divelab/Sys2Bench huggingface dataset:
Question: A boat goes 100 km downstream in 10 hours, and 75 m upstream in 15 hours. The speed of the stream is?
Options:
A)22 1/7 kmph
B)22 2/2 kmph
C)22 1/4 kmph
D)22 1/2 kmph
E)42 1/2 kmph
Rationale: 100 --- 10 DS = 10
? ---- 1
75 ---- 15 US = 5
? ----- 1 S = (10 - 5)/2
= 2 2 1/2 kmph
Answer:D
Answer: D
Question: Tough and Tricky questions: Exponents.
If 3^m3^m2^m = 9^n, then m/n =
Options:
A)1/3
B)2/3
C)1
D)3/2
E)3
Rationale: I also soved it, but a bit differently. Thank you for reminding me of this much easier and logical way!
What I did was to test powers of 3 that would lead to 9.
So, we have 3 raised to the same power 3 times and 9 raised to another power one time: 3^m3^m3^m = 9^n
What I did was test 3 raised to the power of 2 like this:
3^2*3^2*3^2 = 9*9*9 = 9^3. This means that m=2 and n=3. So, m/n=2/3.B
Answer: B
Question: The tax on a commodity is diminished by 30% but its consumption is increased by 10%. Find the decrease percent in the revenue derived from it?
Options:
A)12%
B)14%
C)16%
D)20%
E)23%
Rationale: Explanation:
100 * 100 = 10000
70 * 110 = 7700
10000------- 2300
100 ------- ? = 23%
E)
Answer: E
Question: If 12 and 15 are the lengths of two sides of a triangular region, which of the following can be the length of the third side?
I. 10
II. 20
III. 30
Options:
A)I only
B)II only
C)I and II only
D)II and III only
E)I, II, and III
Rationale: The length of any side of a triangle must be larger than the positive difference of the other two sides, but smaller than the sum of the other two sides.
Let x be the length of the third side.
15-12 < x < 15+12
3 < x < 27
The answer is C.
Answer: C
Question: Fill in the blank with the correct number in this number series: 3, 9, 8, 7, __, 5, 18, ?
Options:
A)6
B)7
C)9
D)10
E)13
Rationale: This is a simple alternating subtraction and addition series; The first series begins with 3 and adds 5; the second begins with 9 and subtracts 2, and so on.
Answer: E
Answer: E
Question: The larger of two negative consecutive even integers 2t and 2(t-1) is multiplied by 2 and then added to the smaller of the two original integers. Which of the following represents this operation?
Options:
A)6t-2
B)8t-2
C)-2
D)3
E)-2-4t^2
Rationale: larger of 2t-2, 2t (when they are negative) is 2t. the smallest of 2t and 2t-2 when they are positive is 2t-2.
therefore 2* 2t + 2t-2 = 6t-2.
option A.
Answer: A
Question: A passenger sitting near the window in a train moving at 40 km/h, noticed that it took 3 sec. for the oncoming train to pass by. What was the speed of the oncoming train if the length of the oncoming train was 66 metres?
Options:
A)a)39.2km/h
B)b)52km/h
C)c)56km/h
D)d)60km/h
E)e)70km/h
Rationale: im getting A
3 secs to pass a 75 mts train , therefore speed = 22 meters/sec
to convert m/s to km/hrs multiply by 3.6
22*3.6 = 79.2
so its 79.2-40 = 39.2 .
A
Answer: A
Question: A cistern 10 m long and 8 m wide contains water up to a depth of 1 m 50 cm. The total area of the wet surface is:
Options:
A)120 m2
B)136 m2
C)128 m2
D)130 m2
E)134 m2
Rationale: Area of the wet surface	= [2(lb + bh + lh) - lb]
= 2(bh + lh) + lb
= [2 (8 x 1.50 + 10 x 1.50) + 8 x 10] m2
= 134 m2.
answer :E
Answer: E
Question: What is the difference between local value & face value of 9 in the numeral 65793?
