divelab/Sys2Bench huggingface dataset:
Question: A, B and C can do a piece of work in 24, 30 and 40 days respectively. They start the work together but C leaves 4 days before the completion of the work. In how many days is the work done?
Options:
A)14 days
B)21 days
C)22 days
D)11 days
E)43 days
Rationale: D
11 days
x/24 + x/30 + x/40 = 1
x = 11 days
Answer: D
Question: From 2008 to 2009, the number of Easter eggs in a certain egg hunt rose 20%, then fell 17% from 2009 to 2010. From 2008 to 2009, the ratio of Easter eggs to Easter bunnies in the same hunt fell 20%, then rose 22% from 2009 to 2010. By what approximate percent did the number of bunnies change over the full period from 2008 to 2010?
Options:
A)5% increase
B)2% increase
C)1% decrease
D)3% decrease
E)6% decrease
Rationale: Let the number of Easter eggs be x1 in 2008 and x2 in 2010
Given that it rose 20% in 2009 and then fell 17% in 2010
=>x2 = (0.83)(1.2)x1 ---(1)
Let the number of Easter bunnies be y1 in 2008 and y2 in 2010
Given that the ratio of x to y fell 20% in 2009 and then rose 22% in 2010
=> x2/y2 = (0.8)(1.22)(x1/y1)
=> y1/y2 = (0.8)(1.22)(x1/x2) ----(2)
substituting (1) in (2),
y1/y2 = (0.8)(1.22)/(0.83)(1.2)
=> y2/y1 = (0.83)(1.2)/(0.8)(1.22) = 249/244
% change in y2 from y1 = (y2-y1)*100/y1
= (y2/y1 - 1)*100 = (249/244 - 1)*100
= (5/244)*100 = +2%
It's a 2% increase
Answer option "B"
Answer: B
Question: If Juan takes 12 seconds to run y yards, how many seconds will it take him to run x yards at the same rate?
Options:
A)12x/y
B)12y/x
C)x/(12y)
D)13/(xy)
E)xy/12
Rationale: This problem is testing us on the Rate x Time = Distance relationship. This relationship also tells us that Rate = Distance/Time and Time = Distance/Rate.
Ultimately, we are looking for how many seconds it will take Juan to run x yards. Thus, the equation we’ll use is: Time = Distance/Rate. We know the distance is x yards, and we need to find Juan’s rate.
We can find Juan’s rate as follows: Rate = Distance/Time = y yards/12 seconds
Using that rate, we need to determine how long it takes him to run x yards at the same rate. So we have:
Time = Distance/Rate
Time = x yards/(y yards/12 seconds)
Time = (x yards) x (12 seconds/y yards)
Time = 12x/y seconds
Answer A.
Answer: A
Question: The area of a rectangular field is equal to 500 square meters. Its perimeter is equal to 90 meters. Find the width of this rectangle.
Options:
A)5
B)10
C)15
D)20
E)25
Rationale: L * W = 500 : area , L is the length and W is the width.
2 L + 2 W = 90 : perimeter
L = 45 - w : solve for L
(45 - W) * W = 500 : substitute in the area equation
W = 20 and L = 25
correct answer D
Answer: D
Question: The sum of two numbers is 30 and their product is 1050. What will be the sum of their reciprocals?
Options:
A)(1/35)
B)(11/210)
C)(35/4)
D)(75/8)
E)None
Rationale: Solution
x+y=30 xy=1050 1/x+1/y=x+y/xy 30/1050 = (1/35).
Answer A
Answer: A
Question: Tough and Tricky questions: Remainders.
1^1 + 2^2 + 3^3 + ... + 10^10+11^11 is divided by 5. What is the remainder?
Options:
A)0
B)1
C)2
D)3
E)4
Rationale: a number is divisible by 5, if its last digit is divisible by 5
let's look into the sum of last digits of each term of the given expression
1^1=1
2^2=4
3^3=7
4^4=6
5^5=5
6^6=6
7^7=3
8^8=6
9^9=9
10^10=0
11^11=1
adding all these numbers we get 48 which gives a remainder of 3 when divided by 5. so answer must be 3.
bunuel, can you please confirm the answer of this question.
