mathewhe/aqua_rat huggingface dataset:
Question: A frame 2 inches wide is placed around a rectangular picture with dimensions 8 inches by 12 inches. What is the area of the frame, in square inches?
(A) 44
(B) 96
(C) 128
(D) 144
(E) 168
Rationale: A frame 2 inches wide is placed around a rectangular picture with dimensions 8 inches by 12 inches. What is the area of the frame, in square inches?
(12*16)-(8*12) = 96
ANSWER:B
Answer: (B) 96
Question: How many liters of oil at Rs.40 per liter should be mixed with 240 liters of a second variety of oil at Rs.60 per liter so as to get a mixture whose cost is Rs.52 per liter?
(A) 120 liters
(B) 180 liters
(C) 110 liters
(D) 160 liters
(E) 170 liters
Rationale: Explanation:
=8:12=2:3
ANSWER IS D
Answer: (D) 160 liters
Question: A train 300 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 150 m long?
(A) 40
(B) 36
(C) 41
(D) 42
(E) 34
Rationale: Speed = 45 * 5/18 = 25/2 m/sec
Total distance covered = 300 + 150 = 450 m
Required time = 450 * 2/25 = 36 sec
Answer: Option B
Answer: (B) 36
Question: The maximum numbers of students among them 1001 pens and 910 pencils can be distributed in such a way that each student gets the same number of pens and same number of pencils is
(A) 91
(B) 910
(C) 1001
(D) 1911
(E) None
Rationale: olution
Required number of students.
= H.C.F of 1001 and 910.
‹=› 91.
Answer A
Answer: (A) 91
Question: What is the units digit of 26! + 50! + 4! + 4!?
(A) 8
(B) 6
(C) 4
(D) 2
(E) 0
Rationale: Let us first write down the factorials of different numbers:
1! = 1
2! = 2
3! = 6
4! = 24
5! = 120
6! = 720
and so on.
If we notice here, all the numbers after 4! will end with a 0.
Here is why:
If we multiply any number by 10, a 0 is added to that number
And a 10 is formed by a 5 and a 2, 10 = 5*2
Till 4!, we do not have a "5" in multiplication. But after that, we will have atleast one "5" in the multiplication.
Coming back to the question,
Units digit of 26! + 50! + 4! + 4! = ?
By the logic above, 26! and 50! will end in a "0"
4! will end in a 4
Hence the units digit = 0 + 0 + 4 + 4 = 8
Correct Option: A
Answer: (A) 8
Question: There are 13 South American countries, Annie has won a ticket to fly from Denver to one South American country and then directly to another South American Country before returning home to Denver again. Assuming there are four airports in each country, how many flights paths can Annie choose from?
(A) 13.12.11.10.4.4.
(B) 13.12.11.10.4
(C) 13.12.4.4.
(D) 13.12.4
(E) 13.13.13.13
Rationale: flights paths can Annie choose from There are 13 ways to chose the first destination,
then, 12 ways to chose next destination, with option of 4 airports (13x4)
then, to return he has 4 options to chose the airports
Thus, 13*12*4*4 ways.
Using permutations:
If the solution had written 13P1 instead of 13C1 it won't matter. As per the definition - making arrangements of the combinations gives permutations.
Since there are no arrangement for 1 item, permutationscombinations are equal.C
Answer: (C) 13.12.4.4.
Question: In the class of 50 students, 30 speak Tamil and 30 speak Telugu. What is the lowest possible number of students who
speak both the languages?
(A) A)8
(B) B)10
(C) C)20
(D) D)30
(E) E)32
Rationale: let the student who speaks tamil-x
let the student who speaks telugu-y
as (xuy)-(xny)=total
30+30-(xny)=50
=10
B)
Answer: (B) B)10
Question: 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:
(A) 9 1/5 days
(B) 9 3/5 days
(C) 9 2/5 days
(D) 10 days
(E) 10 1/5 days
Rationale: (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 B
Answer: (B) 9 3/5 days
Question: 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?
