divelab/Sys2Bench huggingface dataset:
Question: 3x^2-6x+3 = 0 Find the above equation find the value of x
Options:
A)0
B)1
C)2
D)4
E)6
Rationale: a = 3, b = -6, c = 3
x1,2 = (6 ± √( (-6)2 - 4×3×3)) / (2×3) = (6 ± √(36-36)) / 6 = (6 ± 0) / 6
x1 = x2 = 1
B
Answer: B
Question: Pipe A can fill a tank in 8 hours, pipe B in 10 hours and pipe C in 40 hours. If all the pipes are open, in how many hours will the tank be filled?
Options:
A)2
B)2.5
C)3
D)4
E)None
Rationale: Sol.
Part filled by (A + B + C) in 1 hour = (1/8 + 1/10 + 1/40) = 1/4.
âˆ´ All the three pipes together will fill the tank in 4 hours.
Answer D
Answer: D
Question: If the price of gold increases by 50%, find by how much the quantity of ornaments must be reduced, so that the expenditure may remain the same as before?
Options:
A)331/3%
B)332
C)333
D)335
E)400
Rationale: Explanation:
100
150
------
150-------50
100-------? => 331/3%
A)
Answer: A
Question: Valentine day 14 Feb. 2005 was celebrated by Anand and shilpa on Monday. They were very happy. What day of the week would come on 14 Feb. 2010?
Options:
A)monday
B)tuesday
C)sunday
D)wednesday
E)thursday
Rationale: feb 14 2005 - monday
feb 14 2006 - tuesday
feb 14 2007 - wednesday
feb 14 2008 - thursday
feb 14 2009 - saturday [since 2008 is leap year , 2 days ll go forward]
feb 14 2010 - sunday
ANSWER:C
Answer: C
Question: The average of first 20 natural numbers is?
Options:
A)10.6
B)10.5
C)10.9
D)15.4
E)15.1
Rationale: Sum of 20 natural no. = 420/2 = 210
Average = 210/20 = 10.5
Answer:B
Answer: B
Question: A committee has 5 men and 6 women. What are the number of ways of selecting 2 men and 3 women from the given committee?
Options:
A)200
B)350
C)270
D)874
E)125
Rationale: Explanation:
The number of ways to select two men and three women = 5C2 * 6C3
= (5 *4 )/(2 * 1) * (6 * 5 * 4)/(3 * 2)
= 200
Answer: A
Answer: A
Question: The radius of a circle is increased by 1%. Find how much % does its area increases?
Options:
A)2.06%
B)2.91%
C)9.01%
D)2.01%
E)3.01%
Rationale: r = 100 r = 101
r2 = 10000 r2 = 10201
10000 ---- 201
100 ---- ? => 2.01%
Answer:D
Answer: D
Question: What is 120% of 13/24 of 720?
Options:
A)372
B)434
C)468
D)512
E)564
Rationale: 120% * 13/24 * 360 = 1.2 * 13 * 30 = 468
The answer is C.
Answer: C
Question: In a certain experiment, the data collected is the number of organisms per sample, and this data follows a normal distribution. If the sample of data has a mean of 50 and a standard deviation of 12, which of the following is exactly 1.75 standard deviations more than the mean?
Options:
A)a) 48
B)b) 60
C)c) 71
D)d) 77.5
E)e) 81
Rationale: Standard Deviation is a relatively rare category in the Quant section, although you're like to be tested on it 1 time on Test Day. You'll never be asked to calculate SD though, so you really just need to learn the basic 'concepts' behind it.
Here, we're told two things about a group of numbers:
1) The average of the group is 50
2) The standard deviation of the group is 12
If you go 1 SDupfrom the average, you hit.....50+12 = 62
If you go 1 SDdownfrom the average, you hit.....50-12 = 38
If you go 2 SDsupfrom the average, you hit.....50+2(12) = 74
If you go 2 SDsdownfrom the average, you hit.....50-2(12) = 26
Etc.