Yes, the OA is D. Clicked the wrong button when posting. Edited. Thank you.
D
Answer: D
Question: What is 35% of 4/13 of 780?
Options:
A)62
B)73
C)84
D)95
E)106
Rationale: This problem can be solved easily if we just use approximation: 35% is a little over 1/3, while 4/13 is a little less than 4/12, which is 1/3. Thus, the answer is about 1/3 of 1/3 of 780, or 1/9 of 780. Since the first 1/3 is a slight underestimate and the second 1/3 is a slight overestimate, the errors will partially cancel each other out. Our estimate will be relatively accurate.
The number 780 is between 720 and 810, so (1/9)*780 will be between 80 and 90.
Keeping track not only of your current estimate, but also of the degree to which you have overestimated or underestimated , can help you pinpoint the correct answer more confidently.
The closest answer is 84, so this is the answer to choose.
The answer is C.
Answer: C
Question: If a + b - c = 2d, and if a - b + c =-2e, then a =
Options:
A)2(d + e)
B)d – e
C)(d + e)/2
D)d-2e
E)e-d
Rationale: Add both equations:
a + b - c = 2d
a - b + c =-2e
a+b-c+a-b+c=2d-2e
2a=2d-2e
a=(d-e)
Ans:B
Answer: B
Question: Three partners A , B , C start a business . B's Capital is four times C's capital and twice A's capital is equal to thrice B's capital . If the total profit is Rs 16500 at the end of a year ,Find out B's share in it.
Options:
A)4000
B)5000
C)6000
D)7000
E)None of these
Rationale: Explanation :
Suppose C's capital = x then
B's capital = 4x (Since B's Capital is four times C's capital)
A's capital = 6x ( Since twice A's capital is equal to thrice B's capital)
A:B:C =6 x : 4x : x
= 6 : 4 : 1
B's share = 16500 * (4/11) = 1500*4 = 6000. Answer : Option C
Answer: C
Question: A typist uses a sheet measuring 20cm by 30 cm lenghtwise. If a margin of 2 cm is left on each side and a 3 cm margin on the top and bottom, then what is the percentage of page used by the typist?
Options:
A)62 %
B)63 %
C)64 %
D)65 %
E)66 %
Rationale: Area of the sheet=(20*30)cm2= 600 cm2
Area used for typing=([20-4]*[30-6]) cm2 = 384 cm2
Therefore Required Percentage =(384/600)*100 = 64%
Answer C
Answer: C
Question: A rectangular grassy plot 110 m. by 65 m has a gravel path 2.5 m wide all round it on the inside. Find the cost of gravelling the path at 80 paise per sq. metre
Options:
A)Rs680
B)Rs780
C)Rs880
D)Rs480
E)Rs980
Rationale: area of the plot=110m*65m=7150sq.m
area of plot excluding gravel=105m*60m=6300sq.m
area of gravel =7150sq.m-6300sq.m =850sq.m
cost of building it = 850sq.m*80
= 68000p
in Rs =68000/100=Rs680
ANSWER:A
Answer: A
Question: A semicircle has a radius of 12. What is the approximate perimeter of the semicircle?
Options:
A)58
B)62
C)66
D)70
E)74
Rationale: The perimeter of a circle is 2*pi*r.
The perimeter of a semicircle is 2*pi*r/2 + 2r = pi*r + 2r
The perimeter is pi*12 + 2*12 which is about 62.
The answer is B.
Answer: B
Question: Tom opened a shop investing Rs.30000. Jose joined him 2 months later, investing Rs.45000. They earned a profit of Rs.54000 after completion of one year. What will be Jose's share of profit?
Options:
A)20000
B)24000
C)34000
D)35000
E)30000
Rationale: SoL = ~s- So Anju’s share = [5/9] x 54000 = 30000
E
Answer: E
Question: The radius of a wheel is 22.4 cm. What is the distance covered by the wheel in making 600 resolutions.
Options:
A)843.03 m
B)844.03 m
C)845.03 m
D)846.03 m
E)847.03 m
Rationale: In one resolution, the distance covered by the wheel is its own circumference. Distance covered in 600 resolutions.