(A) 9
(B) 61
(C) 98
(D) 54
(E) 64
Rationale: Explanatory Answer
When a 5 cc cube is sliced into 1 cc cubes, we will get 5 * 5 * 5 = 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 = 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 = 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 = 54 such cubes.
Choice D is the correct answer.
Answer: (D) 54
Question: How many 3-digit numbers are completely divisible 6 ?
(A) 150
(B) 166
(C) 138
(D) 182
(E) 172
Rationale: 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) 150
Question: 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?
(A) 23
(B) 11
(C) 2
(D) 10
(E) 12
Rationale: 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: E
Answer: (E) 12
Question: 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]
(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
Rationale: The chinese ship sailed for 5 months i.e. 5Y miles @Y miles/month, therefore distance from Egyptian port is 5000-5Y. Since A is the only option with this value ...therefore A is the answer
Answer: (A) { (6Q)^2 + (5000-5y)^2 }^1/2
Question: J is 25% less than P and 20% less than T. T is t% less than P. What is the value of t?
(A) 93.5
(B) 90
(C) 6.75
(D) 6.25
(E) 2
Rationale: Usually We can solve every question of this type by choosing appropriate value of the Variable and deriving the value of other related variables.
Let, P = 400
then J = (75/100)*400 = 300
also J = (80/100)*T
i.e. T = 300*100/80 = 375
and T = [1-(t/100)]*P
i.e. 100-t = 100*T/P = 100*375/400 = 93.75
i.e. t = 6.25
Answer: Option D
Answer: (D) 6.25
Question: 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?
(A) 5
(B) 9
(C) 15
(D) 20
(E) 25
Rationale: 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
B
Answer: (B) 9
Question: 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 $28 and both types of chocolate were purchased in whole number of pounds, how many total pounds of chocolate she purchased?
(A) 9
(B) 8
(C) 10
(D) 12
(E) 15
Rationale: If there were all the expensive ones,3.5....
There would be 28/3.5 or 8 of them but since 2.8$ 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
Answer A..
Answer: (A) 9
Question: 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?
(A) $650
(B) $800
(C) $1300
(D) $400
(E) $900
Rationale: 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 B
Answer: (B) $800
Question: 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?
(A) 252
(B) 368
(C) 456
(D) 586
(E) 590
Rationale: 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=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
C
Answer: (C) 456
Question: The ratio of two numbers is 3:4 and their sum is 28. The greater of the two numbers is?
(A) 8
(B) 10
(C) 12
(D) 16
(E) 18
Rationale: 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)
D)
Answer: (D) 16
Question: 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?
(A) 8hrs
(B) 10hrs
(C) 12hrs
(D) 15hrs
(E) 6hrs
Rationale: 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 = 2 hrs
Time saved = 10-2 = 8 hrs
Answer is A
Answer: (A) 8hrs
Question: 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 ?
(A) 720
(B) 600
(C) 660
(D) 6000
(E) 6500
Rationale: 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.
Answer IS A
Answer: (A) 720
Question: 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?
(A) 480
(B) 997
(C) 266
(D) 288
(E) 611
Rationale: 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.
Answer: A
Answer: (A) 480
Question: 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?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: 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: E
Answer: (E) 5
Question: 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.
(A) (z-1)/2
(B) z/2
(C) z/(2-1)
(D) (z+1)/2
(E) z/(2+1)
Rationale: 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 D = (z-1)/2 => 7-1/2 = 4 , the number of positive integers
So, D is the answer
Answer: (D) (z+1)/2
Question: we need to carve out 125 identical cubes from a cube . what is the minimum number of cuts needed?
(A) 8
(B) 9
(C) 10
(D) 11
(E) 12 cuts
Rationale: 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.
ANSWER:E
Answer: (E) 12 cuts
Question: 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?