Here, we're asked for the number that is EXACTLY 1.75 SDs above the mean....
1.75 SDsupwould be.....50 + 1.75(12) = 71
C
Answer: C
Question: A contest will consist of n questions, each of which is to be answered eithertrueorfalse. anyone who answers all n questions correctly will be a winner. what is the least value of n for which the probability is less than 1/10000 that a person who randomly guesses the answer to each question will be a winner?
Options:
A)5
B)10
C)50
D)100
E)1000
Rationale: A contest will consist of n questions, each of which is to be answered eithertrueorfalse. anyone who answers all n questions correctly will be a winner. what is the least value of n for which the probability is less than 1/1000 that a person who randomly guesses the answer to each question will be a winner?
A.5
B.10
C.50
D.100
E.1000
Soln: ans is B
Probability that one question is answered right is 1/2.
Now for minimum number of questions needed to take probability less than 1/1000 is
=> (1/2)^n < 1/10000
n = 100 satisfies this.
D
Answer: D
Question: A palindrome is a number that reads the same forward and backward. For example. 2442 and 111 are palindromes. If 5-digit palindromes are formed using one or more of the digits, 1, 2, 3, how many such palindromes are possible?
Options:
A)12
B)15
C)18
D)24
E)27
Rationale: XYZYX
X can be 1, 2, or 3, thus 3 options.
Y can be 1, 2, or 3, thus 3 options.
Z can be 1, 2, or 3, thus 3 options.
Total 3^3=27.
Answer: E.
Answer: E
Question: A cylindrical container with 6 meters diameter and a height of 8 meters is filled to capacity with water. If the water is then used to fill several smaller cylinders (2 meters radius and 5 meters height), how many smaller cylinders can be filled to capacity before the larger cylinder becomes empty?
Options:
A)5
B)4
C)3
D)2
E)1
Rationale: Calculate the volume of the larger cylinder and divide it by the volume of the smaller cylinder.
volume of cylinder =πr2h
larger cylinder volume=226.19
smaller cylinder volume=62.83
therefore the number of smaller cylinders can be filled to capacity=226.19/62.83=3.6
Answer is C only 3 smaller cylinders can be filled to capacity.
Answer: C
Question: A committee of three people is to be chosen from 5 married couples. What is the number of different committees that can be chosen if two people who are married to each other cannot both serve on the committee?
Options:
A)16
B)24
C)26
D)80
E)32
Rationale: One of the approaches:
Each couple can send only onerepresentativeto the committee. Let's see in how many ways we can choose 3 couples (as there should be 3 members) out of 5 to send only onerepresentativesto the committee:5C3=10.
But each of these 3 couples can send two persons (husband or wife): 2*2*2=2^3=8.
Total # of ways: 5C3*2^3=80.
Answer: D.
Answer: D
Question: Calculate the distance covered by 350 revolutions of a wheel of radius 25.3 cm.
Options:
A)558.6 m
B)556.6 m
C)516.6 m
D)156.6 m
E)256.6 m
Rationale: In one resolution, the distance covered by the wheel is its own circumference. Distance covered in 350 resolutions.
=350 * 2 * 22/7 * 25.3 = 55660 cm = 556.6 m
ANSWER:B
Answer: B
Question: Find the number of different prime factors of 12800
Options:
A)4
B)2
C)3
D)5
E)6
Rationale: Explanation:
L.C.M of 12800 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 5 x 5
2, 5
Number of different prime factors is 2.
Answer: Option B
Answer: B
Question: If f(x)= 5x^2- 2x+6 and g(y)= 3y-3, then g(f(x))
Options:
A)82x^2-9x+38
B)15x^2-6x+15
C)58x^2-4x+58
D)87x^2-5x+96
E)98x^2-7x+94
Rationale: g(f(x))=3(5x^2-2x+6)-3
=15x^2-6x+18-3
=15x^2-6x+15
the answer is B
Answer: B
Question: The parameter of a square is equal to the perimeter of a rectangle of length 40 cm and breadth 20 cm. Find the circumference of a semicircle whose diameter is equal to the side of the square. (Round off your answer to two decimal places)?
