divelab/Sys2Bench huggingface dataset:
Question: Tim is now 16 years older than Donna. If in 4 years Tim will be twice as old as Donna, how old will Tim be in 11 years?
Options:
A)35
B)37
C)39
D)41
E)43
Rationale: T=D+16 so D=T-16.
T+4=2(D+4).
T+4=2(T-16+4).
T+4=2T-24.
T=28.
In 11 years, Tim will be 39 years old.
The answer is C.
Answer: C
Question: Which of the following inequalities is equivalent to −8 < x < 4?
Options:
A)|x - 1| < 7
B)|x + 2| < 6
C)|x + 3| < 5
D)|x - 2| < 6
E)None of the above
Rationale: We know that |x| < a means -a < x < a, where Sum of lower limit of x (i.e -a) and the upper limit of x (i.e a), is 0
Given is, -8 < x < 4, let's say by adding y to this inequality we will get into the above format
-8+y < x+y < 4+y
Now, to move this into the mod format, we need to have (-8+y) + (4+y) = 0 => y = -2
Thus, -6< x+2 < 6 => |x+2| < 6.
Hence, answer is B
Answer: B
Question: The average speed of a car is 1 4/5 times the avg speed of a bike. A tractor covers 575km in 23hrs. How much distance will the car cover in 4hrs if the speed of the bike is twice speed of the tractor?
Options:
A)300 km
B)320 km
C)360 km
D)390 km
E)400 km
Rationale: Sol. Average speed of a tractor = 25 km / h
The speed of a bus in an hour = 25 × 2 = 50 km
The speed of a car in an hour = 9/5 * 50 = 90 km
So, the distance covered by car in 4 h is
90 × 4 = 360 km
Ans.(C)
Answer: C
Question: Two vessels having volumes in the ratio 3:5 are filled with water and milk solutions. The ratio of milk and water in the two vessels are 5:1 and 6:4 respectively. If the contents of both the vessel are empties into a larger vessel, find the ratio of milk and water in the larger vessel.
Options:
A)12:5
B)11:5
C)13:5
D)14:5
E)9:5
Rationale: Vessel A = 300 gallons --> milk = 250, water = 50;
Vessel B = 500 gallons --> milk = 300, water = 200;
Vessel A + B = 800 gallons --> milk = 550, water 250
The ratio =550/250-->11:5
Answer: B
Answer: B
Question: If A:B = 1/3: 1/3 B:C = 1/2:1/3 then A:B:C?
Options:
A)9:9:6
B)9:6:8
C)9:6:2
D)9:6:4
E)9:6:1
Rationale: A:B = 1/3:1/3 = 3:3
B:C = 1/2:1/3 = 3:2
--------------------
A:B:C = 9:9:6
Answer:A:
Answer: A
Question: How many different arrangements of letters are possible if three letters are chosen from the letters A through I and the letters E and A must be among the letters selected?
Options:
A)36
B)38
C)40
D)42
E)44
Rationale: Besides A and E, there are 7 letters and we can choose one of them.
7C1 = 7
Three letters can be arranged in 3! ways.
The number of arrangements is 7*3! = 42
The answer is D.
Answer: D
Question: Two trains 135 meters and 165 meters in length respectively are running in opposite directions, one at the rate of 80 km and the other at the rate of 65 kmph. In what time will they be completely clear of each other from the moment they meet?
Options:
A)7.18
B)7.12
C)7.3
D)7.45
E)7.51
Rationale: T = (135 + 165)/ (80 + 65) * 18/5
T = 7.45
Answer:D
Answer: D
Question: Of the 200 stamps in a collection, 90 are foreign and 80 are more than 10 years old. If 20 stamps are both foreign and more than 10 years old, how many stamps are neither foreign nor more than 10 years old?
Options:
A)50
B)80
C)100
D)130
E)150
Rationale: 20 stamps are both foreign and more than 10 years old.
70 stamps are foreign only.
60 stamps are 10 years old only.
The number of remaining stamps is 200 - (20+70+60) = 50
The answer is A.
Answer: A
Question: What percent of a day is 6 hours?