Options:
A)8453
B)8956
C)8991
D)9890
E)10000
Rationale: (Local value of 9) - (Face value of 9)
= (9000 - 9) = 8991
C
Answer: C
Question: A man covers a certain distance Win a train. If the train moved 4km/hr faster, it would take 30 min less. If it moved 2km/hr slower, it would take 20 mins more. Find the distance?
Options:
A)200 km
B)50 km
C)20 km
D)60 km
E)80 km
Rationale: Not really. When you solve the 2 equation above, you get,
6T-4/3 = 5R/6 from simplifying equation 1
4T-2=R/2 from simplifying equation 2
You can now multiply equation 2 by 5 to get
5(4T-2=R/2 ) = 20T-10=5R/2 and then subtract this new equation from equation 1 to get T=3, followed by R=20 to give you distance W= R*T=20*3=60 km.D
Answer: D
Question: If x and y are positive integers and x = 5y + 2, what is the remainder when x is divided by 5?
Options:
A)0
B)1
C)2
D)3
E)4
Rationale: This question asks what IS...(the answer), so we know that the answer will be consistent. As such, we can TEST VALUES to quickly get the solution.
We're told that X and Y are POSITIVE INTEGERS and X = 5Y + 2. We're asked for the REMAINDER when X is divided by 5.
IF....
Y = 1
X = 7
7/5 = 1 remainder 2
Final Answer:
C
Answer: C
Question: We define that K@J is the product of j number from k in increasing order for positive integers K, J. For example, 6@4=6*7*8*9. If A=2020and B=2120, what is the value T of the ratio A/B?
Options:
A)1/2
B)1/3
C)2/3
D)1/4
E)1/5
Rationale: T-> A/B=20*21*……*39/21*22*….*39*40=20/40=1/2.
Therefore, the answer is A.
Answer: A
Question: The cost price of 13 articles is equal to the selling price of 11 articles. Find the profit percent?
Options:
A)18 2/7%
B)18 2/11%
C)12 2/12%
D)13 2/9%
E)14 2/7%
Rationale: 13 CP = 11 SP
11 --- 2 CP
100 --- ? =>18 2/11%
Answer: B
Answer: B
Question: Bradley owns b/2 video game cartridges. If Bradleyâ€™s total is one-half the total owned by Andrew and four times the total owned by Charlie, how many video game cartridges do the three of them own altogether, in terms of b?
Options:
A)(16/3)b
B)(17/4)b
C)(13/8)b
D)(9/2)b
E)(7/12)b
Rationale: Step 1: Categorize the problem
This problem is testing basic algebra and equations, with an extra layer of complexity by having variables in the answer choices.
Step 2: Think like the test maker
What is the key detail or key details in the problem? The key detail to immediately recognize is that the problem gives you Andrew and Charlieâ€™s totals in relation to Bradleyâ€™s total rather than giving you Bradleyâ€™s total in relation to the other two; and then the problem asks you to solve the problem in terms of b. This means that you have to relate Andrew and Charlieâ€™s values in relation to Bradleyâ€™s total. The test maker is attempting to force you to structure the problem in the opposite way that most people are used to structuring information. By gaining this insight, it makes it easier to solve the problem.
Step 3: Solve the problem
b/2 = Bradleyâ€™s total
2*b/2 = Andrewâ€™s total
1/4*b/2 = Charlieâ€™s total
Add each total
b/2 + 2*b/2+ 1/4*b/2 = b/2 + 2*b/2 + b/8 = (13/8)b
Therefore,choose D.
Answer: D
Question: Find the value of y from (12)^3 x 6^2 ÷ 432 = y?
Options:
A)2134
B)2234
C)2540
D)2560
E)144
Rationale: 144
E
Answer: E
Question: On dividing a number by 56, we get 26 as remainder. On dividing the same number by 8, what will be the remainder ?
Options:
A)2
B)3
C)4
D)5
E)6
Rationale: Number=56x+26 (∵ since the number gives 26 as remainder on dividing by 56)
=(7×8×x)+(3×8)+2
Hence, if the number is divided by 8, we will get 2 as remainder.
ANSWER:A
Answer: A
Question: Avinash covers a distance of 8km in 50 minutes. If he covers 3km distance in 2/5th of time then, What speed should he maintain to cover the remaining distance in the remaining time?
