divelab/Sys2Bench huggingface dataset:
Question: A ladder 14 feet long is leaning against a wall that is perpendicular to level ground. The bottom of the ladder is 5 feet from the base of the wall. If the top of the ladder slips down 4 feet, how many feet will the bottom of the ladder slip?
Options:
A)4
B)5
C)8
D)10.72
E)15
Rationale: 14^2-5^2=171
it means that the height is equal to 13.07~=13.
since the top of the ladder slips down 4 feet, then the height of the wall =13-4=9
the bottom =sqrt(14^2-9^2)=sqrt(196-81)=10.72
ans is D
Answer: D
Question: An athlete runs 200 meters race in 10sec. His speed is?
Options:
A)20km/hr
B)15km/hr
C)30km/hr
D)72km/hr
E)40km/hr
Rationale: speed = 200/10 = 20 m/sec
= 20 * 18/5 km/hr = 72km/hr
Answer is D
Answer: D
Question: What is the compound interest paid on a sum of Rs.3000 for the period of 3 years at 10% per annum.
Options:
A)900
B)930
C)990
D)993
E)None of these
Rationale: Solution= Interest % for 1st year= 10
Interest % for 2nd year= 10+ 10% of 10= 10+ 10 *10/100=11
Interest % for 3rd year= 10+ 10%(10+11)=10+ 2.1=12.1
Total % of interest= 10 + 11+12.1=33.1
Total interest = 33.1 % 3000= 3000 * (33.1/100)= 993
Answer D
Answer: D
Question: A ball is bought for Rs.400 and sold at a gain of 20% find its selling price
Options:
A)Rs.400/-
B)Rs.480/-
C)Rs.500/-
D)Rs.520/-
E)Rs.540/-
Rationale: 100 % ------> 400 (100 * 4 = 400)
120 % ------> 480 (120 * 4 = 480)
Selling price = Rs.480/-
B
Answer: B
Question: In a certain apartment building, there are one-bedroom and two-bedroom apartments. The rental prices of the apartment depend on a number of factors, but on average, two-bedroom apartments have higher rental prices than do one-bedroom apartments. Let M be the average rental price for all apartments in the building. If M is $2,800 higher than the average rental price for all one-bedroom apartments, and if the average rental price for all two-bedroom apartments is $8,400 higher that M, then what percentage of apartments in the building are two-bedroom apartments?
Options:
A)30%
B)35%
C)25%
D)40%
E)50%
Rationale: Ratio of 2 Bedroom Apartment: 1 Bedroom Apartment = 2800 : 8400 -----> 1 : 3
Let total number of Apartments be X
No. of 2 Bedroom Apartment = (1 / 4) * X
percentage of apartments in the building are two-bedroom apartments ---->
(1/4) * 100 ---> 25%
Answer : C
Answer: C
Question: A rectangular-shaped carpet that measures x feet by y feet is priced at $18. What is the cost of the carpet, in dollars per square yard? (1 square yard = 9 square feet)
Options:
A)180xy
B)162/(xy)
C)20xy
D)20xy/9
E)xy/180
Rationale: The area of the carpet in feet is xy.
The area in square yards is xy / 9.
The price per square yard is 18 / (xy/9) = 162/(xy).
The answer is B.
Answer: B
Question: What is the difference between the place value of 2 in the numeral 7449?
Options:
A)360
B)165
C)180
D)190
E)200
Rationale: Answer: Option 'A'
400 - 40 = 360
Answer: A
Question: Of the four numbers, whose average is 60, the first is one-fourth of the sum of the last three. The first number is :
Options:
A)17
B)29
C)36
D)48
E)58
Rationale: Explanation:
Let the first number be x,
Then, sum of the four numbers = x + 4x = 5x.
so, 5x/4 = 60 or x = (60 * 4) / 5 = 48. Answer: D
Answer: D
Question: During a certain week, a seal ate 40% of the first 80 smelt it came across, and 30% of the remaining smelt it came across. If the seal ate 40% of the smelt it came across during the entire week, how many smelt did it eat?
