divelab/Sys2Bench huggingface dataset:
Question: What is the total surface area in square meters of a rectangular solid whose length is 6 meters, width is 5 meters, and depth is 2 meters?
Options:
A)100 m2
B)104 m2
C)106 m2
D)108 m2
E)160 m2
Rationale: Surface Area of a cuboid = 2(lb+bh+lh) = 2(6*5+5*2+6*2)=2(30+10+12)=2*52=104 m2
Answer : B
Answer: B
Question: The probability that a visitor at the mall buys a pack of candy is 30%. If three visitors come to the mall today, what is the probability E that exactly two visitors will buy a pack of candy?
Options:
A)0.343
B)0.147
C)0.189
D)0.063
E)0.027
Rationale: 3C2 * (3/10)^2 * 7/10
= 3 * 9/100 * 7/10
= 189/1000
= 0.189=E
Answer - C
Answer: C
Question: How many necklace of 12 beads each can be made from 18 beads of different colours?
Options:
A)18!(6 x 29)
B)18!(6 x 21)
C)18!(6 x 24)
D)18!(6 x 22)
E)18!(6 x 44)
Rationale: Explanation:
Here clock-wise and anti-clockwise arrangements are same.
Hence total number of circular–permutations: \inline {\color{Black} \frac{18P_{12}}{2\times 12}} = \inline {\color{Black} \frac{18!}{6\times 24}}
Answer: C) 18!(6 x 24)
Answer: C
Question: If the sum of a number and its square is 342, What is the number?
Options:
A)16
B)77
C)25
D)87
E)18
Rationale: Explanation:
Let the integer be x.
Then, x + x2 = 342
x2 + x - 342 = 0
(x + 19) (x – 18) = 0
x = 18
ANSWER: E
Answer: E
Question: What sum of money will produce Rs.70 as simple interest in 5 years at 3 1/2 percent?
Options:
A)337
B)500
C)266
D)400
E)211
Rationale: 70 = (P*5*7/2)/100
P = 400
Answer: D
Answer: D
Question: A certain set of numbers has an average (arithmetic mean) of 50 and a standard deviation of 50.5. If p and n, two numbers in the set, are both within 2 standard deviations from the average, then which of the following could be the sum of p and n?
Options:
A)-200
B)-130
C)-104
D)51
E)305
Rationale: 2 standard deviations from the average is frommean - 2*SDtomean + 2*SD, thus from 50-2*50.5=51 to 50+2*50.5=151:
-51 < p < 151
-51 < n < 151
-102 < p+n < 302.
Only option D is in this range.
Answer: D.
Answer: D
Question: The cost of one photocopy is $0.02. However, a 25% discount is offered on orders of more than 100 photocopies. If Saran and David have to make 80 copies each, how much will each of them save if they submit a single order of 160 copies?
Options:
A)$0.32
B)$0.40
C)$0.45
D)$0.48
E)$0.54
Rationale: If Saran and David submit separate orders, each would be smaller than 100 photocopies, so no discount. Each would pay (80)*($0.02) = $1.60, or together, a cost of $3.20 --- that's the combinedno discount cost.
If they submit things together as one big order, they get a discount off of that $3.20 price ---- 25% or 1/4 of that is $0.80, the discount on the combined sale. They each effective save half that amount, or $0.40. Answer =(B).
Answer: B
Question: In the coordinate plane, the points F (-2,1), G (1,2), and H (2,1) lie on a circle with center P. What are the coordinates of point P ?
Options:
A)(0,0)
B)(1,1)
C)(1,2)
D)(1,-2)
E)(2.5, -2.5)
Rationale: I thought I need to find the 4th point that would lie on the circle
Hence my answer was D (1,-2)
But the the center of the circle will lie on (0,0)
A
Answer: A
Question: A person buys an article at Rs.500. At what price should he sell the article so as to make a profit of 10%?