= 600 * 2 * 22/7 * 22.4
= 84403 cm
= 844.03 m
Answer: B
Answer: B
Question: The probability of two events A and B are 0.15 and 0.40 respectively. The probability that both A and B occur is 0.15. The probability that neither A nor B occur is _________
Options:
A)0.45
B)0.4
C)0.5
D)0.05
E)0.6
Rationale: we are apply that formula..............
P(AorB)=P(A)+P(B)-P(A AND B)
=.15+.40-.15
=.40
but the probability of neither A nor B=1-.40
=0.60
ANSWER:E
Answer: E
Question: The area of a square is 144 m². Find its perimeter.
Options:
A)18 m
B)28 m
C)38 m
D)42 m
E)48 m
Rationale: Area of square = side × side
Given; area of square = 144 m²
Therefore, side² = 144 m²
Therefore, side = √(144 m²) = √(2 × 2 × 2 × 2 × 3 × 3) m² = 2 × 2 × 3 m = 12 m
Now, the perimeter of the square = 4 x side = 4 × 12 m = 48 m
ANSWER : E
Answer: E
Question: In a room filled with 7 people, 1 people have exactly 1 sibling in the room and 6 people have exactly 2 siblings in the room. If two individuals are selected from the room at random, what is the probability that those two individuals are NOT siblings?
Options:
A)5/21
B)3/7
C)4/21
D)5/7
E)16/21
Rationale: There are suppose A B C D E F G members in the room 4 people who have exactly one sibling....A B C D....(A is Bs∘SSsibl∈g∘SSand∘SSviceversa)∘SS(C∘SSis∘SSDs∘SSsibl∈g∘SSand∘SSviceversa)∘SS(C∘SSis∘SSDssibl∈gandviceversa)(CisDs sibling and viceversa) (C is Ds sibling and viceversa)...now remaning EFG are 6 people who have exactly 2 siblings....(E has F and G as his/her sibling and so on..)
there are now 3 different set of siblings (A and B)
(C and D);(EFG)
Now first selecting 2 people out of 7 is 7C2=21
first sibling pair----(A and B)--selecting 2 people --2C2=1
second sibling pair (C and D)--selecting 2 people--2C2=1
third sibling pair (E F G)--selecting 2 out of 6 --6C2=15
total= 1+1+15=17
but,a/c to formula P(success)-1-p(fail)
here,p(failure)is selecting 2 people who are siblings
=17/21(21 is 7C2)
=1-17/21
=4/21
ANS C
Answer: C
Question: A train speeds past a pole in 15 sec and a platform 100 m long in 25 sec, its length is?
Options:
A)158 m
B)150 m
C)110 m
D)130 m
E)157 m
Rationale: Let the length of the train be x m and its speed be y m/sec.
Then, x/y = 15 => y = x/15
(x + 100)/25 = x/15 => x = 150 m.
Answer: B
Answer: B
Question: Two pipes can fill a tank in 12 minutes and 15 minutes. An outlet pipe can empty the tank in 10 minutes. If all the pipes are opened when the tank is empty, then how many minutes will it take to fill the tank?
Options:
A)20
B)22
C)24
D)26
E)28
Rationale: Let V be the volume of the tank.
The rate per minute at which the tank is filled is:
V/12 + V/15 - V/10 = 3V/60 = V/20 per minute
The tank will be filled in 20 minutes.
The answer is A.
Answer: A
Question: If x% of y is the same as 4/5 of 80, then the value of xy is?
Options:
A)4250
B)6205
C)5260
D)4852
E)6400
Rationale: x/100 * y = 4/5 * 80
xy = 64*100 = 6400
Answer is E
Answer: E
Question: A bag holds 5 red marbles and 5 green marbles. If you removed two randomly selected marbles from the bag, without replacement, what is the probability that both would be red?
Options:
A)1/6
B)2/5
C)3/10
D)2/9
E)1/2
Rationale: probability of selecting first red marble = 5/10
probability of selecting second red marble without replacement = 4/9
final probability = 5/10 * 4/9 = 2/9
The correct answer is D.