Options:
A)32
B)40
C)55
D)64
E)80
Rationale: Total smelt = x.
Then, 0.4*80+0.3(x-80)=0.4*x --> x=80 --> 0.4*x=32
Answer: A.
Answer: A
Question: If 14m − n = p, then which of the following represents the average (arithmetic mean) of m, n, and p, in terms of m?
Options:
A)2m −1
B)4m
C)5m
D)m/5
E)6m/5
Rationale: 14m - n = p
Add n to both sides:
14m = n + p
Add m to both sides:
15m = n + p + m
Now, divide both sides by 3
5m = (n + p + m)/3 = the average of n, p, and m
C
Answer: C
Question: It takes eight hours for a 600 km journey, if 120 km is done by train and the rest by car. It takes 20 minutes more, if 200 km is done by train and the rest by car. The ratio of the speed of the train to that of the cars is:
Options:
A)2 : 3
B)3 : 2
C)3 : 4
D)4 : 3
E)2 : 1
Rationale: Explanation:
Let the speed of the train be x km/hr and that of the car be y km/hr.
Then,	120/x+480/y=8 =>1/x+4/y=1/15....(i)
And, 200/x+400/y=25/3	=>1/x+2/y=1/24....(ii)
Solving (i) and (ii), we get: x = 60 and y = 80.
Ratio of speeds = 60 : 80 = 3 : 4.
ANSWER IS C
Answer: C
Question: The average age of a husband and a wife is 23 years when they were married FOUR years ago but now the average age of the husband, wife and child is 19 years(the child was born during the interval). What is the present age of the child?
Options:
A)6
B)5
C)8
D)4
E)2
Rationale: 27 * 2 = 54
20 * 3 = 60
-----------
6 years.Answer: A
Answer: A
Question: John and David work at a hospital with 10 other workers. For an internal review, 2 of the 10 workers will be randomly chosen to be interviewed. What is the probability that John and David will both be chosen?
Options:
A)1/45
B)1/35
C)1/25
D)1/15
E)1/10
Rationale: Probability that John and David will both be chosen out of 8 workers
= (2/10)*(1/9)
= 1/45
Answer A
Answer: A
Question: If x is a positive, single-digit integer such that 4/3*x, 2x, x, and x + 2, and 3x – 2 form a non-ordered list of consecutive integers, which of the following could be the median of that list?
Options:
A)3
B)4
C)5
D)6
E)8
Rationale: Soln:
Given that x is positive and single digit and based on 4/3*x being one of them,
Assume x as 3
this gives the list as 4, 6, 3, 5, 7
when ordered, 3,4,5,6,7
hence median is 5
Answer is C
Answer: C
Question: In May, the groundskeeper at Spring Lake Golf Club built a circular green with an area of 95π square feet. In August, the groundskeeper doubled the distance from the center of the green to the edge of the green. What is the total area of the renovated green?
Options:
A)190π
B)210π
C)240π
D)320π
E)380π
Rationale: Area = πR^2, so doubling the radius results in an area that is 4 times the original area.
4(95π) = 380π
The answer is E.
Answer: E
Question: If a < b < c , which of the following must be true?
(I) a^2 < b^2
(II) b − a < c
(III) a^2 < b^2 < c^2
Options:
A)None
B)I only
C)II only
D)III only
E)II and III
Rationale: (I) a^2 < b^2. Not necessarily true fractions: try a=0.1 and b=0.2.
(II) b − a < c. Not necessarily true: try a=-1, b=0, and c=1.
(III) a^2 < b^2 < c^2. Not necessarily true: try a=-1, b=0, and c=1.
None of the options must be true.
Answer: A.
Answer: A
Question: A bag contains 23 purple jellybeans, 12 green jellybeans, and 15 yellow jellybeans; these jellybeans are the only items in the bag. If a person picks a jellybean at random out of the bag, what is the probability that the jellybean will be green?