Options:
A)20 Kmph
B)15 Kmph
C)30 Kmph
D)32 Kmph
E)34 Kmph
Rationale: Total distance = 8 Km
Total time = 50 Km
Time taken to cover the distence of 3 Km = 50*2/5 = 20 min = 1/3 hours
Remaining distance = 8 - 3 = 5 Km
Required speed = 5/1/3 = 15 Kmph
B
Answer: B
Question: In store A there are 10 pairs of pants for every 40 store B has. The price ratio between the pants in store B and the pants in store A is 3:4. If all the pants were sold in both places until the stock ran out, what is the ratio between the total amount stores A earned to the total amount store B earned?
Options:
A)3:16.
B)2:3.
C)1:3.
D)3:4.
E)2:5
Rationale: Amount for Store a = 10 * 4 = 40
Amount for Store b = 40 * 3 = 120
Ratio of Total Amount Would be = 40/120 = 1:3
ANSWER:C
Answer: C
Question: Cream costs twice as much as skim milk. A certain brand of milk is 3/5 cream and 2/5 skim milk. What fraction of the cost of this brand is due to the cream?
Options:
A)1/2
B)1/3
C)2/3
D)3/4
E)4/5
Rationale: Let x be the cost of the skim milk in the mixture.
The cost of the cream is (3/2)*x*2 = 3x.
The total cost is x+3x = 4x and the fraction due to the cream is 3x / 4x = 3/4
The answer is D.
Answer: D
Question: What is the total number of integers between 20 and 80 (exclusive)that are divisible by 10?
Options:
A)5
B)7
C)4
D)9
E)3
Rationale: 30,40,50,60,70
total 5
Answer is A
Answer: A
Question: If the sum of the first n even positive integers is S, what is the sum of the first n positive integers, in terms of S ?
Options:
A) S/2
B) S
C) 2S
D) 2S + 2
E) 4S
Rationale: Answer is A
Given sum of 2 , 4 , 6 ....2n = S
sum of 1 2 3.....n = [sum(2 4 6....2n) ]/2 = S/2
Answer: A
Question: Working simultaneously and independently at an identical constant rate, 5 machines of a certain type can produce a total of x units of product P in 4 days. How many of these machines, working simultaneously and independently at this constant rate, can produce a total of 2x units of product P in 2 days?
Options:
A)11
B)13
C)15
D)18
E)20
Rationale: The rate of 5 machines is rate=job/time=x/4 units per day --> the rate of 1 machine 1/5*(x/4)=x/20 units per day;
Now, again as {time}*{combined rate}={job done}
then 2*(m*x/20)=2x --> m=20.
Answer: E.
Answer: E
Question: Exactly 36% of the numbers in set E are even multiples of 3. If 40% of the even integers in set E are not multiples of 3, what percent of the numbers in set E are not even integers?
Options:
A) 76%
B) 60%
C) 50%
D) 40%
E) 24%
Rationale: Everything is correct except the red part with a typo: it should be N=0.6E --> even numbers are 60% of E --> 40% of E are not even integers.
Answer: D.
Answer: D
Question: In what ratio should two varieties of sugar of Rs.18 per kg and Rs.24 kg be mixed together to get a mixture whose cost is Rs.20 per kg?
Options:
A)16.59
B)16.5
C)16.56
D)13.5
E)16.51
Rationale: Let the quantities of A and B mixed be 3x kg and 7x kg.
Cost of 3x kg of A = 9(3x) = Rs. 27x
Cost of 7x kg of B = 15(7x) = Rs. 105x
Cost of 10x kg of the mixture = 27x + 105x = Rs. 132x
Cost of 5 kg of the mixture = 132x/10x (5) = Rs. 66
Profit made in selling 5 kg of the mixture = 25/100 (cost of 5 kg of the mixture) = 25/100 * 66 = Rs. 16.50
Answer:B
Answer: B
Question: The average of first 7 prime numbers is?