Options:
A)47.14
B)45.15
C)43.23
D)41.44
E)41.51
Rationale: Let the side of the square be a cm.
Parameter of the rectangle = 2(40 + 20) = 120 cm Parameter of the square = 120 cm
i.e. 4a = 120
a = 30
Diameter of the semicircle = 30 cm
Circimference of the semicircle
= 1/2(âˆ)(30)
= 1/2(22/7)(30) = 660/14 = 47.14 cm to two decimal places
Answer: A
Answer: A
Question: The average of marks obtained by 120 boys was 35. If the average of marks of passed boys was 39 and that of failed boys was 15, the number of boys who passed the examination is?
Options:
A)100
B)110
C)120
D)130
E)140
Rationale: Let the number of boys who passed = X.
Then, 39 x X + 15 x (120 - X) = 120 x 35
24X = 4200 - 1800
=> X = 2400/24
X = 100.
Hence, the number of boys passed = 100.
ANSWER:A
Answer: A
Question: The vertices of a rectangle in the standard (x,y) coordinate place are (0,0), (0,4), (8,0) and (8,4). If a line through (1,1) partitions the interior of this rectangle into 2 regions that have equal areas, what is the slope of this line?
Options:
A)1/3
B)2/5
C)4/7
D)1
E)7/4
Rationale: We should know that a rectangle can be divided into two equal areas by a straight line only when the straight line passes through the center of the rectangle.
The center of the rectangle is the point (4,2).
The slope of line passing through points (1,1) and (4,2) = (2-1)/(4-1) = 1/3
The answer is A.
Answer: A
Question: The speed of a train is 72 kmph. What is the distance covered by it in 20 minutes?
Options:
A)20 kmph
B)28 kmph
C)25 kmph
D)22 kmph
E)24 kmph
Rationale: 72 * 20/60
=24 kmph
Answer: E
Answer: E
Question: The average number of shirts with Salman, Ambani and Dalmiya is 60, if all of them reached a shopping mall in Delhi and purchased 1 shirts each of them then average number of shirt each of them now has
Options:
A)66
B)63
C)62
D)64
E)61
Rationale: Required average
= Old average + New average
= 60 + 1 = 61
answer :E
Answer: E
Question: What is the missing number in the series?
4,9,20,43,90,?
Options:
A)175
B)185
C)195
D)205
E)215
Rationale: 4*2+1=9
9*2+2=20
20*2+3=43
43*2+4=90
similarly 90*2+5=185
ANSWER:B
Answer: B
Question: The total age of A and B is 12 years more than the total age of B and C. C is how many years younger than A?
Options:
A)12
B)76
C)97
D)16
E)19
Rationale: (A + B) - (B + C) = 12
A - C = 12
Answer:A
Answer: A
Question: 337.62+8.591+44.5=?
Options:
A)448.62
B)258.42
C)987.63
D)390.711
E)182.45
Rationale: 337.62
8.591
44.5
----------
390.711
Answer is D
Answer: D
Question: The largest natural number which exactly divides the product of any four consecutive natural numbers is:
Options:
A)65
B)12
C)24
D)120
E)6
Rationale: Required number
= 1*2*3*4
=24
ANSWER:C
Answer: C
Question: In how many ways 4 boys and 4 girls can be seated in a row so that they are alternate.
Options:
A)144
B)288
C)12
D)576
E)None
Rationale: Solution: Let the Arrangement be,
B G B G B G B G
4 boys can be seated in 4! Ways.
Girl can be seated in 4! Ways.
Required number of ways,
= 4!*4! = 576.
Answer: Option D
Answer: D
Question: Pipe P can fill a tank in 3 hours, pipe Q in 9 hours and pipe R in 24 hours. If all the pipes are open, in how many hours will the tank be filled?