Options:
A)15%
B)20%
C)24%
D)30%
E)35%
Rationale: p = 23 , g=12 , y=15
total = 50
p(green)=(12/50)*100 = 24% . Ans = C
Answer: C
Question: A cistern can be filled by a tap in 4 hours while it can be emptied by another tap in 9 hours. If both the taps are opened simultaneously, then after how much time will the cistern get filled ?
Options:
A)4.5 hrs
B)5 hrs
C)6.5 hrs
D)7.2 hrs
E)9.2 hrs
Rationale: Net part filled in 1 hour= 1/4 -1/9= 5/36
Therefore the cistern will be filled in 36/5 hours or 7.2 hours.
ANSWER:D
Answer: D
Question: A lady grows Cauliflower in her garden that is in the shape of a square. Each Cauliflower takes 1 square foot of area in her garden. This year, she has increased her output by 223 Cauliflower when compared to last year. The shape of the area used for growing the Cauliflower has remained a square in both these years. How many Cauliflowers did she produce this year?
Options:
A)12541
B)12542
C)12544
D)12545
E)Cannot be determined
Rationale: Explanatory Answer
The shape of the area used for growing Cauliflower has remained a square in both the years.
Let the side of the square area used for growing Cauliflower this year be X ft.
Therefore, the area of the ground used for cultivation this year = X2 sq.ft.
Let the side of the square area used for growing Cauliflower last year be Y ft.
Therefore, the area of the ground used for cultivation last year = Y2 sq.ft.
As the number of Cauliflower grown has increased by 223, the area would have increased by 223 sq ft because each Cauliflower takes 1 sq ft space.
Hence, X2 - Y2 = 223
(X + Y)(X - Y) = 223.
223 is a prime number and hence it will have only two factors. i.e., 223 and 1.
Therefore, 223 can be expressed as product of 2 numbers in only way = 223* 1
i.e., (X + Y)(X - Y) = 223 * 1
So, (X + Y) should be 223 and (X - Y) should be 1.
Solving the two equations we get X = 112 and Y = 111.
Therefore, number of Cauliflower produced this year = X2 = 1122 = 12544.
Alternative Approach : Use answer choices
The area in both the years are squares of two numbers.
That rules out choice A,B and D. as 12541,12542 and 12545 are not the square of any number.
Check Choice C: If this year's produce is 12544, last year's produce would have been 12544 - 223 = 12321
12321 is the square of 111.
So, 12544 is the answer.
Choice C.
Answer: C
Question: If f and g are distinct prime numbers less than 10, which of the following cannot be the product of f and g?
Options:
A)6
B)9
C)10
D)14
E)15
Rationale: prime numbers less than 10 are 2, 3, 5, 7
all except 9 is product of any two numbers picked from above set.
Ans: B
Answer: B
Question: Each cell of a certain kind of bacteria produces two more cells. The life span of each cell is 10 minutes and each cell multiples only once in its life time, when it is exactly one minute old. If a new cell is placed in an empty box at time t = 0, then how many live cells will be there in the box just after t = 20 minutes?
Options:
A)2048 × 1023
B)1024 × 1023
C)(1024)²
D)1023 × 1025
E)1023 × 1026
Rationale: see total cells created after
1min be 2^1
2min be 2^2
3 min be 2^3.......
thus after 20 min 2^20 will be created
now after 10 min 1 cell will die (2^0)
after 11 min 2 cells die (2^1)
similarly after 20 min 2^10 cells die
thus total cells remained=(2^20)-(1024)
or (1024)^2-1024
or1024*(1024-1)
i.e, 1024*1023
ANSWER:B
Answer: B
Question: Two twins sisters Sita and Geeta were standing back to back and suddenly they started running in opposite directions for 6 km each. Then they turned left and ran for another 4.5 km.
What is the distance (in kilometers) between the the two twins when they stop?
Options:
A)12
B)15
C)18
D)21
E)24
Rationale: The distance between them is the hypotenuse of a right angle triangle with sides 9 km and 12 km.
hypotenuse = sqrt(9^2 + 12^2) = 15
The answer is B.