Options:
A)6.25%
B)20%
C)25%
D)12.5%
E)None of these
Rationale: Explanation :
Total hours in a day = 24
Required percentage = (6/24) × 100 = 25%
Answer : Option C
Answer: C
Question: Vijay sells a cupboard at 12% below cost price. Had he got Rs.1500 more, he would have made a profit of 12%. What is the cost price of the cupboard?
Options:
A)7450
B)14900
C)6250
D)6000
E)None of these
Rationale: Explanation:
Cost price = 1500/(0.12 + 0.12) = 1500/0.24
= Rs.6250
ANSWER C
Answer: C
Question: A cistern is normally filled in 8 hours but takes two hours longer to fill because of a leak in its bottom. If the cistern is full, the leak will empty it in?
Options:
A)27
B)20
C)40
D)73
E)72
Rationale: 1/8 - 1/x = 1/10
x = 40
Answer: C
Answer: C
Question: If w,x,y,z are consecutive positive integers ; then which of the following is always odd?
[1] w*x+(y+2)^2*z
[2] w^x + z^y
[3] 51y
Options:
A)1
B)2
C)3 and 2
D)1 and 2
E)2 and 3
Rationale: Plug in some numbers
w = 1
x = 2
y = 3
z = 4
Check the options -
[1] w*x+(y+2)^2*z = 1*2 + (3+2)^2 * 4 => 2 + 25*4 = 102{ Not an odd Number }
[2] w^x + z^y = 1^2 + 4^3 => 1 + 64 = 65{ Odd number }
[3] 51y = 51*3 = 153 odd
[2] and [3]
C
Answer: C
Question: The avg weight of A,B & C is 84 kg. If D joins the group, the avg weight of the group becomes 80 kg.If another man E who weights is 4 kg more than D Replaces A, Then the avgof B,C,D&E becomes 79 kg. What is the weight of A?
Options:
A)76
B)65
C)75
D)89
E)90
Rationale: A + B + C = 3 *84 = 252
A + B + C + D = 4 * 80 = 320 ---- (i)
So, D = 68& E = 68 + 4 = 72
B + C + D +E = 79 * 4 = 316 --- (ii)
From Eq. (i) & (ii)
A-E = 320 – 316 = 4
A = E +4 = 72 + 4 = 76
A
Answer: A
Question: If x,y ,and z are positive real numbers such that x(y+z) = 62, y(z+x) =82 , and z(x+y) = 100, then xyz is
Options:
A)120
B)50
C)60
D)70
E)90
Rationale: xy+xz = 62 --------------------------------------1)
yz+yx = 82---------------------------------------2)
xz+zy = 100---------------------------------------3)
Re-writing equation 3 as follows:
xz+zy = 82+ 18
xz+zy = yz+yx + 18
xz = yx + 18 ............... (4)
Adding (1)(4)
2xz = 80
xz = 40
xyz has to be multiple of 40, only 120 fits in
Answer = A
Answer: A
Question: If a function f is defined by f(x)= -1/x for all non zero numbers x. If f(a) = -1/3 and f(ab) = 1/9 then b= ?
Options:
A)1/6.
B)-1/3.
C)1/3.
D)-3.
E)12.
Rationale: f(a) = -1/3 = -1/a, and thus a = 3
f(ab) = 1/9, and thus ab = -9
3b = -9
b = -3
The answer is D.
Answer: D
Question: Nicole cycles at a constant rate of 20 kilometers per hour, and is passed by Jessica, who cycles at a constant rate of 40 kilometers per hour. If Jessica cycles at her constant rate for x minutes after passing Nicole, then stops to wait for her, how many minutes will Jessica have to wait for Nicole to catch up to her?
Options:
A)a) x minutes
B)b) x/2 minutes
C)c) 2x/3 minutes
D)d) 3x/2 minutes
E)e) 2x minutes
Rationale: Speed of nicole = 20km/h or 20/60 km/min = 1/3 km/min.
Once jessica passed the nicole, the distance between the nicole and jessica will increase at the rate of (30-20) = 10km/h or 1/6 km/min
now jessica is cycling for x minutes after passing the nicole, so in those x minutes distance between jessica and nicole would be (1/6)*x = x/6 km.
So, the time taken by nicole to travel x/6 km = (x/6)/(1/3) = 3x/2. hence answer should be D.
Answer: D
Question: For the symbol, m”n=n^2−m for all values of m and n. What is the value of 5”3?