Answer: D
Question: If you drove at average speed of 66 miles per hour, what distance, in miles, did you drive in 99 minutes?
Options:
A)100.2 miles
B)112.7 miles
C)120.5 miles
D)108.9 miles
E)105.6 miles
Rationale: We first convert the speed into miles per minute.
66 / 60 = 1.2 miles per minute
We now use the speed and the time to find the distance.
1.2 (miles/minute) * 99 minutes = 108.9 miles
correct answer D
Answer: D
Question: How many pieces of 85 cm length can be cut from a rod of 17 meters long?
Options:
A)50
B)40
C)30
D)20
E)10
Rationale: Number of pieces = 1700/85 = 20
The answer is D.
Answer: D
Question: The midpoints of three of the edges of a cube are
labelled A, B, and C as shown in the diagram. What
is the measure of L ABC ?
Options:
A)90o
B)105o
C)120o
D)135o
E)150o
Rationale: Let D be the point on the base of the cube such that CD is perpendicular to
the base. Let s be the length of the sides of the cube. Then AB = BC = AD =
p
2s/2.
Using the Pythagorean Theorem in 4ADC, we get AC =
p
3s/
p2. By the Law of
Cosines AC2 = AB2 +BC2 −2AB · BC · cos(\ABC). We get cos(\ABC) = −1/2, so
L ABC = 120o.
correct answer C
Answer: C
Question: If an integer n is to be chosen at random from the integers 1 to 96, inclusive, what is the probability that n(n + 1)(n + 2) will be divisible by 6?
Options:
A)2/3
B)3/8
C)1/2
D)5/8
E)3/4
Rationale: I get 5/8 as well
1 to 96 inclusive means we have 48 odd and 48 even integers
E O E / 6 = Integer, therefore we have 48 / 96 numbers divisible by 6
O E O / 6 = Not Integer
We cannot forget multiples of 6 from 1 to 96
We have 16 numbers that are multiple of 8
Therefore, 48/96 + 16/96 = 64/96 = 2/3
answer : A
Answer: A
Question: In how many different number of ways 4 boys and 3 girls can sit on a bench such that girls always sit together.
Options:
A)720
B)740
C)770
D)780
E)790
Rationale: 720
Option 'A'
Answer: A
Question: A person purchases 90 clocks and sells 40 clocks at a gain of 10% and 50 clocks at a gain of 20%. If he sold all of them at a uniform profit of 15%, then he would have got Rs. 40 less. The cost price of each clock is:
Options:
A)50
B)90
C)80
D)28
E)93
Rationale: Let C.P. of clock be Rs. x.
Then, C.P. of 90 clocks = Rs. 90x.
[(110% of 40x) + (120% of 50x)] - (115% of 90x) = 40
44x + 60x - 103.5x = 40
0.5x = 40 => x = 80
Answer: Option C
Answer: C
Question: Find large number from below question The difference of two numbers is 1385. On dividing the larger number by the smaller, we get 6 as quotient and the 15 as remainder
Options:
A)1235
B)1345
C)1678
D)1767
E)1659
Rationale: Let the smaller number be x. Then larger number = (x + 1385).
x + 1385 = 6x + 15
5x = 1370
x = 274
Large number = 274+1385 = 1659
E
Answer: E
Question: There are 6 girls and 6 boys. If they are to be seated in a row, what is the probability that boys and girls sit alternately?
Options:
A)1/12!
B)12C6/12!
C)6!6!/12!
D)2∗6!6!/12!
E)6!7!/12!
Rationale: Total number of ways in which 6 boys and 6 girls can sit in a row = 12!/6!∗6!
Number of ways in which 6 boys and 6 girls can sit alternately = 2 (BGBG..... or GBGB.....)
Probability = 2∗6!∗6!/12!
Answer: D
Answer: D
Question: A car is traveling 85 kilometers per hour. How many meters does the car travel in one minute?