Answer: B
Question: In a certain alphabet, 13 letters contain a dot and a straight line. 24 letters contain a straight line but do not contain a dot. If that alphabet has 40 letters, all of which contain either a dot or a straight line or both, how many letters contain a dot but do not contain a straight line?
Options:
A)3
B)8
C)14
D)20
E)28
Rationale: We are told that all of the letters contain either a dot or a straight line or both, which implies that there are no letters without a dot and a line (no line/no dot box = 0).
First we find the total # of letters with lines: 13 +24 = 37;
Next, we find the total # of letters without line: 40 - 37 = 3;
Finally, we find the # of letters that contain a dot but do not contain a straight line:3 - 0 = 3.
A
Answer: A
Question: 24 is divided into two parts such that 7 times the first part added to 5 times the second part gives 146. The first part is
Options:
A)11
B)13
C)16
D)17
E)None
Rationale: Explanation:
Let the first and second parts be a and 24 a, then
7a+5(24−a)=146
⇒7a+120−5a=146
⇒2a=26 or a = 13
Correct Option: B
Answer: B
Question: If a code word is defined to be a sequence of different letters chosen from the 10 letters A, B, C, D, E, F, G, H, I, and J, what is the ratio of the number of 6-letter code words to the number of 4-letter code words?
Options:
A)5 to 4
B)30 to 1
C)2 to 1
D)5 to 1
E)6 to 1
Rationale: Number of ways to form 6-letter code: 10!/4! = 10*9*8*7*6*5
Number of ways to form 4-letter code: 10!/6! = 10*9*8*7
Ratio: 30 to 1
Answer : B
Answer: B
Question: An amount of Rs. 3000 becomes Rs. 3600 in four years at simple interest. If the rate of interest was 1% more, then what was be the total amount?
Options:
A)3729
B)2799
C)3720
D)2884
E)2881
Rationale: A = P(1 + TR/100)
=> 3600 = 3000[1 + (4 * R)/100] => R = 5%
Now R = 6%
=> A = 3000[1 + (4 * 6)/100] = Rs. 3720.
Answer:C
Answer: C
Question: Jaime earned enough money by selling seashells at 22 cents each to buy several used paperback books at 55 cents each. If he spent all of the money he earned selling seashells to buy the books, what is the least number of seashells he could have sold ?
Options:
A)5
B)11
C)17
D)25
E)30
Rationale: Let's TEST Answer A: 5 seashells...
With 5 seashells, Jamie would have 5(22) = 110 cents. This would allow him to buy 2 books for 110 cents total, so this is the correct answer.
A
Answer: A
Question: Which number is the odd one out ?
9654 4832 5945 7642 7963 8216 3646
Options:
A)3646
B)9654
C)5945
D)7963
E)8216
Rationale: The product of first two digits in a number equals the last two digits, except in 3646. Hence, it is the odd one.
The answer is 3646.
ANSWER:A
Answer: A
Question: Mr. Karan borrowed a certain amount at 6% per annum simple interest for 9 years. After 9 years, he returned Rs. 8410/-. Find out the amount that he borrowed.
Options:
A)s. 5266
B)s. 5269
C)s. 5461
D)s. 5218
E)s. 52192
Rationale: Explanation:
Let us assume Mr. Karan borrowed amount is Rs. A. (the principal)
By formula of simple interest, S.I. = PRT / 100
Where P = The principal, R = Rate of interest as a %, T = Time in years
S.I. = (P * 6 * 9)/100 = 54 P/100
Amount = Principal + S.I.
8410 = P + (54P/100)
8410 = (100P + 54P)/100
8410 = 154P/100
P = (8410 * 100)/154 = Rs. 5461.039
ANSWER: C
Answer: C
Question: If 15648 books need to be placed in boxes and each box can contain at most 9 books. How many books will be in the last unfilled box?
Options:
8
Options:
A)12 books
B)6 books
C)24 books
D)18 books
E)5 books
Rationale: The number of books that can be placed in boxes of 9 books is the first number that is divisible by 9 that occurs before 15648.