Options:
A)550
B)882
C)772
D)652
E)271
Rationale: Cost price = Rs.500
profit = 10% of 500 = Rs.50
Selling price = Cost price + Profit
= 500 + 50 = 550
Answer:A
Answer: A
Question: A certain musical scale has has 13 notes, each having a different frequency, measured in cycles per second. In the scale, the notes are ordered by increasing frequency, and the highest frequency is twice the lowest. For each of the 12 lower frequencies, the ratio of a frequency to the next higher frequency is a fixed constant. If the lowest frequency is 220 cycles per second, then the frequency of the 7th note in the scale is how many cycles per second?
Options:
A)220 * sqrt 2
B)220 * sqrt (2^7)
C)220 * sqrt (2^12)
D)220 * the twelfth root of (2^7)
E)220 * the seventh root of (2^12)
Rationale: Let the constant be k.
F1 = 220
F2 = 220k
F3 = 220 k * k = 220 * k^2
F13= 220 * k^12
we know F13 = 2 *F1 = 2 * 220 = 440
440/220 = k^12
k = twelfth root of 2
for F7...
F7 = 220 * k^6 ( as we wrote for F2 and F3)
F7 = 220 * (twelfth root of 2) ^ 6
F7 = 220 * sqrt (2)
The answer is A.
Answer: A
Question: From a bunch of nine keys, three particular keys have to be used to open a combination lock, such that the second key can be used only after the first key and the third key can be used only after the second key. What are the chances of opening the lock in a random selection of three keys?
Options:
A)1/224
B)1/350
C)1/492
D)1/504
E)1/600
Rationale: The probability is 1/9*1/8*1/7 = 1/504.
The answer is D.
Answer: D
Question: Last month, John rejected 0.5% of the products that he inspected and Jane rejected 0.7 percent of the products that she inspected. If total of 0.75 percent of the products produced last month were rejected, what fraction of the products did Jane inspect?
Options:
A)1/6
B)1/2
C)5/8
D)5/4
E)15/16
Rationale: X - fraction of products Jane inspected
(1 - X) - fraction of products John inspected
0.7(X) + 0.5(1-X) = 0.75
0.2X = 0.75 - 0.5
X = 0.25/0.2
X = 5/4
Therefore the answer is D: 5/4.
Answer: D
Question: If it takes 4 movers 40 minutes to unpack their van, how long would 5 movers take?
Options:
A)38 minutes
B)35 minutes
C)32 minutes
D)29 minutes
E)26 minutes
Rationale: 4 * 40 = 5 * x
x = 32
Answer: C
Answer: C
Question: The annual interest rate earned by an investment increased by 5 percent from last year to this year. If the annual interest rate earned by the investment this year was 26.25 percent, what was the annual interest rate last year?
Options:
A)25%
B)24%
C)23%
D)22%
E)21%
Rationale: let i = interest rate
i(this year) = i(last year) + 0.05i(last year) = 1.05i(last year)
26.25 = 1.05 x i(last year)
i(last year) = 26.25/1.05 = 2625/105 = 25%
Answer : A
Answer: A
Question: no.of zeros in 1*2^2*3^3*....49^49
Options:
A)240
B)250
C)260
D)270
E)280
Rationale: count the number of 5's
5^5 => 5 5's
10^10 = 2^10*5^10 => 10 5's
15^15 => 15 5's
20^20 => 20 5's
25^25 =(5^2)^25 = 5^50 => 50 5's
30^30 => 30 5's
35^35 => 35 5's
40^40 => 40 5's
45^45 -> 45 5's
total no. of 5's = 5 + 10 + 15 + 20 + 50 + 30 + 35 + 40 + 45 = 250
i.e. product has a term 5^250 , also no. of 2's is much more than 250
no.of zeros in 1*2^2*3^3*....49^49 = 250
ANSWER:B
Answer: B
Question: The sum of all the integers k such that –20 < k < 24 is
Options:
A)0
B)-2
C)-25
D)-49
E)-37
Rationale: -19------------------0-----------------23
values upto+23 cancels outwe are left with only -19-18 sum of which is - 37. hence option D.