Options:
A)2 hours
B)2.1 hours
C)3 hours
D)3.5 hours
E)4.5 hours
Rationale: Explanation:
Part filled by (P + Q + R) in 1 hour = (1/3 + 1/9 + 1/24) = 35/72
All the three pipes together will fill the tank = 72/35 = 2.1 hours
ANSWER B
Answer: B
Question: Salad dressing P is made up of 30% vinegar and 70% oil, and salad dressing Q contains 10% vinegar and 90% oil. If the two dressings are combined to produce a salad dressing that is 25% vinegar, dressing P comprises what percentage of the new dressing?
Options:
A)75%
B)60%
C)40%
D)25%
E)20%
Rationale: Let x be the percentage of dressing P in the new dressing.
0.3x + 0.1(1-x) = 0.25
0.2x = 0.15
x = 0.75 = 75%
The answer is A.
Answer: A
Question: Find value of x: 3x^2+5x+2 = 0
Options:
A)-1
B)1
C)2
D)3
E)4
Rationale: a = 3, b = 5, c = 2
x1,2 = (-5 ± √(52 - 4×3×2)) / (2×3) = (-5 ± √(25-24)) / 6 = (-5 ± 1) / 6
x1 = (-5 + 1)/6 = -4/6 = -2/3
x2 = (-5 - 1)/6 = -6/6 = -1
A
Answer: A
Question: What percent is 150 of 90?
Options:
A)133 1/3 %
B)166 2/3 %
C)135 1/3 %
D)140 1/3 %
E)143 1/3 %
Rationale: 150/90 = 5/3
5/3 × 100 = 500/3 = 166 2/3 %
B
Answer: B
Question: The compound interest earned by Sunil on a certain amount at the end of two years at the rate of 8% p.a. was Rs.2828.80. Find the total amount that Sunil got back at the end of two years in the form of principal plus interest earned.
Options:
A)Rs. 19828.87
B)Rs. 19828.80
C)Rs. 19828.81
D)Rs. 19828.89
E)Rs. 19828.83
Rationale: Explanation:
Let the sum be Rs.P
P{ [ 1 + 8/100]2 - 1 } = 2828.80
P(8/100)(2 + 8/100) = 2828.80 [a2 - b2 = (a - b) ( a + b)] P = 2828.80 / (0.08)(2.08) = 1360/0.08 = 17000 Principal + Interest = Rs. 19828.80
Answer: B
Answer: B
Question: There has been successive increases of 15% and then 10% in the price of gas from the previous month. By what percentage should a driver reduce gas consumption so that the expenditure does not change?
Options:
A)12%
B)15%
C)18%
D)21%
E)24%
Rationale: Let P be the original price per unit of gas.
Let x be the original gas consumption.
Let y be the reduced gas consumption.
y*1.1*1.15*P = x*P
y = x / (1.1*1.15) which is about 0.79x which is a decrease of about 21%.
The answer is D.
Answer: D
Question: A train running at the speed of 60 km/hr crosses a pole in 9 seconds. Find the length of the train.
Options:
A)150
B)388
C)266
D)299
E)261
Rationale: Speed = 60*(5/18) m/sec = 50/3 m/sec
Length of Train (Distance) = Speed * Time
(50/3) * 9 = 150 meter.Answer: A
Answer: A
Question: 22 people are there, they are shaking hands together, how many hand shakes possible, if they are in pair of cyclic sequence.
Options:
A)21
B)22
C)44
D)45
E)46
Rationale: n for cyclic hand shake and n-1 for linear handshake.
so here no of hand shake is 22.
ANSWER:B
Answer: B
Question: a dealer buys 4 varieties of rice costing rs. 40,rs.42,rs.54 and rs.50 per kg in the ratio 6:5:10:9 and mixes all the four varieties and sells at 50% profit. What is the selling price per kg of rice?
Options:
A)68
B)70
C)72
D)75
E)77
Rationale: CP = 40*6+42*5+54*10+50*9=1440
SP = 1.5*1440=2160
Total no.of kgs=6+5+10+9=30
SP per kg=2160/30=72
ANSWER:C
Answer: C
Question: The population of a town is 7500. It decreases annually at the rate of 10% p.a. What was its population 2 years ago?
