divelab/Sys2Bench huggingface dataset:
Question: Three runners R, B and C run a race, with runner R finishing 12m ahead of runner B and 18m ahead of runner C, while runner B finishes 8m ahead of runner C. Each runner travels entire distance at a constant speed. What was the length of the race?
Options:
A)36m
B)48m
C)60m
D)72m
E)84m
Rationale: Let distance of race be x mtrs. Then when R finishes x m , B has run (x- 12)mtrs and C has run x-18 mtrs. so at this point B is 6 m ahead of C. Now to finish race b needs to run another 12 m, so he runs another 12 m. when B finishes race he is 8 m ahead of C. so last 12 m B has run, C has run 10 m.
as speeds are constant, we have equation,
x-12/ x-18 = 12/10 > x = 48.
Answer B
Answer: B
Question: Jake remembers only the last four letters of his five-letter Klingon name. If he is sure that the first letter is neither "N" nor "Z", and assuming that there are only 10 letters in the Klingon alphabet, what is the probability that he will give the correct name when asked for it by the space attendant?
Options:
A)A)8/100
B)B)1/8
C)C)1/9
D)D)4/5
E)E)9/10
Rationale: Total letters 10, out of which the first letter is anything of 10 but N or X...
So there are 8 possible letters for first place..
And only one of them is correct..
So 1/8..
Answer: B
Answer: B
Question: Five years ago, John’s age was half of the age he will be in 2 years. How old is he now?
Options:
A)14years
B)12years
C)16years
D)17years
E)18years
Rationale: Let John=j,j-5=(j+2)/2,then j=12years
ANSWER:B
Answer: B
Question: A certain musical scale has has 13 notes, each having a different frequency, measured in cycles per second. In the scale, the notes are ordered by increasing frequency, and the highest frequency is twice the lowest. For each of the 12 lower frequencies, the ratio of a frequency to the next higher frequency is a fixed constant. If the lowest frequency is 110 cycles per second, then the frequency of the 7th note in the scale is how many cycles per second?
Options:
A)110 * sqrt 2
B)110 * sqrt (2^7)
C)110 * sqrt (2^12)
D)110 * the twelfth root of (2^7)
E)110 * the seventh root of (2^12)
Rationale: Let the constant be k.
F1 = 110
F2 = 110k
F3 = 110 k * k = 110 * k^2
F13= 110 * k^12
we know F13 = 2 *F1 = 2 * 110 = 220
220/110 = k^12
k = twelfth root of 2
for F7...
F7 = 110 * k^6 ( as we wrote for F2 and F3)
F7 = 110 * (twelfth root of 2) ^ 6
F7 = 110 * sqrt (2)
The answer is A.
Answer: A
Question: In a fort, there are 1200 soldiers. If each soldier consumes 3 kg per day, the provisions available in the fort will last for 30 days. If some more soldiers join, the provisions available will last for 25 days given each soldier consumes 2.5 kg per day. Find the number of soldiers joining the fort in that case.
Options:
A)627
B)528 soldiers
C)626
D)657
E)673
Rationale: Assume x soldiers join the fort. 1200 soldiers have provision for 1200 (days for which provisions last them)(rate of consumption of each soldier)
= (1200)(30)(3) kg.
Also provisions available for (1200 + x) soldiers is (1200 + x)(25)(2.5) k
As the same provisions are available
=> (1200)(30)(3) = (1200 + x)(25)(2.5)
x = [(1200)(30)(3)] / (25)(2.5) - 1200 => x = 528.
Answer:B
Answer: B
Question: Danny is sitting on a rectangular box. The area of the front face of the box is half the area of the top face, and the area of the top face is 1.5 times the area of the side face. If the volume of the box is 648, what is the area of the side face of the box?
Options:
A)32
B)78
C)84
D)90
E)72
Rationale: Lets suppose length= l, breadth= b, depth= d
Front face area= l*w = 1/2 w*d (l=1/2 d or d=2l)
top face area= w*d
side face area= w*d = 1.5 d*l (w=1.5l)
Volume = l*w*d= 648
l*1.5l*2l= 648
l=6
Side face area= l*d= l*2l= 6*2*6=72
E is the answer
Answer: E
Question: If 3x+4y=88 and 3x-4y=14, what is the value of x subs y?