Options:
A)5
B)3
C)2
D)4
E)0
Rationale: 5”3= 9 - 5=4
Answer: D
Answer: D
Question: 5 books consisting of 2 financial management, 2 marketing management and 1 system management are placed on a shelf at random order. What is the probability that the books of each kind are all together.
Options:
A)1/120
B)1/64
C)1/32
D)1/48
E)1/56
Rationale: Since the denominator will be 5! . And there is no way to divide 5 from numerator and denominator. Use a multiple of 5 in the denominator only answer .
A
Answer: A
Question: There r 4 prime numbers in ascending order. The multiplication of first 3 is 385 and that of last 3is 1001. what is the last number is
Options:
A)11
B)12
C)15
D)13
E)17
Rationale: Explanation:
abcbcd=3851001=>ad=513
abcbcd=3851001=>ad=513
So d = 13
D
Answer: D
Question: A train passes a station platform in 36 sec and a man standing on the platform in 20 sec. If the speed of the train is 54 km/hr. What is the length of the platform?
Options:
A)120 m
B)240 m
C)300 m
D)400 m
E)None of these
Rationale: Speed = 54 * 5/18 = 15 m/sec.
Length of the train = 15 * 20 = 300 m.
Let the length of the platform be x m . Then,
(x + 300)/36 = 15 => x = 240 m.
ANSWER:B
Answer: B
Question: The Guests at a football banquet consumed a total of 406 pounds of food. if no individual guest consumed more than 2.5 pounds of food, What is the minimum number of guests that could have attended the banquet?
Options:
A)160
B)161
C)162
D)163
E)164
Rationale: To minimize one quantity maximize other.
162*2.5 (max possible amount of food a guest could consume) = 405 pounds, so there must be more than 162 guests, next integer is 163.
Answer: D.
Answer: D
Question: A man invests some money partly in 12% stock at 108 and partly in 10% stock at 60.To obtain equal dividends from both,he must invest the money in the ratio :
Options:
A)3 : 4
B)3 : 2
C)4 : 5
D)16 : 15
E)None
Rationale: Solution
For an income of Rs. 1 in 12% stock at 108, investment = Rs. (108/12)= Rs. 9 .
For an income of Rs. 1 in 10% stock at 60, investment = Rs.(60/10) = Rs. 6.
∴ Ratio of investments = 9 :6 =3:2
Answer B
Answer: B
Question: John want to buy a $100 Trouser at the store, but he think itâ€™s too expensive. Finally, it goes on sale for $75. What is the percent decrease?
Options:
A)20%
B)30%
C)40%
D)25%
E)60%
Rationale: The is always the difference between our starting and ending points. In this case, itâ€™s 100 â€“ 75 = 25. The â€œoriginalâ€ is our starting point; in this case, itâ€™s 100. (25/100)*100 = (0.25)*100 = 25%.
D
Answer: D
Question: The value of (log9 27 + log8 32) is:
Options:
A)7/2
B)19/6
C)5/3
D)7
E)8
Rationale: Let log9 27 = x. Then, 9x = 27
=> (32)x = 33 => 2x = 3 => x= 3/2
Let log8 32 = y. Then
8y = 32 => (23)y = 25 => 3y = 5 => y=5/3
ANSWER:C
Answer: C
Question: A train 120 m long passed a pole in 12 sec. How long will it take to pass a platform 380 m long?
Options:
A)25 sec
B)50 sec
C)75 sec
D)100 sec
E)125 sec
Rationale: Speed = 120/12 = 10 m/sec.
Required time = (120 + 380)/10 = 50 sec
Answer:B
Answer: B
Question: If 2 + 2/x = 3 - 3/x, then x =
Options:
A)-5
B)2/3
C)1
D)3/2
E)5
Rationale: We're given the equation 2 + 2/X = 3 - 3/X. We're asked for the value of X.
The common-denominator of these 4 numbers is X, so we have to multiple 2 of the numbers to give them that denominator...
2X/X + 2/X = 3X/X - 3/X
We can then eliminate that denominator, which gives us....
2X + 2 = 3X - 3
5 = X
Final Answer:E
Answer: E
Question: mixture contains alcohol and water in the ratio 4 : 3. If 5 liters of water is added to the mixture, the ratio becomes 4: 5. Find the quantity of alcohol in the given mixture.