In order to divide the sum in 9 parts, the amount must be divisible by 9
Divisibility rule of 9: The sum of the digits must be divisible by 9
Sum of digits of 15648 =24 and 18 is divisible by 9.
Hence, we need to remove 6 to this number for it to be divisible by 9
Correct Option:B
Answer: B
Question: The simple interest at x% for x years will be Rs. x on a sum of:
Options:
A)x
B)x^2
C)100x
D)100x^2
E)50x^2
Rationale: Explanation :
P = ?
R = x%
Simple Interest,SI = x
T = x years
P=100× SI/RT=100 × x / x × x=100/x
Answer : Option C
Answer: C
Question: For an integer n greater than 1, n* denotes the product of all the integers from 1 to n inclusive. How many prime numbers are there between 7*+2 and 7*+7, inclusive ?
Options:
A)0
B)1
C)2
D)3
E)4
Rationale: Given that n* denotes the product of all the integers from 1 to n, inclusive so, 7* + 2 = 7! + 2 and 7* + 7 = 7! + 7.
Now, notice that we can factor out 2 our of 7! + 2 so it cannot be a prime number, we can factor out 3 our of 7! + 3 so it cannot be a prime number, we can factor out 4 our of 7! + 4 so it cannot be a prime number, ... The same way for all numbers between 7! + 2 and 7! +7, inclusive. Which means that there are no primes in this range.
Answer: A.
Answer: A
Question: What will be the cost of building a fence around a square plot with area equal to 289 sq ft, if the price per foot of building the fence is Rs. 54?
Options:
A)3672
B)920
C)7290
D)6928
E)3729
Rationale: Explanation:
Let the side of the square plot be a ft.
a2 = 289 => a = 17
Length of the fence = Perimeter of the plot = 4a = 68 ft.
Cost of building the fence = 68 * 54 = Rs. 3672.
Answer: Option A
Answer: A
Question: If the time is currently 1:30 pm, what time will it be in exactly 646 hours?
Options:
A)11:30 am
B)12:30 pm
C)1:30 pm
D)2:30 pm
E)3:30 pm
Rationale: 646 = 26(24) + 22/24
The time will be 22 hours later than 1:30 pm which is 11:30 am.
The answer is A.
Answer: A
Question: A train 250 m long passed a pole in 25 sec. How long will it take to pass a platform 650 m long?
Options:
A)90 sec
B)89 sec
C)54 sec
D)27 sec
E)22 sec
Rationale: Speed = 250/25 = 10 m/sec.
Required time = (250 + 650)/10
= 90 sec.
Answer: A
Answer: A
Question: A barrel full of beer has 2 taps one midway,,which draw a litre in 6 minutes and the other at the bottom,which draws a litre in 4 minutes. The lower tap is lower normally used after the level of beer in the barrel is lower than midway.The capacity of the barrel is 36 litres. A new assistant opens the lower tap when the barrel is full and draws out some beer. As a result the lower tap has been used 24 minutes before the usual time. For how long was the beer drawn out by the new assistant ?
Options:
A)15 minutes
B)16 minutes
C)17 minutes
D)18 minutes
E)None of these
Rationale: Sol. The top tab is operational till 18 litres is drawn out.
∴ Time after which the lower tap is usually open
= 18 × 6 = 108 minutes
∴ Time after which it is open now = 108 – 24 = 84 minutes
∴ Litres drawn = 84/6 = 14 litres
∴ 18 – 14 = 4 litres were drawn by the new assistant.
∴ Time = 4 × 4 = 16 minutes Answer B
Answer: B
Question: One side of a rectangle is 3 cm shorter than the other side. If we increase the length of each side by 1 cm, then the area of the rectangle will increase by 16 cm2. Find the lengths of all sides.