Options:
A)9300
B)8000
C)8500
D)9500
E)10000
Rationale: Formula :
( After =100 denominator
Ago = 100 numerator)
7500 Ã— 100/90 Ã— 100/90 = 9259
A)
Answer: A
Question: In 1998 the profits of company N were 10 percent of revenues. In 1999, the revenues of company N fell by 20 percent, but profits were 12 percent of revenues. The profits in 1999 were what percent of the profits in 1998?
Options:
A)80%
B)105%
C)96%
D)124.2%
E)138%
Rationale: 0,096R = x/100*0.1R
Answer C
Answer: C
Question: 5 men are equal to as many women as are equal to 8 boys. All of them earn Rs.90 only. Men’s wages are?
Options:
A)6Rs
B)7Rs
C)8Rs
D)4Rs
E)2Rs
Rationale: 5M = xW = 8B
5M + xW + 8B ----- 90 Rs.
5M + 5M + 5M ----- 90 Rs.
15M ------ 90 Rs. => 1M = 6Rs.
Answer: A
Answer: A
Question: There were two candidates in an election. Winner candidate received 75% of votes and won the election by 500 votes. Find the number of votes casted to the winning candidate?
Options:
A)228
B)744
C)750
D)199
E)231
Rationale: W = 75% L = 25%
75% - 25% = 50%
50% -------- 500
75% -------- ? => 750
Answer: C
Answer: C
Question: Population of a city in 20004 was 1000000. If in 2005 there isan increment of 15% , in 2006 there is a decrements of 35 % and in 2007 there is an increment of 45%, then find the population of city atthe end of the year 2007
Options:
A)1056787
B)1076658
C)1079767
D)1079977
E)1083875
Rationale: Required population = P (1 + R1/100)(1 - R2/100)(1 + R3/100)
= P (1 + 15/100)(1 - 35/100)(1 + 45/100)
= 1083875
E
Answer: E
Question: If n is a positive integer and n^2 is divisible by 72, then the largest positive integer T that must divide n is?
Options:
A)6
B)12
C)24
D)36
E)48
Rationale: Q: If n is a positive integer and n^2 is divisible by 72, then the largest positive integer T that must divide n is:
A 6, B 12, C 24, D 36, E 48
n^2 is divisible by 72, but it must also be greater than 72. If n is an integer, then n^2 must be a perfect square. The factorization of 72 is (8)(9), so if it is multiplied by 2, it will be (2)(8)(9) = (16)(9) = 144, a perfect square. So n^2 must be at least 144 or a multiple of 144, which means that n must be 12 or a multiple of 12.B
Answer: B
Question: A man leaves a point P at 6 a.m. and reaches the point Q at 10 a.m. another man leaves the point give at 8 a.m. and reaches the point P at 12 noon. At what time do they meet?
Options:
A)2 a.m
B)6 a.m
C)9 a.m
D)5 a.m
E)1 a.m
Rationale: 9 a.m.
Answer:C
Answer: C
Question: Mr. Hernandez, who was a resident of State X for only 10 months last year, had a taxable income of $22,500 for the year. If the state tax rate were 4 percent of the year’s taxable income prorated for the proportion of the year during which the taxpayer was a resident, what would be the amount of Mr. Hernandez’s State X tax for last year?
Options:
A) $900
B) $750
C) $600
D) $300
E) $60
Rationale: Total tax for the year = 22,500 x 4% = 900
As stated Annual tax is prorated as per the duration of stay.
Prorated Tax = 900 (10/12) = 750
Answer B
Answer: B
Question: Nicole cycles at a constant rate of 18 kilometers per hour, and is passed by Jessica, who cycles at a constant rate of 30 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)x/3
B)2x/3
C)x
D)3x/2
E)2x
Rationale: In x minutes, Jessica travels (x/60)*30 = x/2 miles
The time it takes Nicole to travel x/2 miles is (x/2) / 18 = x/36 hours = 5x/3 minutes
Jessica needs to wait 5x/3 - x = 2x/3 minutes.