Options:
A)1250m/min
B)1360m/min
C)2560m/min
D)1670m/min
E)1416.67m/min
Rationale: Convert hour into minutes ( 1 hour = 60 minutes) and kilometers into meters (1 km = 1000 m) and simplify
85 kilometers per hour = 85 km/hr
= (85 × 1000 meters) / (60 minutes) = 1,416.67 meters / minute
correct answer is E)1416.67m/min
Answer: E
Question: A can do a piece of work in 4 days. B can do it in 5 days. With the assistance of C they completed the work in 2 days. Find in how many days can C alone do it?
Options:
A)87 days
B)20 days
C)16 days
D)19 days
E)36 days
Rationale: C = 1/2 - 1/4 - 1/5 = 1/20
=> 20 days
Answer:B
Answer: B
Question: A certain country had a total annual expenditure of $7.2 x 10^11 last year. If the population of the country was 240 million last year, what was the per capita expenditure?
Options:
A) $ 500
B) $1,000
C) $2,000
D) $3,000
E) $5,000
Rationale: Total expenditure / Population = per capita expenditure
Hence, (7,2 x 10^11) / 240 000 000 = (7,2 x 10^11) / (2,4 x 10^8) = 3 x 10^(11-8) =
3 x 10^3 = 3000.
Answer is D.
Answer: D
Question: Two employees M and N are paid a total of $583 per week by their employer. If M is paid 120 percent of the salary paid to N, how much is N paid per week?
Options:
A)$245
B)$255
C)$265
D)$275
E)$285
Rationale: 1.2N + N = 583
2.2N = 583
N = 265
The answer is C.
Answer: C
Question: Product of two co-prime numbers is 117. Their L.C.M should be:
Options:
A)1
B)117
C)116
D)equal to their H.C.F
E)Cannot be calculated
Rationale: H.C.F of co-prime numbers is 1.
So, L.C.M = 117/1 = 117.
ANSWER:B
Answer: B
Question: Brand A coffee costs twice as much as brand B coffee. If a certain blend is 1/2 brand A and 1/2 brand B. what fraction of the cost of the blend is Brand A?
Options:
A)a. 1/3
B)b. 2/5
C)3. 1/2
D)4. 2/3
E)5. 3/4
Rationale: Assume Cost of A= Ca = 200 , Cost of B = Cb=100
The blend contains 0.5 A and 0.55 B ---> Cost of the blend = Cbl = 0.5*200+0.5*100= 150
Thus fraction of A in the blend = 0.5*200/150 = 2/3.
Answer : D
Answer: D
Question: A motorboat, whose speed in 15 km/hr in still water goes 30 km downstream and comes back in a total of 4 hours 30 minutes. The speed of the stream (in km/hr) is:
Options:
A)5
B)6
C)7
D)8
E)9
Rationale: Let the speed of the stream be x km/hr. Then,
Speed downstream = (15 + x) km/hr,
Speed upstream = (15 - x) km/hr.
=5
Answer:A
Answer: A
Question: Set A = {1, 2, 3, 4, 5, 6, d}
Which of the following possible values for d would cause Set A to have the smallest standard deviation?
Options:
A) 1
B) 2.5
C) 3
D) 3.5
E) 7
Rationale: I agree. The mean of the set d=1,2,3,4,5,6 is 3.5 . Now if we add one extra number to the set, in order for the standard deviation to be minimum, that number must be as close as possible to the original set (1,2,3,4,5,6). Therefore we have to choose the number closest to 3,5 from the options we have, leaving D as the best choice.
Answer D.
Answer: D
Question: A take twice as much time as B or thrice as much time to finish a piece of work. Working together, they can finish the work in 3 days. B can do the work alone in?
Options:
A)18
B)12
C)11
D)19
E)114
Rationale: Suppose A, B and C take x, x/2 and x/3 respectively to finish the work.
Then, (1/x + 2/x + 3/x) = 1/3
6/x = 1/3 => x = 18
So, B takes 9 hours to finish the work.
Answer: A
Answer: A
Question: Three friends Alice, Bond and Charlie divide $1105 amongs them in such a way that if $10, $20 and $15 are removed from the sums that Alice, Bond and Charlie received respectively, then the share of the sums that they got will be in the ratio of 11 : 18 : 24. How much did Charlie receive?
