + b) only with the help of l . b. Therefore a cannot be found .   Area of the square cannot be found.   480nswer: 480
Answer: A
For a finite sequence of non zero numbers, the number of variations in the sign is defined as the number of pairs of consecutive terms of the sequence for which the product of the two consecutive terms is negative. What is the number of variations in sign for the sequence 10, -3, 20, 5, -4, 6, -7 , 12? Choose the correct choice from the following answers:	A) 1	B) 2	C) 3	D) 4	E) 5

Solution: The questions basically asks: how many pairs of consecutive terms are there in the sequence such that the product of these consecutive terms is negative.   10*(-3)=-30=negative;   -3*20=-60=negative;   5*(-4)=-20=negative.   6 * (-7) = -42 > negative   -7 * 12 = -84 >>negative   So there are 5 pairs of consecutive terms.   Answer: 5
Answer: E
How many positive numbers are in a sequence of z numbers, if the sequence alternates between positive and negative numbers and z is an odd number. The sequence starts with a negative number.  Choose the most appropriate option:  A) (z-1)/2  B) z/2  C) z/(2-1)  D) (z+1)/2  E) z/(2+1)

Solution: Lets put values for z, say z=7 since it's odd   and first number is neg so sequence will be {neg,pos,neg,pos,neg,pos,neg} we can see that it has 3 negative terms   so putting z=7 in the options,   option (z+1)/2 = (z-1)/2 => 7-1/2 = 4 , the number of positive integers   So, (z+1)/2 is the answer
Answer: D
we need to carve out 125 identical cubes from a cube . what is the minimum number of cuts needed?  Pick one.
A) 8	B) 9	C) 10	D) 11	E) 12 cuts

Solution: Total no. of cubes=n^3   here n^3 = 125 which makes n=5,   also minimum no. of cuts required =3(n-1)   hence, 3(5-1)=12 cuts.   ANSW12 cutsR:12 cuts
Answer: E
2 hours after train A leaves Lucknow a train B leaves the same stationtraveling in the same direction at an average speed of 28 km/hr. After traveling 6 hrsthe train B overtakes the train A. What is the average speed of the train A?  Pick one: A) 15 km/hr B) 16 km/hr C) 17 km/hr D) 21 km/hr E) None of these

Solution: Explanation :   Total distance covered by B=28*6= 
28*6 = 168
168kmTotal time taken by A to cover same distance=2+6= 
2+6 = 8
8 hrsaverage speed of A=168/8= 
168/8 = 21
21 km/hr   Answer : 21 km/hr
Answer: D
A train moves with a speed of 189 kmph. Its speed in metres per second is
Choose the correct choice from the following options:
A) 60.8  B) 18  C) 30  D) 52.5  E) None

Solution: Solution   Speed	= 189 Kmph   = (189 x 5/18)m/sec   = 52.5 m/sec.   Answer 52.5
Answer: D
Rajesh can finish 1/3 of his home work in one hour. Seema can finish 3/7 of
her homework in 65 minutes and Ramya can finish 3/4 of her homework in
three and a half hours. If all of them start their home work at 12.00 PM and can
go to play as soon as they all finish their homework. When can they start to
play, if they take a break at 3.00 PM for 35 minutes?
Pick.
A) 4:30pm	B) 5:15pm	C) 6:30pm	D) 5:10pm	E) 3:45pm

Solution: ajesh can finish his work in 3 hr,   ramya can finish her work in 2.5 hr   seema can finish in 4.6 hr   so 5:15pm they can go to play   ANSWER:5:15pm
Answer: B
In the xy-coordinate system, if (m, n) and (m + 3, n + k) are two points on the line with the equation x = 2y + 5, then k =	Choose the correct option:
A) 1/2	B) 1	C) 2	D) 3/2	E) 4

Solution: Since (m, n) and (m + 2, n + k) are two points on the line with the equation x = 2y + 5 they should satisfy m=2n +5 and m+3 =2 *(n+k)+5.   By 1st equation we have m-2n=5 and by 2nd equation m-2n = 2k+2 ---> 5=2k+2 --->k=3/2.   The answer is, therefore, (3/2).
Answer: D
A person purchased a TV set for Rs. 16000 and a DVD player for Rs. 6250. He sold both the items together for Rs. 31150. What percentage of profit did he make?	Choose the correct option
A) 20% B) 96% C) 40% D) 75% E) 23%

Solution: The total CP = Rs. 16000 + Rs. 6250   = Rs. 22250 and SP = Rs. 31150   Profit(%)   = (31150 - 22250)/22250 * 100= 
(31150 - 22250)/22250 * 100 = 40
40%   Answer: 40%
Answer: C
A letter lock consists of four rings each marked with six different letters. The number of distinct unsuccessful attempts to open the lock is at the most ?	Choose the correct option.
A) 1340
B) 1290
C) 1295
D) 1288
E) 167