Options:
A)17/4
B)25/4
C)27/4
D)25/4
E)19/4
Rationale: Given 3x+4y=88 ---Eq 1
3x -4y =14 -- Eq 2
Sum both eqns we get 6x = 102 => x = 17
Sum 3x in eq 2 => 51 - 4y = 14.
=> y= 37/4
Now XY = 14 - 37/4 = 19/4.
Option E is correct answer.
Answer: E
Question: The operation T is defined by x T y=1/x+1/y for all nonzero numbers x and y. If z is a number greater than 1, which of the following must be true.
I. z T z/z-1=1
II.x T (-z)=0
III. 2/z T 2/z=z
Options:
A)a.) I
B)b.) I and II only
C)c) I and III only
D)d) II and III only
E)e) I, II and III only
Rationale: Statement I is TRUE
Statement II is not TRUE
Statement III is TRUE
Answer : C
Answer: C
Question: In the first 10 overs of a cricket game, the run rate was only 3.2. What should be the rate in the remaining 40 overs to reach the target of 262 runs?
Options:
A)6.25
B)6.22
C)6.29
D)5.75
E)6.13
Rationale: Required run rate
= [262 - (3.2 * 10)]/40
= 230/40
= 5.75
Answer: D
Answer: D
Question: A trader bought a car at 20% discount on its original price. He sold it at a 40% increase on the price he bought it. What percent of profit did he make on the original price?
Options:
A)19%
B)72%
C)12%
D)16%
E)32%
Rationale: Original price = 100
CP = 80
S = 80*(140/100) = 112
100 - 112 = 12%
Answer:C
Answer: C
Question: The total of the ages of Amar, Akbar and Anthony is 62 years. What was the total of their ages three years ago ?
Options:
A)51 years
B)55 years
C)74 years
D)53 years
E)78 years
Rationale: Explanation:
Required sum = (62 - 3 x 3) years = (62 - 9) years = 53 years.
Answer: Option D
Answer: D
Question: What is the greater of the two numbers whose product is 2560, given that the sum of the two numbers exceeds their difference by 64?
Options:
A)90
B)100
C)110
D)70
E)None of these
Rationale: Let the greater and the smaller number be g and s respectively.
gs = 2560
g + s exceeds g - s by 64 i.e., g + s - (g - s) = 64
i.e., 2s = 64 => s = 32.
g = 2560/s = 80.
ANSWER:E
Answer: E
Question: A and B can do a work in 4days, B and C in 5days, C and A in 7days. If A,B and C work together , they will complete the work in?
Options:
A)3days
B)5days
C)7days
D)1days
E)2dasy
Rationale: A+B 1day work = 1/4
B+C 1day work = 1/5
C+A 1day work = 1/7
Adding we get 2(A+B+C) = 1/4 + 1/5 + 1/7 = 83/140
A+B+C 1 day work = 83/280
A,B,C can finish the work in 280/83 days = 3days approximately
Answer is A
Answer: A
Question: What is the greatest possible straight line distance, in inches, between any two points on a rectangular box that is 5 inches wide, 3 inches long, and 4 inches high?
Options:
A)2√5
B)5
C)5√2
D)10
E)50
Rationale: The maximum possible distance in a cuboid is the diagonal.
Diagonal length = sqrt(length^2 + breadth^2 + height^2) = sqrt(50)
= 5√2
(Option C)
Answer: C
Question: Suresh can complete a job in 15 hours. Ashutosh alone can complete the same job in 30 hours. Suresh works for 9 hours and then the remaining job is completed by Ashutosh. How many hours will it take Ashutosh to complete the remaining job alone?