E
Answer: E
Question: 12 men work 8 hours per day to complete the work in 10 days. To complete the same work in 8 days, working 12 hours a day, the number of men required?
Options:
A)11 days
B)12 days
C)9 days
D)8 days
E)10 days
Rationale: That is, 1 work done = 12 × 8 × 10
Then, 12 8 × 10 = ? × 12 × 8
? (i.e. No. of men required) = 12 × 8 × 10/12× 8 = 8 days
E)
Answer: E
Question: A, B and C can do a work in 90, 30 and 15 days respectively. If they work together, in how many days will they complete the work?
Options:
A)5
B)6
C)7
D)8
E)9
Rationale: One days's work of A, B and C = 1/90 + 1/30 + 1/15
= (1 + 3 + 6)/90 = 1/9
A, B and C together can do the work in 9 days.
Answer:E
Answer: E
Question: Tough and Tricky questions: Ratios
2/5 of a certain class left on a field trip. 1/3 of the students who stayed behind did not want to go on the field trip (all the others did want to go). When another vehicle was located, 1/2 of the students who did want to go on the field trip but had been left behind were able to join. What fraction of the class ended up going on the field trip?
Options:
A)1/2
B)2/3
C)11/15
D)23/30
E)3/5
Rationale: let total no. of students be 30
students left on a field trip = 2/5(30) =12
thus 18 students left behind
1/3(18)=6 students did not want to go. thus 12 students want to go on the trip
1/2(12)=6 were able to join the other students on the field trip.
thus total number of students that went on a field trip =12+6 =18
thus required fraction = 18/30 =3/5
E
Answer: E
Question: 2 trains in same direction at 50km/hr,32 km/hr.A man in slower train observes 15 sec elapse before the faster train completely passed by him what is length of faster train?
Options:
A)65 meters
B)75 meters
C)85 meters
D)95 meters
E)55 meters
Rationale: relative speed= 18k/hr= 5 m/sec
distance covered= length of faster train= 5*15= 75 meters
ANSWER:B
Answer: B
Question: There are 6 physics books and 1 chemistry book on shelf P and 5 physics books on shelf Q. One book is moved from shelf P to shelf Q. A student picks up a book from shelf Q. What is the probability that the chemistry book is taken by the student?
Options:
A)1/42
B)1/21
C)1/15
D)1/12
E)1/10
Rationale: P(a chemistry book is moved to shelf Q) = 1/7
P(a chemistry book is then chosen from shelf Q) = 1/6
P(the student takes a chemistry book) = 1/7 * 1/6 = 1/42
The answer is A.
Answer: A
Question: What sum of money will produce Rs.90 as simple interest in 4 years at 3 1/2 percent?
Options:
A)742.85
B)622.85
C)632.85
D)652.85
E)642.85
Rationale: 90 = (P*4*7/2)/100
P = 642.85
ANSWER:E
Answer: E
Question: If 2x = 3y = 10, then 9xy = ?
Options:
A) 1,200
B) 200
C) 150
D) 40
E) 20
Rationale: 2x = 10;x=5
3y = 10;y=10/3
Multiply: 9xy=9*5*10/3=150
Answer: C.
Answer: C
Question: the present average age of a couple and their daughter is 35 years. Fifteen years from now, the age of the mother will be equal to the sum of present ages of the father and the daughter. Find the present age of mother?
Options:
A)18 years
B)19 years
C)11 years
D)45 years
E)12 years
Rationale: Explanation:
(f + m + d)/3 = 35
=> f + m + d = 105 --- (1)
m + 15 = f + d
Substituting f + d as m + 15 in (1), we get
2m + 15 = 105
2m = 90 => m = 45 years.
Answer: D
Answer: D
Question: What is the area of a square field whose diagonal of length 24 m?
Options:
A)256
B)289
C)200
D)288
E)178
Rationale: d2/2 = (24 * 24)/2
= 288
Answer: D
Answer: D
Question: The speed of a boat in still water is 60kmph and the speed of the current is 30kmph. Find the speed downstream and upstream?