(A) 15 km/hr
(B) 16 km/hr
(C) 17 km/hr
(D) 21 km/hr
(E) None of these
Rationale: Explanation :
Total distance covered by B=28*6=168kmTotal time taken by A to cover same distance=2+6=8 hrsaverage speed of A=168/8=21 km/hr
Answer : D
Answer: (D) 21 km/hr
Question: A train moves with a speed of 189 kmph. Its speed in metres per second is
(A) 60.8
(B) 18
(C) 30
(D) 52.5
(E) None
Rationale: Solution
Speed	= 189 Kmph
= (189 x 5/18)m/sec
= 52.5 m/sec.
Answer D
Answer: (D) 52.5
Question: 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?
(A) 4:30pm
(B) 5:15pm
(C) 6:30pm
(D) 5:10pm
(E) 3:45pm
Rationale: 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:B
Answer: (B) 5:15pm
Question: 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 =
(A) 1/2
(B) 1
(C) 2
(D) 3/2
(E) 4
Rationale: 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, (D).
Answer: (D) 3/2
Question: 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?
(A) 20%
(B) 96%
(C) 40%
(D) 75%
(E) 23%
Rationale: The total CP = Rs. 16000 + Rs. 6250
= Rs. 22250 and SP = Rs. 31150
Profit(%)
= (31150 - 22250)/22250 * 100
= 40%
Answer: C
Answer: (C) 40%
Question: 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 ?
(A) 1340
(B) 1290
(C) 1295
(D) 1288
(E) 167
Rationale: Since each ring consists of six different letters, the total number of attempts possible with the four rings is
= 6 * 6 * 6 * 6= 1296. Of these attempts, one of them is a successful attempt.
Maximum number of unsuccessful attempts
= 1296 - 1
= 1295.
Answer: C
Answer: (C) 1295
Question: How many liters of water must be added to 20 liters of milk and water containing 10% water to make it 60% water?
(A) 12
(B) 15
(C) 18
(D) 22
(E) 25
Rationale: By rule of alligation:
60% - 10% = 50%
100% - 60% = 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 E.
Answer: (E) 25
Question: (32323 + 7344 + 41330) - (317 x 91) = ?
(A) 54210
(B) 54250
(C) 52150
(D) None of these
(E) 521500
Rationale: 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 = 52150
Answer is C
Answer: (C) 52150
Question: X divided by Y equals 54.36 what is a possible remainder?
(A) 5
(B) 26
(C) 27
(D) 34
(E) 44
Rationale: 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 C.
Answer: (C) 27
Question: 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 ?
(A) 10.7 Seconds
(B) 10.8 Seconds
(C) 10.9 Seconds
(D) 11.8 Seconds
(E) None of these
Rationale: Explanation:
Relative Speed = 60+40 = 100 Kmph
= 100*(5/18) = 250/9 m/sec
Distance to be covered = 140 + 160 = 300 metres
Time = Distance/Speed
Time=300∗9/250=54/5=10.8 seconds
Option B
Answer: (B) 10.8 Seconds
Question: 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)
(A) 23.57
(B) 23.54
(C) 23.5
(D) 24.55
(E) 25.14
Rationale: 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: E
Answer: (E) 25.14
Question: How many positive integers less than 100 have a remainder of 5 when divided by 13?
(A) 5
(B) 7
(C) 8
(D) 9
(E) 10
Rationale: We have to include 5 also.As 13*0 + 5 =5
If somebody says to divide 5 by 13 ,we will be telling we have 0 quotient and remainder as 5.
Answer is A
Answer: (A) 5
Question: 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:
(A) 3776
(B) 2687
(C) 1200
(D) 2688
(E) 2671
Rationale: Ratio of their shares = 800 : 1200 = 2:3
Deepak's share = 2000 * 3/5 = Rs. 1200.
Answer: C
Answer: (C) 1200
Question: By what least number 4320 be multiplied to obtain a number which is a perfect cube?
(A) 15
(B) 25
(C) 30
(D) 40
(E) 50
Rationale: Clearly, 4320 = 23 * 33 * 22 * 5.