Options:
A)4
B)5
C)6
D)12
E)None of these
Rationale: The part of job that Suresh completes in 9 hours
= 9â„15 = 3â„5
Remaining job = 1 - 3â„5 = 2â„5
Remaining job can be done by Ashutosh in 2â„5 Ã— 30 = 12 hours
Answer D
Answer: D
Question: Two trains run in opposite directions on a circular track. Train A travels at a rate of 4π miles per hour and Train B runs at a rate of 6π miles per hour. If the track has a radius of 6 miles and the trains both start from Point T at the same time, how long, in hours, after the trains depart will they again meet at Point T?
Options:
A)3
B)6
C)9
D)18
E)22
Rationale: I don't agree with your solutions, first. And second the answer choices don't seem to contain the right answer.
My solution is as follows, and I ask anyone to correct me if I am wrong.
Solution 1
Let the distance covered by train A be X, thus that covered by the train B will be 12*3.14-X
dA = X dB = 12*3.14 - X
Times taken by A and B are
tA= X/4*3.14 , tB = (12*3.14 - X)/6*3.14 (ii)
Since they have been traveling for the same period of time, then
X/4*3.14 = (12*3.14 - X)/6*3.14
X/2 =(12*3.14 -X)/3
3X = 2(12*3.14 -X)
5X = 24*3.14
X = 24*3.14/5
Plugging that in either equation of (ii) yields t = 6/5
Solution 2
We add the speed of A and B: totalSpeed T= 4*3.14 + 6*3.14 = 10*3.14
Total distance covered = 12*3.14
t ime = distance / speed = 12*3.14/10*3.14 = 6/5.
tA =( X/4*3.14) =(24*3.14/5)/4*3.14 = 6/5=B
Answer: B
Question: Yesterday's closing prices of 1,760 different stocks listed on a certain stock exchange were all different from today's closing prices. The number of stocks that closed at a higher price today than yesterday was 20 percent greater than the number that closed at a lower price. How many of the stocks closed at a higher price today than yesterday?
Options:
A) 960
B) 726
C) 1,100
D) 1,320
E) 1,694
Rationale: Lets consider the below -
The number of stocks that closed at a higher price = H
The number of stocks that closed at a lower price = L
We understand from first statement -> H+L = 1760 ----(1)
We understand from second statement -> H = (120/100)L => H = 1.2L ----(2)
Solve eq (1)(2) to get H = 960.
A is my answer.
Answer: A
Question: If s,u, and v are positive integers and 2s=2u+2v, which of the following must be true?
i. s=u
ii. u is not equal to v
iii. s > v
Options:
A)None
B)I only
C)II only
D)III only
E)II and III
Rationale: Given: 2s=2u+2v --> s=u+v. Now, since s, u, and v are positive integers then s is more than either u or v, so I is never true and III is always true. As for II: it's not necessarily true, for example 4=2+2. So, we have that only option III must be true.
Answer: D
Answer: D
Question: For all real numbers v, an operation is defined by the equation v* = v - v/3. If (v*)* = 4, then v=
Options:
A)6
B)9
C)12
D)15
E)18
Rationale: (v*)* = (v - v/3) - (v - v/3) / 3
4 = 2v/3 - 2v/9 = 4v/9
v = 9
The answer is B.
Answer: B
Question: Five 6 faced dice are thrown together. The probability that all the three show the same number on them is?
Options:
A)1/32
B)1/1296
C)1/33
D)1/38
E)1/34
Rationale: The three dice can fall in 6 * 6 * 6 * 6 * 6 = 7776 ways.
Hence the probability is 6/7776
= 1/1296
Answer: B
Answer: B
Question: Which is greatest in 16 ( 2/3) %, 2/5 and 0.17 ?
Options:
A)16 (2/3)
B)0.17
C)2/5
D)all are equal
E)none
Rationale: 16 (2/3)% =[ (50/3)* )1/100)]
= 1/6 = 0.166,
2/15 = 0.133.
Clearly,
0.17 is the greatest.
Answer is B.
Answer: B
Question: An article is bought for Rs.675 and sold for Rs.800, find the gain percent?
Options:
A)38%
B)28%
C)18%
D)22%
E)13%
Rationale: 675 ---- 125
100 ---- ? =>
=18%
Answer:C
Answer: C
Question: The product A of the first 10 prime numbers is closest to which of the following?