Options:
A)10
B)99
C)27
D)22
E)29
Rationale: Let the quantity of alcohol and water be 4x litres and 3x litres respectively
20x = 4(3x+5)
8x = 20
x = 2.5
Quantity of alcohol = (4 x 2.5) litres = 10 litres.
Answer: A
Answer: A
Question: A goods train runs at the speed of 72 km/hr and crosses a 250 m long platform in 26 sec. What is the length of the goods train?
Options:
A)228
B)2000
C)267
D)270
E)274
Rationale: Speed = 72 * 5/18 = 20 m/sec.
Time = 26 sec.
Let the length of the train be x meters.
Then, (x + 250)/26 = 20
x = 270 m.
Answer: D
Answer: D
Question: Larry, Michael, and Lily have five donuts to share. If any one of the men can be given any whole number of donuts from 0 to 5, in how many different ways can the donuts be distributed?
Options:
A) 21
B) 42
C) 120
D) 504
E) 5040
Rationale: Larry, Michael, and Lily have five donuts to share to get the answer, see how can we get sum5with 3 numbers.
1) 0,0,5 = 3 combinations or 3! /2!
2) 0,1,4 = 6 combinations or 3!
similarly
3) 0,2,3 = 6 combinations
4) 1,1,3 = 3 combination
5) 2,2,1 = 3 combination
total =21=A
Answer: A
Question: A lady starts from P towards Q and realizes that at a point R, if he walks 50 km further he will be at a point S, which is as far away from R as it is from Q. What is the distance between P and Q if the distance between P and R is half the distance from R to Q?( Assume that P, Q, R and S are all on the same straight line)
Options:
A)150 km
B)200 km
C)250 km
D)125 km
E)155 km
Rationale: P___50_____ R ___50_____S____50 ___Q
The above figure gives the locations of P, R, S &Q in relation to each other.
ANSWER:A
Answer: A
Question: A box contains nine bulbs out of which 4 are defective. If four bulbs are chosen at random, find the probability that atleast one bulb is good?
Options:
A)125/119
B)125/129
C)125/126
D)125/129
E)125/192
Rationale: Required probability
= 1 - 1/126
= 125/126
Answer:C
Answer: C
Question: A certain car can travel 32 kilometers on a liter of fuel. If the fuel tank’s contents decrease by 3.9 gallons over a period of 5.7 hours as the car moves at a constant speed, how fast is the car moving, in miles per hour? (1 gallon = 3.8 liters; 1 mile = 1.6 kilometers)
Options:
A)52
B)65
C)78
D)91
E)104
Rationale: Fuel used 3.9 gallons ;convert to liters--> 3.9 x 3.8 liters
Time = 5.7 hours
1 mile = 1.6 kilometers ;convert to miles--> 1km = 1/1.6 mile
Speed (km/hour)= D/T = 32 (km*) x 3.9 x 3.8 / 5.7
replace (km*) to miles ; multiply by 1/1.6 mile
Speed (miles/hour)= 32 x 3.9 x 3.8 / 5.7 x 1.6 = 78 miles/hour
Ans :A
PS :i felt the factors were easy to cancel out ,so didn't require much rounding off
= 32 x 3.9 x 3.8 / 5.7 x 1.6
= 52
A
Answer: A
Question: The owner of a furniture shop charges his customer 24% more than the cost price. If a customer paid Rs. 8339 for a computer table, then what was the cost price of the computer table?
Options:
A)Rs.6725
B)Rs.6729
C)Rs.6710
D)Rs.6725
E)Rs.6721
Rationale: :
CP = SP * (100/(100 + profit%))
= 8339(100/124)
= Rs.6725.
Answer: D
Answer: D
Question: Find the invalid no.from the following series 13, 18, 25, 30, 37, 40
Options:
A)13
B)18
C)40
D)30
E)37
Rationale: The differences between two successive terms from the beginning are 7, 5, 7, 5, 7, 5. So, 40 is wrong.
C
Answer: C
Question: Pascal has 96 miles remaining to complete his cycling trip. If he reduced his current speed by 4 miles per hour, the remainder of the trip would take him 16 hours longer than it would if he increased his speed by 50%. What is his current speed O?