Options:
A)10 and 3
B)9 and 6
C)10 and 7
D)3 and 10
E)10 and 10
Rationale: Let x be the length of the longer side x>3, then the other side's length is x−3 cm. Then the area is S1 = x(x - 3) cm2. After we increase the lengths of the sides they will become (x+1) and (x−3+1)=(x−2) cm long. Hence the area of the new rectangle will be A2=(x+1)⋅(x−2) cm2, which is 16 cm2 more than the first area. Therefore
A1+16=A2
x(x−3)+16=(x+1)(x−2)
x2−3x+16=x2+x−2x−2
2x=18
x=9. So, the sides of the rectangle are 9 cm and (9−3)=6 cm long.
So answer is B.
Answer: B
Question: Jim drove 768 miles of a 1200 miles journey. How many more miles does he need to drive to finish his journey?
Options:
A)432 miles
B)532 miles
C)632 miles
D)732 miles
E)832 miles
Rationale: The number of miles to drive to finish his journey is given by
1200 - 768 = 432 miles
correct answer A
Answer: A
Question: The value of 2*x+x/4+ x(xx) when x = 4 is:
Options:
A)57
B)63
C)75
D)73
E)45
Rationale: 2*x+x/4+ x(xx)
2*4+4/4+4(4*4)
2*4+4/4+4(16)
2*4+4/4+64
2*4+1+64
8+1+64=73
answer D
Answer: D
Question: In the sequence S, each term after the first is twice the previous term. If the first term of sequence S is 3, what is the sum of the 14th, 15th, 16th, 17th and 18th terms in sequence S?
Options:
A)3(2^16)
B)9(2^15)
C)21(2^14)
D)9(2^14)
E)63(2^13)
Rationale: The terms in the sequence can be shown as
a(n) = 2* a(n-1)
So, the sequence will look like: 3, 2*3, (2^2) *3,...
And the nth term will be given as 2^(n-1) *3
Therefore, a(14) = (2^13)*3, a(15) = (2^14) *3, a(16) = (2^15) *3, a(17) = (2^16) *3 and a(18) = (2^17) *3
So, a(14) + a(15) + a(16)+ a(17)+ a(18) = (2^13) *3 + (2^14) *3 + (2^15) *3+ (2^16) *3+ (2^17) *3
= 3* (2^13) *(1+2+4+8+16) = 3* (2^13) *31
= 63 * (2^13)
Answer : E
Answer: E
Question: The length of the bridge, which a train 130 m long and traveling at 45 km/hr can cross in 30 sec is?
Options:
A)165 m
B)886 m
C)245 m
D)286 m
E)281 m
Rationale: Speed = 45 * 5/18
= 25/2 m/sec.
Time = 30 sec
Let the length of bridge be x meters.
Then, (130 + x)/30
= 25/2
x = 245 m.
Answer: C
Answer: C
Question: The radius of a cylindrical vessel is 9cm and height is 3cm. Find the whole surface of the cylinder?
Options:
A)308 sq cm
B)220 sq cm
C)440 sq cm
D)132 sq cm
E)678.8 sq cm
Rationale: r = 9 h = 3
2πr(h + r) = 2 * 22/7 * 9(12) = 678.8
ANSWER:E
Answer: E
Question: The ratio of red boxes to blue boxes in a certain warehouse is 5 to 25. If the number of the red boxes were doubled and the number of blue boxes were increased by 150 the ratio would be halved. How many total boxes are in the warehouse?
Options:
A)60
B)74
C)111
D)148
E)244
Rationale: Ratio = R/B = 5/25 or R = 5/25 B -----------(1)
2R/B+150 = 5/25*1/2 = 1/10 or we can say that 20R=B+150 -------------(2)
solving (1) and (2) we get
B=50 and R =10
so total boxes is B + R = 50+10=60
Hence A. 60 is the correct answer
Answer: A
Question: There are 5 locks and 5 keys and each of the 5 keys matches each of the 5 locks. What is the minimum and the maximum trial numbers of attempts R needed to confirm that each of the 5 keys matches each of the 5 locks?
Options:
A)5,15
B)4,15
C)5,10
D)4,10
E)5,20
Rationale: Assume you have locks 1-5 and keys A-E.