Options:
A)6.5 x 10^7
B)6.5 x 10^8
C)6.5 x 10^9
D)6.5 x 10^10
E)6.5 x 10^11
Rationale: The first 10 primes are: 2, 3, 5, 7, 11, 13, 17, 19, 23, and 29.
So, we need to find approximate value of 2*3*5*7*11*13*17*19*23*29.
# of different approximations are possible. For example:
2*5=10
3*17=~50 (actually more than 50);
7*13=~100 (actually less than 100);
11*19=~200 (actually more than 200)
23*29=667=A
2*3*5*7*11*13*17*19=~10*50*100*200*667=10^7*667=6.67*10^9.
Answer: C.
Answer: C
Question: If x and y are perfect squares, then which five of the following is not necessarily a perfect square?
Options:
A)x^2
B)xy
C)4x
D)x+y
E)x^5
Rationale: If x=y=1^2=1, then each option but A is a perfect square, therefore A is NOT necessarily a perfect square.
Answer: A.
Answer: A
Question: There are 7 non-collinear points. How many triangles can be drawn by joining these points?
Options:
A)12
B)27
C)35
D)28
E)11
Rationale: A triangle is formed by joining any three non-collinear points in pairs.
There are 7 non-collinear points
The number of triangles formed = 7C3
= 35
Answer: C
Answer: C
Question: A train is 435 meter long is running at a speed of 45 km/hour. In what time will it pass a bridge of 140 meter length
Options:
A)20 seconds
B)30 seconds
C)46 seconds
D)50 seconds
E)None of these
Rationale: Explanation:
Speed = 45 Km/hr = 45*(5/18) m/sec
= 25/2 m/sec
Total distance = 435+140 = 575 meter
Time = Distance/speed
=575∗2/25=46seconds
Option C
Answer: C
Question: The angle between the minute hand and the hour hand of a clock when the time is 4.20, is:
Options:
A)0º
B)10º
C)5º
D)20º
E)30º
Rationale: Angle traced by hour hand in 13/3 hrs =(360/12 x 13/3)º = 130º. Angle traced by min. hand in 20 min. = (360/60	x 20)º = 120º. Required angle = (130 - 120)º = 10ºAnswer : B
Answer: B
Question: Speed of a boat in standing water is 8 kmph and the speed of the stream is 2 kmph. A man rows to place at a distance of 210 km and comes back to the starting point. The total time taken by him is:
Options:
A)48 hours
B)51 hours
C)36 hours
D)56 hours
E)None
Rationale: Sol.
Speed upstream = 6 kmph; Speed downstream = 10 kmph.
∴ total time taken = [210/6 + 210/10] hours = 56 hours.
Answer D
Answer: D
Question: Jill invests $10000 in an account that pays an annual rate of 3.96%, compounding semi-annually. Approximately how much does she have in her account after two years?
Options:
A)$10079.44
B)$10815.83
C)$12652.61
D)$14232.14
E)$20598.11
Rationale: Solution: first of all, notice the magic word “approximately” — the test-writer is letting us know estimation is perfectly fine. Furthermore, the answer choices are nicely spread out, which will facilitate estimating.
OK, get ready for some fast & furious estimation. The interest rate 3.96% is an ugly number, so I’m going to approximate that as 4%. It compounds semiannually, so that means that there’s 2% every six months, and that happens four times in two years. Well, 2% of $10000 is $200. If you get $200, or a little more, on four occasions, that’s a little more than $800 in interest. We expect an answer slightly higher than $10800, so of course (B) is just right.
Notice, I estimated so that everything up until the last sum was single-digit math. Single-digit calculations are a good standard for which to strive when you are practicing estimation.
By the way, if you find the bank that will do answer (E), double your money in only two years, that’s terrific, but it probably is something wildly illegal, a Ponzi scheme or worse! In the real world, that just doesn’t happen. On word problems, especially in financial situations, you should always have your antenna up for what’s realistic or unrealistic.
answer (B)
Answer: B
Question: If n is an integer, which of the following CANNOT be a factor of 3n+4?