Options:
A)10.11
B)11.11
C)8.29
D)13.11
E)14.11
Rationale: Sum of 7 prime no. = 58
Average = 58/7 = 8.29
ANSWER: C
Answer: C
Question: In how many ways, a committee of 10 members can be selected from 8 men and 6 ladies, consisting of 6 men and 4 ladies?
Options:
A)150
B)360
C)420
D)310
E)455
Rationale: (6 men out 8) and (4 ladies out of 6) are to be chosen
Required number of ways = 8C6*6C4 = 420
Answer is C
Answer: C
Question: The average salary of all the workers in a workshop is Rs. 8000. The average salary of 7 technicians is Rs. 12000 and the average salary of the rest is Rs. 6000. The total number of workers in the workshop is:
Options:
A)23
B)19
C)22
D)20
E)21
Rationale: Let the total number of workers be x. Then,
8000x = (12000 * 7) + 6000(x - 7)
= 2000x = 42000
= x = 21.
ANSWER:E
Answer: E
Question: The product of two positive integers is 1023 and their difference is 2. What is the bigger number?
Options:
A)29
B)31
C)33
D)35
E)37
Rationale: Let's use trial and error to find the two numbers.
32*30 = 960 (too low)
33*31 = 1023
The answer is C.
Answer: C
Question: If x, y, and z are positive integers, and 4x = 5y = 6z, then the least possible value of x + y + z is
Options:
A)15
B)28
C)37
D)42
E)60
Rationale: Take LCM of 4,5 and 6 = 60
Now 4x = 60 => x =15
5y = 60 => y = 12
6z = 60 => z =10
115+12+10 = 37.
Option C.
Answer: C
Question: Find out the wrong number in the given sequence of numbers.
36, 54, 18, 27, 9, 18.5, 4.5
Options:
A)18.8
B)18.5
C)18.0
D)18.1
E)18.7
Rationale: Explanation:
The terms are alternatively multiplied by 1.5 and divided by 3. However, 18.5 does not satisfy it.
Answer: B) 18.5
Answer: B
Question: If “GREEN” is given number code as 49, what is the difference between the number codes of “VIOLET” and “PINK” ?
Options:
A)55
B)45
C)33
D)60
E)40
Rationale: Explanation:
Case – Codes : A - 1, B - 2, C - 3, D - 4, E - 5, F - 6, G - 7, H - 8, I - 9, J - 10, K - 11, L - 12, M - 13, N - 14, O - 15, P - 16, Q - 17, R - 18, S - 19, T - 20, U - 21, V - 22, W - 23, X - 24, Y - 25, Z - 26
GREEN = 7 + 18 + 5 + 5 + 14 = 49
Thus we get,
VIOLET = 22 +9 +15+12 + 5 + 20 = 83
PINK = 16 + 9 + 14 + 11 = 50
Thus, difference is 83 – 50 = 33.
ANSWER C
Answer: C
Question: The average of a set of five distinct integers is 420. If each number is less than 2,000, and the median of the set is the greatest possible value, what is the sum of the two smallest numbers?
Options:
A)-4,494
B)-3,997
C)-3,894
D)-3,194
E)The answer cannot be determined from the information given
Rationale: Sum of the set = 420*5=2100 Each number is less than 2000 and median of the set is the greatest possible value.
Therefore last 3 numbers can be 1999,1998 and 1997. Their sum=5994.
Therefore sum of two smallest numbers= 2100-5994= -3894
Answer=C
Answer: C
Question: How long will a boy take to run round a square field of side 45 meters, if he runs at the rate of 9km/hr?
Options:
A)72sec
B)45sec
C)1min
D)32sec
E)25sec
Rationale: Speed = 9 km/hr = 9*5/18 = 5/2 m/sec
Distance = 45*4 = 180m
Time taken = 180*2/5 = 72sec
Answer is A
Answer: A
Question: A customer pays 50 dollars for a coffee maker after a discount of 20 dollars
What is the original price of the coffe maker?
Options:
A)70
B)80
C)90
D)50
E)60
Rationale: Solution
Let x be the original price.
x - 20 = 50
x - 20 + 20 = 50 + 20
x + 0 = 70
x = 70
Answer A
Answer: A
Question: How many positive integers between 1 and 100 are there such that they are multiples of 15?