Options:
A) 6
B) 8
C) 10
D) 12
E) 16
Rationale: Let the current speed be x miles per hour.
Time taken if speed is 50% faster (i.e. 3x/2 = 1.5x) = 96/1.5x
Time taken if speed is reduced by 4 miles/hr (i.e. (x-4)) = 96/(x-4)
As per question, 96/(x-4) - 96/1.5x = 16
Solving this O we get x = 8.
B.
Answer: B
Question: If L is the least positive integer that is divisible by every integer from 1 to 9 inclusive, then L/2 is =
Options:
A) 5040
B) 2520
C) 1890
D) 1260
E) 630
Rationale: The integer should be divisible by: 2, 3, 4, 5, 6, 7, 8 and 9, that is 2, 3, 2^2, 5, 2*3, 7, 2^3 and 3^2. The least common multiple of these integers is the product of 7, 5, 3^2 and 2^3. Then, L/2 is (7 * 5 * 3^2 * 2^3)/2 = 7*5*9*4 = 1260.
Answer: D.
Answer: D
Question: A cistern 9 m long and 6 m wide contains water up to a breadth of 2 m 25 cm. Find the total area of the wet surface.
Options:
A)142 m sqaure
B)122 m sqaure
C)135 m sqaure
D)188 m sqaure
E)None of these
Rationale: Explanation:
Area of the wet surface =
2[lb+bh+hl] - lb = 2 [bh+hl] + lb
= 2[(6*2.25+9*2.25)]+9*6 = 122 m square
Option B
Answer: B
Question: Which number is the odd one out?
159
248
963
357
951
852
Options:
A)154
B)248
C)536
D)645
E)135
Rationale: B
248
In the rest there is the same difference between each digit, eg: 8 (â€“3) 5 (â€“3) 2.
Answer: B
Question: In a class 40% of the students enrolled for Math and 70% enrolled for Economics. If 15% of the students enrolled for both Math and Economics, what % of the students of the class did not enroll for either of the two subjects?
Options:
A)5%
B)15%
C)0%
D)25%
E)20%
Rationale: We know that (A U B) = A + B - (A n B), where (A U B) represents the set of people who have enrolled for at least one of the two subjects Math or Economics and (A n B) represents the set of people who have enrolled for both the subjects Math and Economics.
Note: (A U B) = A + B - (A n B) => (A U B) = 40 + 70 - 15 = 95%
That is 95% of the students have enrolled for at least one of the two subjects Math or Economics.
Therefore, the balance (100 - 95)% = 5% of the students have not enrolled for either of the two subjects.
ANSWER:A
Answer: A
Question: If the average of a sequence of consecutive multiple of 18 is 153, and the greatest term is 270, how many terms W in the sequence are smaller than the average?
Options:
A)5
B)6
C)7
D)8
E)9
Rationale: Let the sequence have N terms starting 18*K
--> 18K, 18(K+1), 18(K+2), .... , 18(K+N-1) is the sequence.
The sum of the sequence is
---> 18K + 18(K+1) + 18(K+2) + .... + 18(K+N-1) =18*(K+(K+1)+...+(K+N-1)) = 18*(N*(2K+N-1)/2).
So the average is
153=[18*(N*(2K+N-1)/2)]/N = 18*(2K+N-1)/2 = 9 *(2K+N-1) ---> by cancelling 9 we get 2K+N-1=17 --> 2K+N=18 ---*).
On the other hand, since the greatest term is 270, 18(K+N-1)=270 --> by cancelling 18 we get K+N-1=15 --> K+N=16 ---**).
By *), **) we have K=2, N=14.
Since 153/18 = 8.5, 18*8<153<18*9. So the number of terms W which are smaller than the average is 18*2, 18*3, ..... ,18*8 ---> 7. The answer is C.
Answer: C
Question: 150 ml of 30% sulphuric acid was added to approximate 400 ml of 12% sulphuric acid solution. Find the approximate concentration Q of the acid in the mixture?
Options:
A)1/2
B)1/3
C)1/4
D)1/6
E)1/5
Rationale: Do not need any computation
30%-----------21%---------12%
if volume of both sol. were equal the concentration Q would be 21%=1/5, but 12% is more than 3 times
only possibility is 1/6
D
Answer: D
Question: In a simultaneous throw of 2 dice, what is the probability of getting a doublet?