Options:
A)4
B)5
C)6
D)7
E)8
Rationale: 3n+4=3(n+1)+1 cannot be a multiple of 3, it's 1 more than multiple of 3: ... 4, 7, 10, 13, 16, ... Hence it cannot be a multiple of 2*3=6 as well.
Answer: C.
Answer: C
Question: The parameter of a square is equal to the perimeter of a rectangle of length 22 cm and breadth 16 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)77.14 cm
B)47.14 cm
C)84.92 cm
D)29.85 cm
E)23.57 cm
Rationale: Let the side of the square be a cm.
Parameter of the rectangle = 2(22 + 16) = 76 cm Parameter of the square = 76 cm
i.e. 4a = 76
A = 19
Diameter of the semicircle = 19 cm
Circimference of the semicircle
= 1/2(∏)(19)
= 1/2(22/7)(19) = 418/14 = 29.85 cm to two decimal places
ANSWER:D
Answer: D
Question: n a contest, a bowl contains 10 keys, one of which will open a treasure chest and nine of which will not. If a contestant selects the key that opens the treasure chest, she wins the contents of that chest. If Anna is allowed to draw two keys, simultaneously and at random, from the bowl as the first contestant, what is the probability that she wins the prize?
Options:
A)1/10
B). 1/9
C)1/5
D)19/90
E)2/9
Rationale: The total possibilities existing while withdrawing two keys are: 10C2 = 45
For Anna to win, 9 combinations exist assuming Key 1 to unlock the treasure E.g(1,2), (1,3)....(1,9)
P = 9/45 = 1/5
Option C
Answer: C
Question: Special codes are designated by either a 3-letter or a 4-letter code that is created by using the 26 letters of the alphabet. Which of the following gives the maximum number of different codes that can be designated with this system?
Options:
A)2(26)^4
B)26(26)^3
C)27(26)^3
D)26(26)^4
E)27(26)^4
Rationale: 26^3+26^4 = 26^3(1+26)=27*26^3
The answer is C.
Answer: C
Question: The manager of a produce market purchased a quantity of tomatoes for $0.80 per pound. Due to improper handling, 10 percent of the tomatoes, by weight, were ruined and discarded. At what price per pound should the manager sell the remaining tomatoes if she wishes to make a profit on the sale of the tomatoes equal to 12 percent of the cost of the tomatoes.
Options:
A)$0.94
B)$0.96
C)$0.99
D)$1.00
E)$1.20
Rationale: Assume the manager bought 100 tomatoes.
Cost Price = 80
Given: 10% are damaged --> Available tomatoes to sell = 90
90 * x - 80 = 0.12 * 80
90x - 80 = 9.6
90x = 89.6
x = 89.6/90 = 0.995
x is slightly under 0.9955 = 0.99
Answer: C
Answer: C
Question: A bag contains $510 in the form of 50 p, 25 p and 20 p coins in the ratio 2 : 3 : 4. Find the number of coins of each type.
Options:
A)200, 400, 500
B)300, 200, 600
C)800, 400, 600
D)400, 600, 800
E)600, 700, 900
Rationale: Let the number of 50 p, 25 p and 20 p coins be 2x, 3x and 4x.
Then 2x × 50/100 + 3x × 25/100 + 4x × 20/100 = 510
x/1 + 3x/4 + 4x/5 = 510
(20x + 15x + 16x)/20 = 510
⇒ 51x/20 = 510
x = (510 × 20)/51
x = 200
2x = 2 × 200 = 400
3x = 3 × 200 = 600
4x = 4 × 200 = 800.
Therefore, number of 50 p coins, 25 p coins and 20 p coins are 400, 600, 800 respectively.
Answer is D
Answer: D
Question: For all numbers a and b, the operationis defined by ab = (a + 2)(b – 3).