Options:
A)40, 68 kmph
B)40, 30 kmph
C)90, 60 kmph
D)40, 60 kmph
E)90, 30 kmph
Rationale: Speed downstream = 60 + 30 = 90 kmph
Speed upstream = 60 - 30 = 30 kmph
Answer: E
Answer: E
Question: Mary and Mike enter into a partnership by investing $800 and $200 respectively. At the end of one year, they divided their profits such that a third of the profit is divided equally for the efforts they have put into the business and the remaining amount of profit is divided in the ratio of the investments they made in the business. If Mary received $1200 more than Mike did, what was the profit made by their business in that year?
Options:
A)$3000
B)$3500
C)$4000
D)$4200
E)$4500
Rationale: Explanatory Answer
Let the profit made during the year be $3x
Therefore, $x would have been shared equally and the remaining $2x would have been shared in the ratio 8 : 2.
i.e., 80% of 2x would go to Mary and 20% of 2x would go to Mike.
Hence, Mary would get (80 - 20)% of 2x more than Mike
Or60% of 2x = $1200
i.e.,(60/100)*2x = 1200
or 2x = 2000.
Hence, the profit made by the company during the year $3x = $3000.
Answer : A
Answer: A
Question: 8+2+2^2+2^3+2^4+2^5=？
Options:
A)(2^3-1)(2^3+2)
B)2^6+1
C)2^5-1
D)2^5+1
E)2^5-2
Rationale: 8+2+2^2+2^3+2^4+2^5=64
(2^3-1)(2^3+2)=64
the correct answer is A.
Answer: A
Question: Anand and Deepak started a business investing Rs. 25,000 and Rs. 35,000 respectively. Out of a total profit of Rs. 13,800, Deepak's share is?
Options:
A)2777
B)2888
C)8050
D)2882
E)2781
Rationale: Ratio of their shares = 25000 : 35000 = 5:7
Deepak's share = 13800 * 7/12 = Rs. 8050.
Answer: C
Answer: C
Question: In how many ways can the letters of the word RECPECT be arranged?
Options:
A)1800
B)1920
C)2520
D)3453
E)3500
Rationale: RECPECT has 7 words, but E is repeated two times. Thus ways = 7! / 2! = 2520 ways
C
Answer: C
Question: Rahul went to a shop and bought things worth Rs. 25, out of which 30 Paise went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items?
Options:
A)19
B)19.7
C)19.9
D)21.7
E)22.8
Rationale: Total cost of the items he purchased = Rs.25
Given that out of this Rs.25, 30 Paise is given as tax
=> Total tax incurred = 30 Paise = Rs.30/100
Let the cost of the tax free items = x
Given that tax rate = 6%
∴ (25−30/100−x)6/100 = 30/100
⇒ 6(25 −0.3 −x) = 30
⇒ (25 − 0.3 − x) = 5
⇒ x = 25 − 0.3 − 5 = 19.7
B)
Answer: B
Question: When positive integer w is multiplied by positive integer n, the units digit of the product is 3. Which of the following are factors of n?
I. 8
II. 15
III. 30
Options:
A)I only
B)II only
C)I and II only
D)II and III only
E)None of the above
Rationale: ans E..
we can tell the ans w/o using examples..
the units digit of product w*n is 3..
this means w and n are odd positive integers..
therefore n cannot have an even factor so 8 and 30 are out..
n cannot have a factor ending in 5 because in that case the units digit has to be 5 or 0... so 15 is also out
Answer: E
Question: On a certain date, Pat invested $6,000 at x percent annual interest, compounded annually. If the total value of the investment plus interest at the end of 10 years will be $24,000, in how many years total will the total value of the investment plus interest increase to $48,000?
Options:
A)15
B)16
C)18
D)20
E)24
Rationale: 24,000 = 6,000(1 + x)^10
4 = (1+x)^10 = 2^2
(1+x)^10 = ((1+x)^5)^2 = 2^2
Therefore, (1+x)^5 = 2
48,000 = 6000(1 + x)^n
(1+x)^n = 8
(1+x)^n = 2^3
(1+x)^n = ((1+x)^5)^3 = (1+x)^15
Therefore, n = 15.