Solution: Since each ring consists of six different letters, the total number of attempts possible with the four rings is   = 6 * 6 * 6 * 6= 
6 * 6 * 6 * 6 = 1_296
1296. Of these attempts, one of them is a successful attempt.   Maximum number of unsuccessful attempts= 1296 - 1= 
1296 - 1 = 1_295
1295.   Answer: 1295
Answer: C
How many liters of water must be added to 20 liters of milk and water containing 10% water to make it 60% water?
Answers.
A) 12	B) 15	C) 18	D) 22	E) 25

Solution: By rule of alligation:   60% - 10% = 50%   100% - 60% 60  - 10= 
60  - 10 = 50
50%   100% - 60% = 40%   Quantity of pure water : Quantity of the mixture  100  - 60= 
 100  - 60 = 40
40%   Quantity of pure water : Quantity of the mixture= 5 : 4   There are 20 liters of mixture, so we need to add 25 liters of pure water.   The answer is 25.
Answer: E
(32323 + 7344 + 41330) - (317 x 91) = ?	Pick one:
A) 54210
B) 54250
C) 52150
D) None of these
E) 521500

Solution: Its speed and accuracy which decides the winner. You can use various methods including   Vedic mathematics to do complex calculations quickly.   (32323 + 7344 + 41330) - (317 x 91) = 80997 - 28847= 
80997 - 28847 = 52_150
52150   Answer is 52150
Answer: C
X divided by Y equals 54.36 what is a possible remainder?
Options:
A) 5
B) 26
C) 27
D) 34
E) 44

Solution: With the decimal being 36/100, the simplest form is 9/25. If the divisor is a multiple of 25, the remainder must be a multiple of 9. The only number that is so is 27. Answer 27.
Answer: C
Two trains 140 metre and 160 metre long run at the speed of 60 km/hr and 40 km/hr respectively in opposite direction on parallel tracks. What time these will take to cross each other ?	Choose the correct choice from the following answers:  A) 10.7 Seconds  B) 10.8 Seconds  C) 10.9 Seconds  D) 11.8 Seconds  E) None of these

Solution: Explanation:   Relative Speed = 60+40= 
60+40 = 100
100 Kmph= 100*(5/18) = 250/9 m/sec   Distance to be covered = 140 + 160= 
140 + 160 = 300
300 metres   Time= Distance/Speed   Time=300∗9/250=54/5= 
54/5 = 54/5 = around 10.8
10.8 seconds   Option 10.8 Seconds
Answer: B
The perimeter of a square is equal to the perimeter of a rectangle of length 18 cm and breadth 14 cm. Find the circumference of a semicircle whose diameter is equal to the side of the square. (Round off your answer to two decimal places)  Choose one:  A) 23.57  B) 23.54  C) 23.5  D) 24.55  E) 25.14

Solution: Let the side of the square be a cm.   Perimeter of the rectangle = 2(18 + 14) = 64 cm   Perimeter of the square = 64cm   i.e. 4a = 64   A = 16   Diameter of the semicircle = 16 cm   Circumference of the semicircle   = 1/2(∏)(16)   = 1/2(22/7)(16) = 25.14 cm to two decimal places   Answer: 25.14
Answer: E
How many positive integers less than 100 have a remainder of 5 when divided by 13? Choose the correct choice from the following:
A) 5  B) 7  C) 8  D) 9  E) 10

Solution: We have to include 5 also.As 13*0 + 5= 
13*0 + 5 = 5
5   If somebody says to divide 5 by 13 ,we will be telling we have 0 quotient and remainder as 5.   5nswer is 5
Answer: A
Anand and Deepak started a business investing Rs. 800 and Rs. 1200 respectively. Out of a total profit of Rs. 2000, Deepak's share is:
Choose the correct option
A) 3776
B) 2687
C) 1200
D) 2688
E) 2671

Solution: Ratio of their shares = 800 : 1200 = 2:3   Deepak's share = 2000 * 3/5 = Rs. 1200.   Answer: 1200
Answer: C
By what least number 4320 be multiplied to obtain a number which is a perfect cube?	Choose the correct choice from the following.
A) 15 B) 25 C) 30 D) 40 E) 50

Solution: Clearly, 4320 = 23 * 33 * 22 * 5.   To make it a perfect cube, it must be multiplied by 2 * 52   i.e,50.   ANSW50R 50 50
Answer: E
The product of all the prime numbers less than 27 is closest to which of the following powers of 10?  Choose the correct answer:
A) 10^9	B) 10^8	C) 10^7	D) 10^6	E) 10^5