If 3x = –75, then x =
Options:
A) –15
B) –13
C) -14
D) -12
E) 15
Rationale: (3+2)(x-3)=-75..
x-3=-15..
x=-12
D
Answer: D
Question: Find the value of 1/(3+1/(3+1/(3-1/3)))
Options:
A)21/89
B)89/27
C)27/89
D)1/14
E)1/56
Rationale: 1/[3 + (1/(3+1/(3 - 1/3)))]
=> 1/[3 + 1/(3 + 1/(8/3))]
=> 1/[3 + 1/(3 + 3/8)]
=> 1/[3 + 8/27]
=> 1/(89/27)
=> 27/89
C
Answer: C
Question: If x, y, and z are consecutive odd integers, with x < y < z, then which of the following must be true?
I. y-x is even
II. (z-x)/y is an integer
III. xz is even
Options:
A)I only
B)II only
C)III only
D)I and II only
E)I, II, and III
Rationale: consecutive odds are:
2x+1, 2x+3, 2x+5
I. (2x+3)-(2x+1) = 2, so divisible by 2 and even - TRUE
II. ((2x+5)-(2x+1))/(2x+3)=4/(2x+3)=4/(odd number)= Not an integer - NOT TRUE
III. (2x+1)*(2x+5)=4x^2+10x+2x+5=4x^2+12x+5=(2x(x+6)+5)/2 is not integer, so NOT TRUE
ANSWER: A
Answer: A
Question: A man can swim in still water at 3 km/h, but takes twice as long to swim upstream than downstream. The speed of the stream is?
Options:
A)1.7
B)1.0
C)1.2
D)1.5
E)1.16
Rationale: M = 3
S = x
DS = 3 + x
US = 3 + x
3 + x = (3 - x)2
3 + x = 6 -2x
3x = 3
x = 1.0
Answer: B
Answer: B
Question: John buys 100 shares of par value Rs. 20 each, of a company, which pays an annual dividend of 12% at such a price that he gets 10% on his investment. Find the market value of a share.
Options:
A)2
B)24
C)5
D)6
E)8
Rationale: Face value of each share = Rs.20
Total dividend received by John = 100Ã—20Ã—12/100 = Rs.240
Let market value of 100 shares = Rs.x
xÃ—10/100=240
x = 2400
ie, Market value of 100 shares = Rs.2400
Hence, Market value of each share = Rs.24
Answer is B
Answer: B
Question: From theinteger n, if n*n*n is odd, then what is true from below options?
Options:
A)n is odd and n*n is even
B)n is odd
C)n*n is even
D)n is even
E)n*n is odd
Rationale: n is odd and n*n is even
Option A
Answer: A
Question: What is the sum of the different positive prime factors of 660?
Options:
A)5
B)10
C)15
D)17
E)21
Rationale: Prime factorization of 660
=66 * 10
=6*11 * 10
=2*3 * 2*5 * 11
=2^2 * 3 * 5 * 11
Sum of the different positive prime factors of 660 = 2+3+5+11
=21
Answer E
Answer: E
Question: For the positive integers q, r, s, and t, the remainder when q is divided by r is 7 and the remainder when s is divided by t is 3. All of the following are possible values for the product rt EXCEPT
Options:
A)32
B)38
C)44
D)52
E)63
Rationale: For the positive integers q, r, s, and t, the remainder when q is divided by r is 7 and the remainder when s is divided by t is 3. All of the following are possible values for the product rt EXCEPT
A. 32
B. 38
C. 44
D. 52
E. 63
Important property:remainder cannot be greater than the divisor.
Therefore, since the remainder when q is divided by r is 7, then r>7;
Similarly, since the remainder when s is divided by t is 3, then t>3.
Now, all answers, except 38 can be represented as the product of two multiples one of which is greater than 7 and another is greater than 3:
32=8*4
44=11*4
52=13*4
63=9*7
However, 38=1*38 or 19*2, thus rt cannot equal to 38.
Answer: B.
Answer: B
Question: Of the 65 cars on a car lot, 45 have air-bag, 30 have power windows, and 12 have both air-bag and power windows. How many of the cars on the lot have neither air-bag nor power windows?