The answer is A.
Answer: A
Question: What are the last two digits of 43*25*23*72*51*31?
Options:
A)54
B)75
C)00
D)45
E)32
Rationale: 43*25*23*72*51*31=
We have to focus on the last two digits only, so 43*25=75*23=25*72=00
51*00=00 therefore 31*00=00
Hence Answer is C
Answer: C
Question: A can complete a project in 20 days and B can complete the same project in 30 days. If A and B start working on the project together and A quits 10 days before the project is completed, in how many days will the project be completed?
Options:
A)18 days
B)27 days
C)26.67 days
D)16 days
E)12 days
Rationale: Answer
A can complete a project in 20 days. So, A will complete 1/20th of the project in a day.
B can complete a project in 30 days. So, B will complete 1/30th of the project in a day.
Let the total number of days taken to complete the project be x days.
B worked for all x days. However, A worked for (x - 10) days because A quits 10 days before the project is completed.
In a day, A completes 1/20th of the project.
Therefore, A would have completed x−10/20th of the project in (x - 10) days.
In a day, B completes130130th of the project.
Therefore, B would have completed x/30h of the project in x days.
∴ x−10/20+x/30= 1
Or x = 18.
Choice A
Answer: A
Question: A mixture of 150 liters of wine and water contains 20% water. How much more water should be added so that water becomes 25% of the new mixture?
Options:
A)14 liters
B)76 liters
C)10 liters
D)11 liters
E)12 liters
Rationale: Number of liters of water in150 liters of the mixture = 20% of 150 = 20/100 * 150 = 30 liters.
P liters of water added to the mixture to make water 25% of the new mixture.
Total amount of water becomes (30 + P) and total volume of mixture is (150 + P).
(30 + P) = 25/100 * (150 + P)
120 + 4P = 150 + P => P =10 liters.
Answer: C
Answer: C
Question: A and B can complete a work in 15 days and 10 days respectively. They started doing the work together but after 2 days B had to leave and A alone completed the remaining work. The whole work was completed in :
Options:
A)8 days
B)10 days
C)12 days
D)15 days
E)18 days
Rationale: Explanation:
(A + B)'s 1 day's work =(1/15 + 1/10)=1/6
Work done by A and B in 2 days =(1/6 X 2)=1/3
Remaining work =(1-1/3)=2/3
Now,	1/15work is done by A in 1 day.
2/3work will be done by a in	(15 X 2/3)= 10 days.
Hence, the total time taken = (10 + 2) = 12 days.
ANSWER IS C
Answer: C
Question: Three grades of milk are 1 percent, 2 percent and 4 percent fat by volume. If x gallons of the 1 percent grade, y gallons of the 2 percent grade, and z gallons of the 4 percent grade are mixed to give x+y+z gallons of a 1.5 percent grade, what is x in terms of y and z?
Options:
A)y + 5z
B)(y +z) / 4
C)2y + 3z
D)3y + z
E)3y + 4.5z
Rationale: Based on the given information, the following equation could be dervied: 1% * x + 2% * y + 4% * z = 1.5% * (x+y+z) Then use algebra to figure out 0.5%*x = 0.5%*y + 2.5%*z. Thus, x = y + 5z.
A
Answer: A
Question: Two trains are running in opposite directions with the same speed. If the length of each train is 120 m and they cross each other in 12 sec, then the speed of each train is?
Options:
A)10
B)18
C)36
D)72
E)16
Rationale: Answer: Option C
Let the speed of each train be x m/sec.
Then, relative speed of the two trains = 2x m/sec.
So, 2x = (120 + 120)/12 => x = 10
Speed of each train = 10 m/sec.
= 10 * 18/5 =- 36 km/hr.
Answer: C
Question: One half of a two digit number exceeds its one third by 6. What is the sum of the digits of the number?