Options:
A)5
B)4
C)7
D)1
E)6
Rationale: Multiples of 15 = 15,30,45,-----90
Number of multiples of 15 => 90-15/15+1= 6
Answer is E
Answer: E
Question: A man took some money for borrowed, for 3 years the total will be Rs.4000 and 5 years it will be Rs.5000/-. Then how much amount he borrowed?
Options:
A)Rs.2000/-
B)Rs.2500/-
C)Rs.2770/-
D)Rs.2800/-
E)Rs.2820/-
Rationale: 3 years --------> Rs.4000/-
5 years --------> Rs.5000/-
~ ~
------------------------------
2 years ---------> Rs.1000/-
1 year ----------> Rs.500/-
3years * Rs.500/- = Rs.1500/-
P = Rs.4000/- - Rs.1500/- = Rs.2500/-
P = Rs.2500/-
B
Answer: B
Question: Trains A and B start simultaneously from stations 350 miles apart, and travel the same route toward each other on adjacent parallel tracks. If Train A and Train B travel at a constant rate of 40 miles per hour and 30 miles per hour, respectively, how many miles will Train A have traveled when the trains pass each other, to the nearest mile?
Options:
A) 112
B) 133
C) 150
D) 167
E) 200
Rationale: Since we know the distance (350) and the combined rate (70), we plug it into the formula:
Distance = Rate * Time
350 = 70 * Time
We can solve for the time they will meet cause we added the rate of Train A and Train B together.
So the time will be 350/70 from dividing 70 on both sides to isolate Time in the equation above.
Time will be 5 hours so now you can plug that in for Train A’s distance.
Distance = Rate * Time
Distance = 40 * 5
Distance = 200 according to answer choice E.
Answer: E
Question: A single discount equivalent to the discount series of 20%, 15% and 5% is?
Options:
A)31.5
B)31.8
C)31.6
D)35.4
E)31.1
Rationale: 100*(80/100)*(85/100)*(95/100)
= 64.6
100 - 64.6 = 35.4
Answer:D
Answer: D
Question: A, B and C start a business with each investing Rs 20,000. After 5 months A withdraws Rs 5000, B withdraws Rs 4000 and C invests Rs 6000 more. At the end of the year, a total profit of Rs 69900 was recorded. Find the share of A.
Options:
A)20000
B)21500
C)20500
D)22000
E)21000
Rationale: A : B : C
=(20000×5+15000×7)
:(20000×5+16000×7)
:(20000×5+26000×7)
=(20×5+15×7)
:(20×5+16×7)
:(20×5+26×7)
=205:212:282
A's share =69900×205/(205+212+282)
=69900×205/699
=20500
Answer is C.
Answer: C
Question: The current of a stream runs at the rate of 4 kmph. A boat goes 10 km and back to the starting point in 2 hours, then find the speed of the boat in still water?
Options:
A)A)7
B)B)2
C)C)8.9
D)D)11.4
E)E)3
Rationale: S = 4
M = x
DS = x + 4
US = x - 4
10/(x + 4) + 10/(x - 4) = 2
x = 11.4
Answer:D
Answer: D
Question: The speeds of 3 trains in the ratio 2:6:14. The ratio between time taken by them to travel the same distance is?
Options:
A)6:4:3
B)21:7:3
C)4:8:9
D)6:5:2
E)4:8:7
Rationale: Ratio of time taken is = 1/2 : 1/6 : 1/14 = 21:7:3
Answer is B
Answer: B
Question: A box contains 6 pairs of shoes (12 shoes in total). If two shoes are selected at random, what it is the probability that they are matching shoes?
Options:
A)1/11
B)1/20
C)1/19
D)1/10
E)1/9
Rationale: The problem with your solution is that we don't choose 1 shoe from 12, but rather choose the needed one AFTER we just took one and need the second to be the pair of it. So, the probability would simply be: 1/1*1/11as after taking one at random there are 11 shoes left and only one is the pair of the first one)=1/11
Answer: A.