Options:
A) 8
B) 2
C) 10
D) 15
E) 18
Rationale: Total -Neither = All Air bag + All Power Windows - Both
or 65 - Neither = 45 + 30 -12 = 63.
=> Neither = 2, hence B.
Answer : B
Answer: B
Question: The G.C.D of 1.08, 0.36 and 0.6 is
Options:
A)0.19
B)0.1
C)0.18
D)0.11
E)0.12
Rationale: Explanation:
Given numbers are 1.08 , 0.36 and 0.60
H.C.F of 108, 36 and 60 is 12 [because G.C.D is nothing but H.C.F]
therefore H.C.F of given numbers = 0.12
Answer: E
Answer: E
Question: A person has 100$ in 10$ and 5$ bill.If the 5$ bill quantity is twice that of 10$ bill.What is quantity of 10$.
Options:
A)2
B)6
C)7
D)8
E)5
Rationale: Let amount of 10$ be x.Then amount of 5$ be 2x. Now 5*2x+10*x=100.Thus x=5.Answer:E
Answer: E
Question: A room contains 160 people, 15 percent of whom are women. A group of people, 20 percent of whom are women, leaves the room. Of the people remaining in the room, 10 percent are women. How many people left the room?
Options:
A)10
B)20
C)40
D)60
E)80
Rationale: Say group of x people left the room.
# of women in the room was 0.15*160=24;
# of women in the group that left 0.2x;
# of women in the room after the group left it is 0.1(160-x);
So, 24-0.2x= 0.1(160-x) --> x=80.
Answer: E.
Answer: E
Question: In how many ways Chief Minister and Minister be elected from a team of 12 members?
Options:
A)124
B)129
C)132
D)154
E)165
Rationale: To do this, if captain is elected first, then we have 12 ways of doing this.
For election of vice-captain, we have only 11 ways left, coz 1 way is already consumed. (Situations like this is called dependent situation. One selection depends upon other selection.)
So, the ans is 12*11 = 132 ways.
C
Answer: C
Question: In how many ways can a Chief Minister and a Vice Minister be elected from a team of 8 members?
Options:
A)32
B)40
C)48
D)56
E)64
Rationale: There are 8 choices for the Chief Minister.
Then there are 7 choices for the Vice Minister.
The total number of ways is 8*7 = 56.
The answer is D.
Answer: D
Question: If a boat goes 7 km upstream in 42 minutes and the speed of the stream is 5 kmph, then the speed of the boat in still water is :
Options:
A)3.5 km/hr
B)4.2 km/hr
C)5 km/hr
D)10.5 km/hr
E)None of these
Rationale: Solution
Speed of stream = 1/2 (15-8) km/hr= 3.5kmph . Answer A
Answer: A
Question: In a certain game, a large bag is filled with blue, green, purple and red chips worth 1, 5, x and 11 points each, respectively. The purple chips are worth more than the green chips, but less than the red chips. A certain number of chips are then selected from the bag. If the product of the point values of the selected chips is 140800, how many purple chips were selected?
Options:
A)1
B)2
C)3
D)4
E)5
Rationale: 140800 = 1*5^2*8^3*11
The factors of 8 must come from the purple point value, so there are 3 purple chips.
The answer is C.
Answer: C
Question: Two numbers are less than a third number by 30% and 37%. How much percent is the second number is less than the first?
Options:
A)10%
B)15%
C)20%
D)25%
E)30%
Rationale: Let the third number be x
first number = 70% of x = 7x/10; second number = 63% of x = 63x/100;
Difference = 7x/10 - 63x/100 = 7x/100; Required percentage = 7x/100 * 10/7x * 100 = 10%
Answer is A
Answer: A
Question: A candidate appearing for an examination has to secure 40% marks to pass paper I. But he secured only 40 marks and failed by 20 marks. What is the maximum mark for paper I?
Options:
A)110
B)120
C)130
D)140
E)150
Rationale: he secured 40 marks nd fail by 20 marks so
total marks for pass the examinatn=60
let toal marks x
x*40/100=60
x=150
ANSWER:E
Answer: E