Minimum: assume you are lucky to find the correct key/combo on the first try. So, 1 -> A, 2 -> B, 3 ->C, and 4 -> D, then 5 must match with E. Therefore, you only need to try 4 combos at a minimum.
Maximum: assume that it takes as many guesses as possible. So, with the first key you try A, B, C, and D with no success, therefore E must be the match (so 4 attempts). For key 2 you no longer have E available so you try A, B, and C, with no success, therefore D must be the match (3 attempts). And so on for key 3 (2 attempts) and key 4 (1 attempt). Key 5 matches with the remaining lock for a total of R=4 + 3 + 2 + 1 = 10 attempts.D
Answer: D
Question: A train 100 m in length crosses a telegraph post in 12 seconds. The speed of the train is?
Options:
A)16 kmph
B)30 kmph
C)54 kmph
D)18 kmph
E)19 kmph
Rationale: S = 100/12 * 18/5
= 30 kmph
Answer: B
Answer: B
Question: a,b and c are positive integers less than or equal to 9. If a,b and c are assembled into the six-digit number abcabc, which of the following must be a factor of abcabc?
Options:
A)7
B)9
C)11
D)3
E)none of these
Rationale: The sum of the digits in place 1,3 and 5 is a+c+b is equal to the sum of the digits in place 2,4 and 6 which is b+a+c. thus the number abcabc is divisible by 11. thus 11 must be a factor of abcabc.
Answer: C
Answer: C
Question: If p and q are positive integers each greater than 1, and 17(p+1)=20(q+1), what is the least possible value of p+q?
Options:
A)35
B)42
C)44
D)46
E)none
Rationale: 17(p+1)=29(q+1) --> (p+1)/(q+1) = 20/17 --> the least positive value of p+1 is 20, so the least value of p is 19 and the least positive value of q+1 is 17, so the least value of q is 16 --> the least value of p+q is 19+16=35.
Answer: A
Answer: A
Question: JOHN and ANDREW can finish John work 30 days if they work together. They worked together for 20 days and then ANDREW left. JOHN finished the remaining work in another 20 days. In how many days JOHN alone can finish the work?
Options:
A)40
B)50
C)55
D)58
E)60
Rationale: Amount of work done by JOHN and ANDREW in 1 day = 1/30
Amount of work done by JOHN and ANDREW in 20 days = 20 × (1/30) = 20/30 = 2/3
Remaining work – 1 – 2/3 = 1/3
JOHN completes 1/3 work in 20 days
Amount of work JOHN can do in 1 day = (1/3)/20 = 1/60
=> JOHN can complete the work in 60 days
E
Answer: E
Question: Stacy has a 81 page history paper due in 3 days. How many pages per day would she have to write to finish on time?
Options:
A)9
B)27
C)10
D)8.5
E)6
Rationale: 81/3=27
Answer : B
Answer: B
Question: The compound interest earned by Sunil on a certain amount at the end of two years at the rate of 8% p.a. was Rs.2828.80. Find the total amount that Sunil got back at the end of two years in the form of principal plus interest earned.
Options:
A)19828.77
B)19828.8
C)19828.82
D)19888.82
E)19828.22
Rationale: Let the sum be Rs.P
P{ [ 1 + 8/100]2 - 1 } = 2828.80
P(8/100)(2 + 8/100) = 2828.80 [a2 - b2 = (a - b) ( a + b)] P = 2828.80 / (0.08)(2.08) = 1360/0.08 = 17000 Principal + Interest = Rs. 19828.80
Answer: B
Answer: B
Question: The area of a square field 3136 sq m, if the length of cost of drawing barbed wire 3 m around the field at the rate of Rs.1 per meter. Two gates of 1 m width each are to be left for entrance. What is the total cost?
Options:
A)399
B)272
C)666
D)277
E)311
Rationale: Answer: Option C
Explanation:
a2 = 3136 => a = 56
56 * 4 * 3 = 672 â€“ 6 = 666 * 1 = 666 Answer: C
Answer: C