Options:
A)3
B)5
C)7
D)9
E)11
Rationale: x/2 – x/3 = 6 => x =6
3 + 6 = 9
ANSWER:D
Answer: D
Question: If 2 = (6x)/(x - xy/z) then which of the following is true?
Options:
A)y = -2z
B)y = 2z
C)2y = z
D)-2y = z
E)y = -z
Rationale: 2 = (6x)/(x - xy/z)
=> 2 = (6xz)/(x*(z - y))
=> 2x = (6xz)/(z - y)
=> (z - y) = 3z
=> y = -2z
Hence Ans is B
Answer: B
Question: A bag contains 50 black balls and 10 white balls. One ball is drawn at random. What is the probability that the
ball is white?
Options:
A)1
B)1/6
C)1/3
D)1/2
E)None of these
Rationale: Explanation:
Total cases = 50 + 10 = 60
Favourable cases = 10
So probability = 10/60 = 1/6
Answer: B
Answer: B
Question: In a survey, 56 percent of the people surveyed stated truthfully that they were married, while 30 percent of the people surveyed who were married at that time chose not to include that information in the survey. What percent of the people surveyed were actually married at the time of the survey?
Options:
A)20%
B)60%
C)40%
D)75%
E)80%
Rationale: Let the total survey population be 100x. Now, 56x are married.
Again, let the total no of married people in the survey be 100y. Thus, 30% of them lied about being married. Thus, 70% were honest about it.
Thus, 70y = 56x
And, therefore 100y = 80x.
Thus, 80% were actually married.
ANSWER:E
Answer: E
Question: Which answer is closest to the √151?
Options:
A)12.1
B)12.2
C)12.3
D)12.4
E)12.5
Rationale: Try filling the numbers into the answer y x y =
Find the closest to 151.
Answer C
Answer: C
Question: At a raffle, 20% of the attendees bought more than five tickets, 65% of the remaining bought four tickets or less. What percentage of the attendees bought five tickets?
Options:
A)28% of the attendees bought five tickets.
B)52% of the attendees bought five tickets.
C)20% of the attendees bought five tickets.
D)72% of the attendees bought five tickets.
E)None of these.
Rationale: Explanation:Let total number of attendees be 100,Then, number of attendees who bought more than five tickets = 20.Number of attendees who bought four tickets or less= 65% of 80 = 52.Total number with five tickets = 100 – 20 – 52 = 28.Thus, 28% of the attendees bought five tickets.Answer: Option A.
Answer: A
Question: Thomas and Matt has some money with them in the ratio of 3:4. If their father gives Rs.30 to each of them then the ratio becomes 4:5. What would be the ratio if Thomas spend Rs.40 and Matt spend Rs. 20 from what they have now?
Options:
A)1:2
B)2:3
C)3:4
D)4:5
E)5:6
Rationale: Let money of Thomas and Matt be x and y respectively.
x/y = 3/4 => x = 3/4 y
(x+30)/(y+30) = 4/5
=> 5x+150 = 4y+120 => 5x = 4y-30
But x = 3/4 y
5* 3/4 y = 4y-30
15y = 16y-120 => y = 120
=> x = 3*120/4 => x=90
Ratio of their money, if Thomas spend Rs.40 and Matt spend Rs. 20 => (90-40)/(120-20) = 50/100. => 1:2
Answer:A
Answer: A
Question: If 20! × 20!/20^n is an integer, what is the largest possible value of n?
Options:
A)20
B)16
C)8
D)4
E)1
Rationale: 20! × 20!/20^n is an integer.
Or 20! × 20!/(2^2n*5^n)
This means we need to find the power of 5 in the numerator. We can safely say that the number of powers of 5 will be lower than the number of powers of 4 in the numerator.
Largest power of 5 in 20! = [20/5] + [20/25] = 4
Since there are 2 20!'s, power of 4 in the numerator = 2*4 = 8
Hence the largest value of b for which 20! × 20!/20^n is integer = 8
ANSWER:C
Answer: C
Question: If a, b, and c are consecutive even positive integers, which of the following could be equal to a + b + c ?