Solution: OA: 10^8
Answer: B
A works thrice as much as B. If A takes 60 days less than B to do a work then find the number of days it would take to complete the work if both work together? Answers:  A) 22.5 days  B) 21.5 days  C) 23.5 days  D) 24.5 days  E) 25.5 days

Solution: if A finishes the job in x days   B finishes it in 3x days   3x = x + 60   thus   x = 30   in one hour   1/t = 1/30 + 1/90 = 4/90   where t is the number of days they finish the job together.   t = 90/4= 
90/4 = 45/2 = around 22.5
22.5 days   22.5 daysNSWER:22.5 days
Answer: A
1⁄5 of a number is equal to 5⁄8 of the second number. If 35 is added to the first number then it becomes 4 times of second number. What is the value of the second number? Choose the most appropriate option
A) 125 B) 70 C) 40 D) 25 E) None of these

Solution: Let x be the first number and y be the second number.   1⁄5x = 5⁄8y   \ x⁄y = 25⁄8......(i)   x + 35 = 4y   or, 25⁄8y + 35 = 4y   \ y = 40   Answee 40
Answer: C
Calculate the L.C.M of 7/10, 8/ 9, 3/8, 5/12 is :	Choose the correct option: A) 840 B) 70 C) 740 D) 140 E) 940

Solution: Required L.C.M =L.C.M. of 7, 8, 3, 5/H.C.F. of 10, 9, 8, 12 =840/1= 
840/1 = 840
840   840nswer is 840
Answer: A
A man can row a boat at 13 kmph in still water. If the speed of the stream is 5 kmph, what is the time taken to row a distance of 33 km downstream? Choose the correct choice from the following answers:
A) 11/3 B) 11/4 C) 11/5 D) 11/6 E) 11/7

Solution: Speed downstream = 13+5= 
13+5 = 18
18 kmph.   Time required to cover 60 km downstream= d/s = 33/18=11/6 hours. Answer:11/6
Answer: D
Find the compound interest and the amount on Rs.8000 at 5% per annum for 3 years when C.I is reckoned yearly?
Choose one:	A) 1261	B) 1632	C) 9177	D) 1682	E) 1672

Solution: 1261 = 8000(21/20)3   = 9261   = 8000   ---------   1261   1261nswer:1261
Answer: A
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 A revolutions per second, how many revilutions per minute does the larger rim makes in terms of A?
Choose the correct answer:	A) a) 48pi/A	B) b) 75m	C) c) 48A	D) d) 24A	E) e) A/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 A rev per sec so the inches coverd SR per sec = 28 * pi* A   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 X   Theis is in sec we need the answer in min so 48A   answer is c) 48A
Answer: C
The population of a town increased from 75,000 to 82,500 in a decade. The average percent increase of population per year is :
Answers:
A) 4.37% B) 5% C) 6% D) 1% E) None of these

Solution: Solution   Increase in 10 year= (82500 - 75000)= 
(82500 - 75000) = 7_500
7500.   Increase%=( 7500/75000x 100 )% = 10%   âˆ´ Required average = ( 10/10 )= 
( 10/10 ) = 1
1%   Answer 1%
Answer: D
P beats Q by 5 seconds in a race of 1000 m and Q beats R by 5 metres in a race of 100 m. By how many seconds does P beats R in a race of 1000 m?	Choose the correct answer.
A) 5 sec B) 7 sec C) 10 sec D) Can't be determined E) None of these

Solution: Explanation :   If P takes t seconds to run 1000 m, then Q takes (t+5) sec.   In (t+5) sec Q runs 100 m whereas R runs only 950 m.   R runs 1000 m in (1000/950)x(t+5)sec.   P takes t seconds to cover 1000m , while R takes (20t/19+100/95)sec.   From the data given, we cannot determine t .   Answer : Can't be determined
Answer: D
An artist wishes to paint a circular region on a square poster that is 4 feet on a side. If the area of the circular region is to be 1/2 the area of the poster, what must be the radius of the circular region in feet?	Answers:  A) 1/pi  B) sqrt(8/pi)  C) 1  D) 2/sqrt(pi)  E) pi/2

Solution: Area of the poster is 4x4 = 16   1/2 the area = 8   pi*r^2 = 8   r^2 = 8/pi   r = sqrt(8/pi) answer : 1
Answer: C
A certain machine produces 850 units of product P per hour. Working continuously at this constant rate, this machine will produce how many units of product P in 7 days?  Choose the most appropriate option:
A) 7,000
B) 24,000
C) 40,000
D) 142,800
E) 168,000

Solution: Since 7 days consist of 24*7 hours the total hours of a week is 168 hours.   Since every hour the machine produces 850 units of product P the total product during 168 hours is 850*168=142,800.   Correct Option : 142,800
Answer: D
A and B began business with Rs.6000 and Rs.4000 after 8 months, A withdraws Rs.1000 and B advances Rs.1000 more. At the end of the year, their profits amounted to Rs.630 find the share of B. Choose the correct choice from the following answers:
A) 240	B) 288	C) 273	D) 877	E) 361