The answer is B.
Answer: B
Question: For the past n days, the average (arithmetic mean) daily production at a company was 50 units. If today's production of 115 units raises the average to 55 units per day, what is the value of n?
Options:
A)8
B)10
C)12
D)14
E)16
Rationale: The daily production was raised by 5 units for n days, which has a weighting of 5n.
5n = 115-55 = 60
n = 12
The answer is C.
Answer: C
Question: What is the 23th digit to the right of the decimal point in the decimal form of 1/11?
Options:
A)1
B)6
C)3
D)5
E)0
Rationale: To solve ,we first have to use some long division.Long division allows us to get 1/11 in decimal form, which is 0.090909… where “09” is repeating.
We see that the 1st, 3rd, 5th digit to the right of the decimal point is a 0 and that the 2nd, 4th, 6th digit to the right of the decimal point is a 9. In other words, each odd-positioned digit is a 0, and each even-positioned digit is a 9.
Then the 23th digit to the right of the decimal point and we see that 23 is odd, then 23th digit is a 0.
Answer E.
Answer: E
Question: A certain company expects quarterly earnings of $0.80 per share of stock, half of which will be distributed as dividends to shareholders while the rest will be used for research and development. If earnings are greater than expected , shareholders will receive an additional $0.04 per share for each additional $0.10 of per share earnings. If quarterly earnings are $1.10 per share, what will be the dividend paid to a person who owns 100 shares of the company's stock?
Options:
A)$92
B)$96
C)$52
D)$120
E)$240
Rationale: EPS Actual> EPS expected.
each gets and additional .12 per share.
Thus .52*100 --> $52
answer is C
Answer: C
Question: How many integers from 0 to 48, inclusive, have a remainder of 1 when divided by 3 ?
Options:
A)15
B)16
C)17
D)18
E)19
Rationale: My ans is also C.17.
Explanation:
1 also gives 1 remainder when divided by 3, another number is 4, then 7 and so on.
Hence we have an arithmetic progression: 1, 4, 7, 10,..... 46, which are in the form 3n+1.
Now we have to find out number of terms.
tn=a+(n-1)d, where tn is the nth term of an AP, a is the first term and d is the common difference.
so, 46 = 1+(n-1)3
or, (n-1)3 = 45
or, n-1 = 15
or, n = 16
B
Answer: B
Question: Of the five numbers in a sequence, the first term is 18,000, and each of the following terms is 20% of the previous term. What is the value range of the five numbers?
Options:
A)19,375.00
B)19,750.90
C)19,975.25
D)17,984.50
E)17,971.20
Rationale: 1st number= 18,000
2nd number = 20% of 18,000= 3600
3rd number= 20% of 3600= 720
4th number = 20% of 720= 144
5th number= 20% of 144= 28.8
Range = 18,000-28.8= 17971.20
E is the answer
Answer: E
Question: If x^2 + 1/x^2 = 9, what is the value of x^4 + 1/x^4 ?
Options:
A)10
B)72
C)79
D)16
E)18
Rationale: IMPORTANT: I notice that if we SQUARE x², we get x⁴, and if we SQUARE 1/x², we get 1/x⁴, so let's see what happens if we take the equation x² + 1/x² = 9 andSQUAREboth sides:
(x² + 1/x²)²= 81
So, (x² + 1/x²)(x² + 1/x²) = 81
Expand to get: x⁴ + 1 + 1 + 1/x⁴ = 81
Simplify: x⁴ + 1/x⁴ = 79
Answer: C
Answer: C
Question: Which of the following must be subtracted from 2^96 so that the resulting integer will be a multiple of 3?
Options:
A)2
B)5
C)3
D)1
E)4
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 : D
Answer: D
Question: list of salaries of 8 employees are listed below. What is the median salary?