Answer: A
Question: If the sixth day of a month is two days earlier than Wednesday, What day will it be on the 20th day of the month?
Options:
A)Saturday
B)Monday
C)Sunday
D)Wednesday
E)Friday
Rationale: Explanation:
Given that sixth day of a month is two days earlier than Wednesday
=> Sixth day is Monday
=> 13th is Monday
=> 20th is Monday
Answer: Option B
Answer: B
Question: One side of the bottom layer of a triangular pyramid has 12 balls. How many are there in the whole pyramid?Note that the pyramid is equilateral and solid.
Options:
A)286
B)364
C)504
D)164
E)154
Rationale: As there are 12 balls along one side, it means that there are 12 layers of balls. The top most layer has 1 ball. The second layer has 3 (1+2) balls. The third layer has 6 (1+2+3) balls. The fourth layer has 10 (1+2+3+4) balls. The fifth layer has 15 (1+2+3+4+5) balls. Similarly, there are 21, 28, 36, 45, 55, 66 and 78 balls in the remaining layers.
Hence, the total number of balls are
= 1 + 3 + 6 + 10 + 15 + 21 +28 + 36 + 45 + 55 + 66 + 78
= 364 balls
ANSWER:B
Answer: B
Question: A train travelling at a speed of 75 mph enters a tunnel 3 1/2 miles long. The train is 1/4 mile long. How long does it take for the train to pass through the tunnel from the moment the front enters to the moment the rear emerges?
Options:
A)2.5 min
B)3 min
C)3.2 min
D)3.5 min
E)None
Rationale: Solution
Total distance covered	= (7/2 + 1/4) miles
= 15 / 4 miles
= (18 x 5 /18) km/hr
Time taken	= (15 / 4 x 75) hrs
= 1 /20 hrs
= (1 / 20 x 60)
= 3 min.
Answer B
Answer: B
Question: Shipment ------No. of Defective Chips/shipment---Total Chips in shipment
S2 -------------- 5 ------------------------ ----------------------12000
S3 -------------- 6 ----------------------------------------------- 18000
S4 -------------- 4 ----------------------------------------------- 16000
A computer chip manufacturer expects the ratio of the number of defective chips to be total number of chips in all future shipments equal to the corresponding ratio for shipmemts S1,S2,S3 and S4 comined as shown in the table above. What is the expected number Y of defective chips in a shipment of 60000 chips?
Options:
A)14
B)20
C)22
D)24
E)25
Rationale: I agree with your solution = 20. But the question is:
There are different combination to get 60,000 chips. For example: 1*S3 + 2*S4 + 2*S2. In this way, we ship 60,000 chips with only 6 + 4*2 + 2*2 = 18 defective chips, better than the average of 20.
The question is to find the expected number Y of defective chips, i guess it assume the minimum #, therefore it might not be 20.
Answer: B
Question: If 12 men or 20 women can do a piece of work in 54 days, then in how many days can 9 men and 12 women together do the work?
Options:
A)10 days
B)30 days
C)20 days
D)80 days
E)40 days
Rationale: E
40 days
Given that 12m = 20w => 3m = 5w
9 men + 12 women = 15 women + 12 women = 27 women
20 women can do the work in 54 days. So, 27 women can do it in (20 * 54) /27 = 40 days.
Answer: E
Question: At a monthly meeting, 3/5 of the attendees were males and 7/8 of the male attendees arrived on time. If 4/5 of the female attendees arrived on time, what fraction of the attendees at the monthly meeting did not arrive on time?
Options:
A)47/200
B)31/200
C)17/100
D)11/100
E)7/50
Rationale: Males who did not arrive on time are 1/8*3/5 = 3/40 of the attendees.
Females who did not arrive on time are 1/5*2/5 = 2/25 of the attendees.
The fraction of all attendees who did not arrive on time is 3/40 + 2/25 = 31/200
The answer is B.
Answer: B
Question: A man spends 2/5 of his salary on house rent,3/10 of his salary on food and 1/8 of his salary on conveyence.if he has Rs.1400 left with him,find his expenditure on food and conveyence.