Options:
A)$495
B)$510
C)$480
D)$375
E)$360
Rationale: Explanatory Answer
Let the sums of money received by A, B and C be x, y and z respectively.
Then x - 10 : y - 20 : z -15 is 11a : 18a : 24a
When $10, $20 and $15 are removed, we are removing a total of $45 from $1105.
Therefore, 11a + 18a + 24a = 1105 - 45 = 1060
i.e., 53a = 1060
or a = 20.
We know that z - 15 = 24a = 24 * 20 = 480
Therefore, z = 480 + 15 = $495
correct choice is (A)
Answer: A
Question: A man is 30 years older than his son. In two years, his age will be twice the age of his son. The present age of this son is
Options:
A)28 years
B)22 years
C)23 years
D)24 years
E)26 years
Rationale: Explanation:
Let's Son age is x, then Father age is x+30.
=> 2(x+2) = (x+30+2)
=> 2x+4 = x+32
=> x = 28 years
Option A
Answer: A
Question: The average weight of A, B and C is 42 kg. If the average weight of A and B be 40 kg and that of B and C be 43 kg, then the weight of B is:
Options:
A)33 kg
B)31 kg
C)32 kg
D)40 kg
E)37 kg
Rationale: Let A, B, C represent their respective weights.
Then, we have: A + B + C = (42 x 3) = 126 .... (i)
A + B = (40 x 2) = 80 .... (ii)
B + C = (43 x 2) = 86 ....(iii)
Adding (ii) and (iii), we get: A + 2B + C = 166 .... (iv)
Subtracting (i) from (iv), we get : B = 40.
B's weight = 40 kg.
D
Answer: D
Question: A and B can do a piece of work in 8 days. With the help of C they finish the work in 5 days. C alone can do that piece of work in?
Options:
A)13 1/3
B)878
C)30
D)88
E)11
Rationale: C = 1/5 â€“ 1/8 = 3/40 => 40/3 = 13 1/3 days
Answer: A
Answer: A
Question: The difference between the squares of two consecutive odd integers
is a square<1000 whose root equals the combined sum of the digits
of the two integers. What is the sum of the digits Q of the larger integer?
Options:
A)Q=2
B)Q=5
C)Q=8
D)Q=10
E)11
Rationale: Really hard. But let's start with few concepts:
1. Square of an odd integer will be odd.
2. Difference of odd and odd will be even.
3. Any odd integer can be expressed as difference of two squares.
4. An even integer can be expressed as difference of two squares only if that even integer is a multiple of 4.
Assume two odd integers to be (2x-1) and (2x+1).
Difference of their squares = (2x+1)^2 - (2x-1)^2
= 4x^2 + 1 + 4x - (4x^2 + 1 - 4x)
= 4x^2 + 1 + 4x - 4x^2 - 1 + 4x
= 8x
Now root of 8x needs to be an integer such that it is equal to the sum of the digits of the two odd integers.
8 = 2^3, so x needs to be such that itcompletesa perfect square.
If we find x, we can find the value of 2x+1 (larger integer) and then sum of its digits.
Let's check the options, starting with c.
For sum to be 8, few possibilities are: 17, 35, 53, 71
If we take 17, the pair is 15 and 17, meaning x = 8.
8x = 64
root of 64 = 4 but 4 is not equal to 1+5+1+7.
Reject.
If we take 35, the pair is 33 and 35, meaning x = 17.
8x = 8*17
Reject since perfect square is not possible.
If we take 53, the pair is 51 and 53, meaning x = 26.
8x = 8*26
Reject since perfect square is not possible.
If we take 71, the pair is 69 and 71, meaning x = 35.
8x = 8*35
Reject since perfect square is not possible.
I tried each option and the possibilities and then got lost.
Then, it occurred to me that I was only checking 2-digit integers. What about 3-digits?
Starting with option a, only 2-digit odd integer whose sum is 2 is 101.
If we take 101, the pair is 99 and 101, meaning x = 50.
8x = 8*50 = 400
root of 400 = 20 which is indeed equal to 9+9+1+1.