Options:
A)1/3
B)1/6
C)1/2
D)2/3
E)1/5
Rationale: n(S) = 6*6 = 36
E = event of getting a doublet = {(1,1),(2,2),(3,3),(4,4),(5,5),(6,6)} = 6
Probability = 6/36 = 1/6
Answer is B
Answer: B
Question: The number 181 can be written as sum of the squares of 2 different positive integers. What is the difference of these 2 different integers?
Options:
A)3
B)2
C)1
D)4
E)5
Rationale: sum of the squares of 2 different positive integers = 181
10^2 + 9^2 = 181
now,
differene of these 2 different integers = 10-9 = 1
Ans - C
Answer: C
Question: Three-fourth of two-third of three-seventh of a number is 27. what is 10% of that number?
Options:
A)12.6%
B)6.3%
C)27%
D)25.2%
E)None of these
Rationale: Explanation :
Solution: Assume the number be x. then, 3/4 of 2/3 of 3/7 of x = 27.
x = 27 * 7/3 *3/2 * 4/3.
x = 126
.'. 10% of 126 = 10/100 * 126 = 12.6
Answer : A
Answer: A
Question: A merchant marks goods up by 80% and then offers a discount on the marked price. The profit that the merchant makes after offering the discount is 35%. What % discount did the merchant offer?
Options:
A)20%
B)25%
C)30%
D)35%
E)40%
Rationale: Let P be the original price of the goods and let x be the rate after the markup.
(1.8P)*x = 1.35P
x = 1.35/1.8 = 0.75 which is a discount of 25%.
The answer is B.
Answer: B
Question: Anand and Deepak started a business investing Rs. 1500 and Rs. 2000 respectively. Out of a total profit of Rs. 1300, Deepak's share is:
Options:
A)1776.25
B)2687
C)8400
D)1688.12
E)1714.28
Rationale: Ratio of their shares = 1500 : 2000= 3:4
Deepak's share = 3000* 4/7 = Rs. 1714.28.
Answer: E
Answer: E
Question: Evaluate: (1 - 1/10)(1 - 1/11)(1 - 1/12)...(1 - 1/99)(1 - 1/100)
Options:
A)5/100
B)6/100
C)7/100
D)8/100
E)9/100
Rationale: (1 - 1/10)(1 - 1/11)(1 - 1/12)...(1 - 1/99)(1 - 1/100)
= (9/10)(10/11)(11/12)...(98/99)(99/100)
= 9/100 : simplify
correct answer E
Answer: E
Question: Amar takes as much time in running 22 meters as a car takes in covering 58 meters. What will be the distance covered by Amar during the time the car covers 2.6 km?
Options:
A)700 m
B)978 m
C)970 m
D)986 m
E)640 m
Rationale: Distance covered by Amar
= 22/58 (2.6km)
= 11/29(2600) = 986 m
Answer: D
Answer: D
Question: In a dairy farm, 55 cows eat 55 bags of husk in 55 days. In how many days one cow will eat one bag of husk ?
Options:
A)34 days
B)40 days
C)46 days
D)50 days
E)55 days
Rationale: Explanation:
Less Cows, More days (Indirect Proportion)
Less bags, Less days (Direct Proportion)
[Cows1 55
Bags 55 1]::55:x
=>x∗55∗1=55∗1∗55
=>x=55
Option E
Answer: E
Question: If $750 is deposited into a savings account at an annual interest rate of 4% that compounds monthly, what is the value of the investment after 6 years?
Options:
A)$950.00
B)$953.03
C)$973.25
D)$900.25
E)$910.00
Rationale: Using CI Formula:
A=P(1+r/n)^n*t
A=750(1+4/6)^4*6
A=953.03
Option: B
Answer: B
Question: How many points (x, y) lie on the line segment between (15, 12 2/3) and (7, 17 2/3) such that x and y are both integers?
Options:
A)1
B)5
C)7
D)8
E)9
Rationale: slope = (17 2/3 - 12 2/3) / (7 - 15) = -5/8
y = mx + b => 12 2/3 = -15*5/8 + b => b = 1
y = -75x/8 + 22
Only integer values work, and the only multiples of 8 between 7 and 15 for x value is 8 , thus 1 point.