To make it a perfect cube, it must be multiplied by 2 * 52
i.e,50.
ANSWER E 50
Answer: (E) 50
Question: The product of all the prime numbers less than 27 is closest to which of the following powers of 10?
(A) 10^9
(B) 10^8
(C) 10^7
(D) 10^6
(E) 10^5
Rationale: OA: B
Answer: (B) 10^8
Question: 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?
(A) 22.5 days
(B) 21.5 days
(C) 23.5 days
(D) 24.5 days
(E) 25.5 days
Rationale: 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 = 22.5 days
ANSWER:A
Answer: (A) 22.5 days
Question: 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?
(A) 125
(B) 70
(C) 40
(D) 25
(E) None of these
Rationale: 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 C
Answer: (C) 40
Question: Calculate the L.C.M of 7/10, 8/ 9, 3/8, 5/12 is :
(A) 840
(B) 70
(C) 740
(D) 140
(E) 940
Rationale: Required L.C.M =L.C.M. of 7, 8, 3, 5/H.C.F. of 10, 9, 8, 12 =840/1=840
Answer is A
Answer: (A) 840
Question: 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?
(A) 11/3
(B) 11/4
(C) 11/5
(D) 11/6
(E) 11/7
Rationale: Speed downstream = 13+5=18 kmph.
Time required to cover 60 km downstream = d/s = 33/18=11/6 hours. Answer:D
Answer: (D) 11/6
Question: Find the compound interest and the amount on Rs.8000 at 5% per annum for 3 years when C.I is reckoned yearly?
(A) 1261
(B) 1632
(C) 9177
(D) 1682
(E) 1672
Rationale: A = 8000(21/20)3
= 9261
= 8000
---------
1261
Answer:A
Answer: (A) 1261
Question: 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?
(A) a) 48pi/A
(B) b) 75m
(C) c) 48A
(D) d) 24A
(E) e) A/75
Rationale: 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
Answer: (C) c) 48A
Question: The population of a town increased from 75,000 to 82,500 in a decade. The average percent increase of population per year is :
(A) 4.37%
(B) 5%
(C) 6%
(D) 1%
(E) None of these
Rationale: Solution
Increase in 10 year= (82500 - 75000) = 7500.
Increase% =( 7500/75000x 100 )% = 10%
âˆ´ Required average = ( 10/10 )% = 1%
Answer D
Answer: (D) 1%
Question: 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?
(A) 5 sec
(B) 7 sec
(C) 10 sec
(D) Can't be determined
(E) None of these
Rationale: 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 : D
Answer: (D) Can't be determined
Question: 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?
(A) 1/pi
(B) sqrt(8/pi)
(C) 1
(D) 2/sqrt(pi)
(E) pi/2
Rationale: 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 : C
Answer: (C) 1
Question: 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?
(A) 7,000
(B) 24,000
(C) 40,000
(D) 142,800
(E) 168,000
Rationale: 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 : D
Answer: (D) 142,800
Question: 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.
(A) 240
(B) 288
(C) 273
(D) 877
(E) 361
Rationale: (6*8 + 5*4):(4*8 + 5*4)
17:13
13/30 * 630 = 273
Answer: C
Answer: (C) 273
Question: 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?
(A) 46 m
(B) 60 m
(C) 58 m
(D) 78 m
(E) 80 m
Rationale: Let breadth = x metres.
Then, length = (x + 60) metres.
Perimeter = 5300/26.5 m = 200 m.
2[(x + 60) + x] = 200
2x + 60 = 100
2x = 40
x = 20.
Hence, length = x + 60 = 80 m
E
Answer: (E) 80 m
Question: 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?
(A) A)5
(B) B)9
(C) C)11
(D) D)13
(E) E)15
Rationale: Explanation:
x + y = 20
2x – 3y = 5
x = 13 y = 7
D)
Answer: (D) D)13