Options:
A)800
B)900
C)100
D)700
E)500
Rationale: let the salary be x ,therefore house rent =2x/5,food=3x/10,conveyence=x/8.
it is given that left over salary is 1400/-
so,x-(2x/5+3x/10+x/10)=1400
by solving x=8000
expenditure on food=3200 and conveyence=1000
ANSWER:C
Answer: C
Question: Four milkmen rented a pasture. A grazed 24 cows for 3 months; B 10 for 5 months; C 35 cows for 4 months and D 21 cows for 3 months. If A's share of rent is Rs. 7200, find the total rent of the field.
Options:
A)37500
B)35500
C)42500
D)22500
E)32500
Rationale: Ratio of shares of A, B, C, D = (24 x 3) : (10 x 5) : (35 x 4) : (21 x 3) = 72 : 50 : 140 : 63.
Let total rent be Rs. x. Then, A’s share = Rs. (72x)/325
(72x)/325=7200 = x=(7200 x 325)/72 = 32500
Hence, total rent of the field is Rs. 32500.
Answer is E.
Answer: E
Question: 6th March, 2005 is Monday, what was the day of the week on 6th March, 2004?
Options:
A)Friday
B)Saturday
C)Wednesday
D)Sunday
E)Monday
Rationale: Number of days from 6th March, 2004 to 5th March 2005 = 365 days
(Though Feb 2004 has 29 days as it is a leap year, it will not come in the required period)
365 days = 1 odd day
Given that 6th March, 2005 is Monday
Hence 6th March, 2004 = (Monday - 1 odd day) = Sunday
Answer: Option D
Answer: D
Question: Five years ago a father was thrice as old as his son. Five years hence the son will only half the age of his father. Find their present ages.
Options:
A)25, 25
B)35, 15
C)15, 35
D)15, 35
E)10, 40
Rationale: Explanation:
Let the present ages of father,and son be 'a' and 'b' respectively.
a - 5= 3(b-5) =>a-3 b =-10 --------(1)
a-2b =5 ------------(2) solving (1) and (2), we get b =15
Substituting b = 15 in second equation,
we get a=35
Answer: B
Answer: B
Question: If a particular is never chosen, in how many ways can a cricketbe chosen out of 15 players?
Options:
A)327
B)340
C)364
D)499
E)456
Rationale: A particular players is never chosen, it means that 11 players are selected out of 14 players.
=> Required number of ways = 14C11
= 14!/11!x3! = 364
C
Answer: C
Question: A and B invests Rs.10000 each, A investing for 8 months and B investing for all the 12 months in the year. If the total profit at the end of the year is Rs.5000, find their shares?
Options:
A)2000,8000
B)2000,4000
C)2000,3000
D)1000,3000
E)4000,3000
Rationale: The ratio of their profits A:B = 8:12 =2:3
Share of A in the total profit = 2/5 * 5000 = Rs.2000
Share of B in the total profit = 3/5 * 5000 = Rs.3000
Answer:C
Answer: C
Question: Rectangular tile each of size 25cm by 16cm must be laid horizontally on a rectangular floor of size 180cm by 120cm,such that the tiles do not overlap and they are placed with edges jutting against each other on all edges. A tile can be placed in any orientation so long as its edges are parallel to the edges of floor. No tile should overshoot any edge of the floor. The maximum number of tiles that can be accommodated on the floor is:
Options:
A)52
B)54
C)55
D)65
E)48
Rationale: Area of tile = 25*16= 400
Area of floor = 180*120 = 21600
No of tiles = 21600/400 = 54
So, the no of tile = 54
ANSWER:B
Answer: B
Question: Two brothers were expected to return here on the same day. Rajat returned 3 days earlier but Rohit returned 4 days later. If Rajat returned on Friday, what was the expected day when both the brothers were to return home and when did Rohit Return?
Options:
A)Wednesday, Sunday
B)Thursday, Monday
C)Monday, Friday
D)Monday, Friday
E)none
Rationale: Rajat returned on Friday -i.e. 3 days earlier
so actual day to return home is Monday.
Rohit returned after days so Friday
ANSWER:C
Answer: C