Solution: (6*8 + 5*4):(4*8 + 5*4)   17:13   13/30 * 630= 
13/30 * 630 = 273
273   Answer: 273
Answer: C
Length of a rectangular plot is 60 mtr more than its breadth. If the cost of fencing the plot at 26.50 per meter is Rs. 5300, what is the length of the plot in mtr? Choose the correct choice from the following options:
A) 46 m  B) 60 m  C) 58 m  D) 78 m  E) 80 m

Solution: Let breadth = x metres.   Then, length = (x + 60) metres.   Perimeter = 5300/26.5= 
5300/26.5 = 200
200 m.   2[(x + 60) + x]= 200   2x + 60 = 100   2x = 40   x = 20.   Hence, length = x + 60 = 80 m   80 m
Answer: E
Sum of two numbers is 20. Two times of the first exceeds by 5 from the three times of the other. Then the numbers will be? Choose the correct answer:
A) A)5	B) B)9	C) C)11	D) D)13	E) E)15

Solution: Explanation:   x + y = 20   2x – 3y = 5   x = 13 y = 7   13)
Answer: D
A 10000 liter tank, half-full of water is being filled from a pipe with a flow rate of 1 kiloliter every 2 minutes. At the same time, the tank is losing water from two drains at a rate of 1 kiloliter every 4 minutes and every 6 minutes. How many minutes does it take to fill the tank completely?	Choose one.
A) 8	B) 12	C) 18	D) 24	E) 60

Solution: In: we have: 1,000/2min = 500 litres per minute   Out: we have: 1,000/4 + 1,000/6   Then do: IN - OUT to figure out the net inflow per minute (you get 83.3). Then divide the total number of litres you need (5,000 by that net inflow to get the minutes) - 60 min. Answer 60.
Answer: E
Jerry wrote down all the positive integers that have at most 7 digits and
contain only the digits 0 and 1. How many times did he write down the
digit 1 ?  Choose one:	A) 128	B) 224	C) 288	D) 448	E) 512

Solution: Jerry wrote down a total of 27 − 1 = 127 numbers (0 is missing). Add 0 to the   numbers Jerry wrote. We divide the resulting 128 numbers in pairs. If x is one of the   numbers Jerry wrote then we put it in pair with 1111111 − x (whose digits are also 0s   and 1s). For example 1100101 is paired with 11010. In this way, we divide the numbers   into 64 distinct pairs so that each number appears exactly once. Note that there are   exactly 7 digits 1 in each pair. So, Jerry wrote the digit 1 exactly 64 × 7 = 448 times.   correct answer 448
Answer: D
Let f(x) = x^2 + bx + c. If f(3) = 0 and f(-3) = 0, then b + c =
Pick one
A) 18 B) 15 C) -15 D) -21 E) -9

Solution: f(x) = x^2 + bx + c. If f(3) = 0 and f(-3) = 0, then b + c =   f(3) = 0= 9+3b+c--- Taking 9 to the other side   -> 3b+c= -9   f(-3) = 0= 9-3b+c --- taking -3b+c to the other side   -> 3b-c=9   When we add these 2 equations, we get 6b= 0---> b= 0   And while substituting b= 0 we get c= -9.   b+c= -9--- Answer -9
Answer: E
The H.C.F. of two numbers is 30 and the other two factors of their L.C.M. are 25 and 24. The larger of the two numbers is
Choose one
A) 276  B) 799  C) 712  D) 750  E) None

Solution: Solution   Clearly, the numbers are (30 x 25) and (30 x 24).   Larger number = (30 x 25)	= 750.   Answer 750
Answer: D
The least number of complete years in which a sum of money put out at 20% compound interest will be more than doubled is	Options.
A) 4 years	B) 5 years	C) 6 years	D) 7 years	E) 8 years

Solution: Explanation:   4 yearss per question we need something like following   P(1+R/100)n>2P   (1+20/100)n>2   (6/5)n>2   6/5×6/5×6/5×6/5>2   So answer is 4 years   Option 4 years
Answer: A
Divide Rs. 1100 among A, B and C so that A receives 1/3 as much as B and C together and B receives 2/3 as A and C together. A's share is? Choose the correct choice from the following options: A) s.800 B) s.400 C) s.600 D) s.900 E) s.1100

Solution: A+B+C = 1100   A = 1/3(B+C); B = 2/3(A+C)   A/(B+C) = 1/3   A = 1/4 * 1100= 
1/4 * 1100 = 275
> 275   ANSWs.1100R:s.1100
Answer: E