A
Answer: A
Question: Two cards are drawn from a pack of 52 cards . the probability that either both are red or both are kings ,is
Options:
A)85/528
B)78/587
C)55/221
D)85/25
E)78/54
Rationale: clearly n(S)=52C2=(52*51)/2=1326
let E1=event of getting both red cards,
let E2=event of getting both kings.
then E1nE2= event getting 2 kings of red cards.
n(E1)=26C2=(26*25)/2*1=325
n(E2)=4C2=(12)/2=6
n(E1nE2)=2C2=1
p(E1)=n(E1)/n(S)=325/1326
p(E2) =n(E1)/n(S)=6/1326
p(E1nE2)=1/1326
p (both red or both kings=p(E1UE2)
p(E1)+p(E2)-p(E1nE2)
325/1326+6/1326-1/1326=330/1326
=55/221
Answer (C)
Answer: C
Question: A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 108 km/hr, what is the length of the platform?
Options:
A)338
B)240
C)287
D)267
E)480
Rationale: Speed = (108 * 5/18) m/sec = 30 m/sec. Length of the train = (30 x 20)m = 600 m. Let the length of the platform be x meters. Then, (x + 600)/36 = 30 ==> x + 600 = 1080 ==>
x = 480 m.
Answer:E
Answer: E
Question: A certain office supply store stocks 2 sizes of self-stick notepads, each in 6 colors. The store packs the notepads in packages that contain either 3 notepads of the same size and the same color or 3 notepads of the same size and of 3 different colors. If the order in which the colors are packed is not considered, how many different packages of the types described above are possible?
Options:
A)6
B)8
C)16
D)24
E)52
Rationale: Notepads of the same color = 6 (we have 6 colors). As we have two sizes then total for the same color=6*2=12
Notepads of the different colors = 6C3=20 (we should choose 3 different colors out of 6). As we have two sizes then total for the different color=20*2=40
Total=40+12=52
Answer: E.
Answer: E
Question: A trader sells 85 meters of cloth for Rs. 8925 at the profit of Rs. 15 per metre of cloth. What is the cost price of one metre of cloth?
Options:
A)Rs.90
B)Rs.76
C)Rs.98
D)Rs.18
E)Rs.02
Rationale: SP of 1m of cloth = 8925/85 = Rs. 105
CP of 1m of cloth = SP of 1m of cloth - profit on 1m of cloth
= Rs. 105 - Rs. 15 = Rs.90.
Answer:C
Answer: C
Question: In an exam, Amar scored 64 percent, Bhavan scored 36 percent and Chetan 44 percent. The maximum score awarded in the exam is 800. Find the average mark scored by all the three boys?
Options:
A)384
B)882
C)270
D)377
E)262
Rationale: Average mark scored by all the three boys
= [64/100 (800) + 36/100 (800) + 44/100 (800)] / 3
= 384
Answer:A
Answer: A
Question: The strength of a school increases and decreases every alternate year. It starts with increase by 10% and there-after the percentage of increase/decrease is the same. Which of the following is definitely true about the strength of the school in 2001 as compared to that in 1996?
Options:
A)Increase approximately by 2%
B)Decrease approximately by 2%
C)Increase approximately by 20%
D)Decrease approximately by 20%
E)None of these
Rationale: Let the strength of school was x in 1998
∴ strength in 2001 will be
= x110⁄100 × 90⁄100 × 110⁄100 × 90⁄100 × 110⁄100 = 1.07811 x
increment = 1.07811 x – x = 0.07811 x
∴ % increase = 7.811 ≈ 8%
Answer E
Answer: E
Question: The area of a square is equal to twice the area of a rectangle of dimensions 32 cm * 64 cm. What is the perimeter of the square?
Options:
A)236
B)256
C)456
D)656
E)756
Rationale: Area of the square = s * s = 2(32 * 64)
=> s = 64 cm
Perimeter of the square = 4 * 64= 256cm.
Answer: Option B
Answer: B
Question: If 9x-3y=12 and 3x-5y=7 then 6x-2y = ?
Options:
A)-5
B)4
C)2
D)8
E)9
Rationale: 9x-3y=12---1
3x-5y=7----2
multiplying second equation with 3 and solving the two equations we get
x=1 and y=-1
6*1-2*-1=8 ANSWER:D
Answer: D