Answer (A).
Answer: A
Question: Each customer of a networking company subscribes to one of two plans: Plan A or Plan B. Plan A costs $25 per month and Plan B costs $75 per month per customer. If the company’s average revenue per customer per month is $100, then what percent of the company's revenue comes from customers with Plan A?
Options:
A)25%
B)30%
C)37.5%
D)56.25%
E)50%
Rationale: If there are A customers with plan A, and B customers with plan B, then the total revenue is $25A + $75B.
Since the average customer pays $100, we know that
$100 = ($25A + $75B) / (A + B)
$100(A + B) = ($25A + $75B)
$100A + $100B = $25A + $75B
$75A = -$25B
A = 3B.
Since there are 3 times as many $75 clients as $75 clients, for every $75 received from Plan B customers, 3($25) = $75 is received from Plan A customers, and the percent of revenue from customers with Plan A is:
$75/($75 + $75) = $75/$150 = 50%.
The correct answer is choice (E).
Answer: E
Question: A batch of cookies was divided among three tins: 2/3 of all the cookies were placed in either the blue tin or the green tin, and the rest were placed in the red tin. If 1/4 of all the cookies were placed in the blue tin, what fraction Q of the cookies that were placed in the other tins were placed in the green tin?
Options:
A)15/2
B)9/4
C)5/9
D)7/5
E)9/7
Rationale: Blue tin or red tin: 2/3 (N)
Red tin: (1/3)N
Blue tin: (1/4)N
What the last statment meant, is it wants this fraction: (# of cookies in green tin)/(# of cookies in red and green tin)
# of cookies in green tin = 2N/3 - N/4 = 8N- 3N/12 = 5N/12
# of cookies in red and green tin = N/3 + 5N/12 = 9N/12
Fraction Q= 5N/12 * 12/9N = 5/9 (C)
Answer: C
Question: If M and N are positive integers that have remainders of 1 and 3, respectively, when divided by 5, which of the following could NOT be a possible value of M+N?
Options:
A)84
B)52
C)34
D)29
E)14
Rationale: M=5p+1
N=5q+3
We need M+N=5p+1+5q+3=5(p+q)+4
Pick numbers for pq
Since it is an addition of pq and the answer to this expression should be an integer (because all the numbers being added are integers),
we just need to choose values so that we get integer multiples of 5 so
p+q=0 ; M+n = 4
p+q=1 ; M+N = 9
P+q=2 ; M+N = 14
and so on, so basically you get something like - 4,9,14,19,24,29,34,..... all the other options were turning up.
Then I directly tried p+q=10 because it was closer to 52 for the first option, i got 54, .
So Answer B.
Answer: B
Question: A water tank is three-fifths full. Pipe A can fill a tank in 10 minutes and pipe B can empty it in 6 minutes. If both the pipes are open, how long will it take to empty or fill the tank completely?
Options:
A)6 min
B)8 min
C)7 min
D)9 min
E)1 min
Rationale: The combined rate of filling/emptying the tank = 1/10 - 1/6 = -1/15
Since the rate is negative, the tank will be emptied.
A full tank would take 15 minutes to empty.
Since the tank is only three-fifths full, the time is (3/5) * 15 = 9 minutes
The answer is D.
Answer: D
Question: The length of a rectangular landscape is 4times its breadth. There is a playground in it whose area is 1200 square mtr & which is 1/3rd of the total landscape. What is the length of the landscape?
Options:
A)90
B)100
C)120
D)130
E)140
Rationale: Sol. x * 4x = 3 * 1200
x = 30
Length = 4 * 30 = 120
C
Answer: C
Question: If n and y are positive integers and 450y = n^3, which of the following must be an integer?
Options:
A)y/(3*2^2*5)
B)y/(3^2*2*5)
C)y/(3*2*5^2)
D)y/(5^3*2^2)
E)y/(5*3*2)
Rationale: Solution:
As y and n are both integers so y is of the form of 3*5*2*2*K
where K= an integer.
to make n as an integer and 450y to be a cube of a number.
Now checking with the answers we get only 1 as K.
So the answer is (1).
Answer: A