Options:
A)141
B)200
C)624
D)391
E)412
Rationale: The key to answering this question quickly is to realize that a+b+c is a multiple of BOTH 2 and 3. With that information, you can quickly eliminate answer choices. If you don't recognize those two Number Properties though, then you can still get to the correct answer (but it will require a bit more work).
We're told that a, b and c are CONSECUTIVE EVEN INTEGERS, so we could write them algebraically as...
A + (A+2) + (A+4) = 3A + 6
We know that 3A + 6 COULD equal one of those five answers; we just have to find it...
Could 3A + 6 = 141
3A = 135
A = 45
This is NOT an EVEN INTEGER, so 141 is NOT the answer
Could 3A + 6 = 200
3A = 194
A = 64.6666
This is NOT an EVEN INTEGER, so 200 is NOT the answer
Could 3A + 6 = 624
3A =618
A = 206
This IS an EVEN INTEGER! The numbers would be 206, 208 and 210. This IS the answer
Final Answer:
C
Answer: C
Question: If each edge of a cube is increased by 50%, find the percentage increase in Its surface area
Options:
A)125%
B)129%
C)185%
D)725%
E)145%
Rationale: Let the edge = a cm
So increase by 50 % = =
Total surface Area of original cube =
TSA of new cube =
==
Increase in area = =
Increase % = = 125%
Answer: a
Answer: A
Question: Find the least number which when divided by 5,6,7, and 8 leaves a remainder 3, but when divided by 9 leaves no remainder
Options:
A)1683
B)1684
C)1685
D)1582
E)1584
Rationale: Explanation :
L.C.M. of 5,6,7,8 = 840.
Required number is of the form 840k + 3
Least value of k for which (840k + 3) is divisible by 9 is k = 2.
Required number = (840 X 2 + 3)=1683
ANSWER IS A
Answer: A
Question: A can do a piece of work in 7 days of 9 hours each and B can do it in 6 days of 7 hours each. How long will they take to do it, working together 8 hours a day?
Options:
A)4 days
B)3 days
C)7 days
D)2 days
E)9 days
Rationale: Sol. A can complete the work in (7 x 9) = 63 hours.
B can complete the work in (6 x 7) = 42 hours.
A’s 1 hour's work = (1/63) and B's 1 hour's work =(1/42)
(A + B)'s 1 hour's work =(1/63)+(1/42)=(5/126)
Both will finish the work in (126/5) hrs.
Number of days. of (42/5) hrs each =(126 x 5)/(5 x 42)=3 days
Ans: B
Answer: B
Question: If the perimeter of a rectangular garden is 800 m, its length when its breadth is 100 m is?
Options:
A)338 m
B)300 m
C)200 m
D)276 m
E)971 m
Rationale: 2(l + 100)
= 800 => l
= 300 m
Answer:B
Answer: B
Question: If a child walks at the rate of 5m/min from his home, he is 6 minutes late for school, if he walks at the rate of 7m/min he reaches half an hour earlier. How far is his school from his home ?
Options:
A)450 min
B)540 min
C)630 min
D)360 min
E)none of these
Rationale: Let the distance between home and school is x.
Let actual time to reach be t.
Thus, x/5 = t + 6 ---- (1)
and x/7 = t - 30 -----(2)
Solving equation 1 and 2
x = 630 min
ANSWER:C
Answer: C
Question: Which of the following must be subtracted from 2^24 so that the resulting integer will be a multiple of 3?
Options:
A)2
B)3
C)1
D)4
E)5
Rationale: {4^1} / 3 =4/3 remainder 1
{4^2} / 3 = 16/3 remainder 1
{4^3} / 3 = 64/3 remainder 1
{4^4} / 3 = 256/3 remainder 1
Actually the same remainder keeps repeating .....
Try with a diff no, say 2
{2^1}/3 = remainder 2
{2^2}/3 = remainder 1
{2^3}/3 = remainder 2
{2^4}/3 = remainder 1
Answer : C
Answer: C