$40,000, $29,000, $35,500, $31,000, $43,000, $30,000, $27,000, $34,000
Options:
A)$28,000
B)$28,500
C)$32,500
D)$30,800
E)$31,500
Rationale: Ordering the data from least to greatest, we get:
$27,000, $29,000, $30,000, $31,000, $34,000, $35,500, $40,000, $43,000
Since there is an even number of items in the data set, we compute the median by taking the mean of the two middlemost numbers.
$31,000 + $34,000 = $65,000
The median salary is $32,500.
Answer : C
Answer: C
Question: A man saves a certain portion of his income during a year and spends the remaining portion on his personal expenses. Next year his income increases by 30% but his savings increase by 100%. If his total expenditure in 2 years is double his expenditure in 1st year, What %age of his income in the first year did he save?
Options:
A)21%
B)22.5%
C)25%
D)30%
E)40%
Rationale: 1st year Income= I
1st year savings= S
1st year Expense= E1
2nd year Income = 1.3I
2nd year savings= 2S (100% increase)
2nd Year expense= E2
E1+ E2= 2E1
E2=E1
That means Expenses are same during both years. With increase of 30% income the savings increased by 100%.
or S= .3I
or S= 30% of Income
D is the answer
Answer: D
Question: A bag contains 6 white and 4 black balls .2 balls are drawn at random. Find the probability that they are of same color?
Options:
A)7/15
B)7/17
C)8
D)8/15
E)9
Rationale: Let S be the sample space
Then n(S) = no of ways of drawing 2 balls out of (6+4) = \inline {\color{Black}10C_{2}} = =45
Let E = event of getting both balls of same colour
Then,n(E) = no of ways (2 balls out of six) or (2 balls out of 4)
=\inline {\color{Black}6C_{2}+4C_{2}} = = 15+6 = 21
Therefore, P(E) = n(E)/n(S) = 21/45 = 7/15
A)
Answer: A
Question: The average of seven numbers is 22. The average of first three numbers is 14 and the average of last three numbers is 19. What is the middle number?
Options:
A)27
B)55
C)31
D)34
E)35
Rationale: The total of seven numbers = 7X22 = 154
The total of first 3 and last 3 numbers is = 3 X 14+3 X 19 = 99
So, the middle number is (154 - 99 ) = 55
B
Answer: B
Question: Tough and Tricky questions: Absolute Values.
If |a| = 1/3 and |b| = 1/2, which of the following CANNOT be the result of a + b?
Options:
A)-5/6
B)-1/6
C)1/6
D)2/3
E)5/6
Rationale: |a| = 1/3
Absolute value of 'a' can have two values = 1/3 and -(1/3)
|b| = 1/2
Absolute value of 'b' can have two values = 1/2 and -(1/2)
Now different combinations of a + b are as follows:
a + b = (1/3) + (1/2) = 5/6
- a - b = -(1/3) - (1/2) = -5/6
a - b = (1/3) - (1/2) = -(1/6)
-a + b = -(1/3) + (1/2) = 1/6
Cross verifying with the given options, left over option is D.
Answer: D
Question: A boat goes 100 km downstream in 10 hours, and 200 Km upstream in 25 hours. The speed of the stream is?
Options:
A)1
B)22 1/7
C)2
D)22 1/2
E)3
Rationale: 100 --- 10 DS = 10
? ---- 1
200 ---- 30 US = 8
? ----- 1 S = (10 - 8)/2
= 1 kmph.
Answer:A
Answer: A
Question: The highest score in an inning was 3/11 of the total and the next highest was 3/11 of the reminder . If the score differ by 9, the total score was :
Options:
A)110
B)121
C)132
D)143
E)None of these
Rationale: Explanation:
Let the score be x. Then the highest score = 3x/11.
Reminder = (x - 3x/11) = 8x/11 .Next the highest score = 3/11 of 8x/11 = 24x/121.
3x/11 - 24x/11 = 9 <=> 33x - 24x = 9 × 121 <=> x = 121..
Answer: B
Answer: B