divelab/Sys2Bench huggingface dataset:
Question: In how many E ways can the wordGMATbe arranged so that no such arrangement has A as the first letter?
Options:
A)6
B)12
C)18
D)24
E)30
Rationale: Number of ways of arranging the word GMAT = 4! = 24
Number of ways of arranging the word GMAT so that A is always in the first = 3! = 6
Number of ways of arranging GMAT so that A is not in the beginning E= 24 - 6 = 18
Answer: C
Answer: C
Question: A, B, K start from the same place and travel in the same direction at speeds of 30km/hr, 40km/hr, 60km/hr respectively. B starts seven hours after A. If B and K overtake A at the same instant, how many hours after A did K start?
Options:
A)3
B)4.5
C)4
D)d) 5.5
E)e) 14
Rationale: The table you made doesn't make sense to me. All three meet at the same point means the distance they cover is the same.
We know their rates are 30, 40 and 60.
Say the time taken by B is T hrs. Then A takes 7+T hrs. And we need to find the time taken by K.
Distance covered by A = Distance covered by B
30*(7+T) = 40*T
T = 21 hrs
Distance covered by B = Distance covered by K
40*T = 60*Time taken by K
Time taken by K = 40*21/60 = 14 hrs
Time taken by A = 7+T = 7+21 = 28 hrs
Time taken by K = 14 hrs
So K starts 28-14 = 14 hrs after A. (ANSWER E)
Answer: E
Question: The simple interest on a sum of money is 4/9 of the principal and the number of years is equal to the rate percent. Find the rate and the time?
Options:
A)6 2/3%
B)6 2/8%
C)7 2/3%
D)6 5/3%
E)4 2/3%
Rationale: 4/9 P = (P*R*R)/100
R = 20/3 = 6 2/3%
Answer:A
Answer: A
Question: If Rs.450 amount to Rs.540 in 4 years, what will it amount to in 6 years at the same rate % per annum?
Options:
A)338
B)277
C)585
D)676
E)181
Rationale: 90 = (450*4*R)/100
R = 5%
I = (450*6*5)/100 = 135
450 + 135 = 585
Answer:C
Answer: C
Question: In an exam, Amar scored 49 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)344
B)826
C)207
D)269
E)208
Rationale: Average mark scored by all the three boys =
[49/100 (800) + 36/100 (800) + 44/100 (800)] / 3
= 344
Answer: A
Answer: A
Question: X starts a business with Rs.45000. Y joins in the business after 3 months with Rs.30000. What will be the ratio in which they should share the profit at the end of the year?
Options:
A)3:1
B)2:1
C)2:5
D)2:3
E)6:1
Rationale: Ratio in which they should share the profit
= Ratio of the investments multiplied by the time period
= 45000 * 12: 30000 * 9
= 45 * 12: 30 * 9
= 3*12: 2 * 9
= 2:1
Answer is B
Answer: B
Question: With both inlets open, a water tank will be filled with water in 36 minutes. The first inlet alone would fill the tank in 2 hours. If in every minutes the second inlet admits 50 cubic meters of water than the first, what is the capacity of the tank ?
Options:
A)9,000
B)4,500
C)1,750
D)1,000
E)2,000
Rationale: The work Done by Inlet A and B together in 1 min = 1/36
The work Done by Inlet A (First Inlet) in 1 min = 1/120
The work Done by Inlet B (Second Inlet) in 1 min = (1/36)- (1/120) =1/51
DIfference of Work done by B and A = B - A = 50 Cubic meter
i.e. (1/51)- (1/120) = 50 Cubic meter
i.e.4500 Cubic Meter
Answer: option B
Answer: B
Question: What is the greatest of 3 consecutive integers whose sum is 27 ?
Options:
A)6
B)7
C)8
D)9
E)11
Rationale: The sum of three consecutive integers can be written as n + (n + 1) + (n + 2) = 3n + 3
If the sum is 24, we need to solve the equation 3n + 3 = 27;
=> 3n = 27;
=> n = 9
The greatest of the three numbers is therefore 9 + 2 = 11 Answer: E
Answer: E
Question: The difference between the simple and the compound interest compounded every six months at the rate of 10% p.a. at the end of two years is 124.05. What is the sum?
Options:
A)10,000
B)6,000
C)12,000
D)8,000
E)None of these
Rationale: Let the sum be x.
Then, [x(1+5/100)4−x]−[x×10×2/100]=124.05
Solving the above eqns, we get x = 8,000.
Answer D
Answer: D
Question: Maria sold 10kg of apples in her first hour at the market, but only 2kg of apples in the second hour. On average, how many kg of apples did she sell in two hours at the market?
Options:
A)6 kg
B)5 kg
C)12 kg
D)24 kg
E)20 kg
Rationale: (10 kg + 2kg)/2 = 6 kg
Correct answer is: A
Answer: A
Question: If 3 cards are selected at random from the deck of 52 cards then What is the probability of one of the selected cards will be King, one of them will be Queen and one of them will be Jack?
A deck of cards has a total of 52 cards, consisting of 4 suits; (spades(Black), hearts(Red), diamond(Red)s, and clubs(Black)); and 13 cards including 1 king, 1 queen and 1 jack in each suit
Options:
A)96/5525
B)48/5525
C)16/5525
D)8/16575
E)1/2197
Rationale: Let K,Q and J represent King, Queen and Jack respectively.
One possible combination is KQJ and this can be arranged in 3! ways.
Probability of KQJ = (4/52)*(4/51)*(4/50)
Total probability = 3! * (4/52)*(4/51)*(4/50) . No need for final calculation. Reduce this to simpler form and you only have 1 option with 16 in the numerator. C is the correct answer.
Answer: C
Question: Tough and Tricky questions: Combinations.
Nine students - 4 boys and 5 girls - are to sit side by side for a makeup exam. How many ways could they arrange themselves given that no two boys and no two girls can sit next to one another?
Options:
A)12
B)36
C)72
D)240
E)5760
Rationale: 4!*5!*2 = 24*120*2 = 5760 ways.
Ans. E) 5760
Answer: E
Question: The distance between two cities A and B is 330 km. A train starts from A at 8 a.m. and travel towards B at 60 km/hr. Another train starts from B at 9 a.m. and travels towards A at 75 Km/hr. At what time will they meet?
Options:
A)10.30 a.m
B)11 a.m
C)10 a.m
D)12 noon
E)None of these
Rationale: Explanation:
Assume that they meet x hours after 8 a.m.
Then,train1,starting from A , travelling towards B, travels x hours till the trains meet
⇒Distance travelled by train1 in x hours = Speed ×Time = 60x
Then, train2, starting from B , travelling towards A, travels (x-1) hours till the trains meet
⇒Distance travelled by train2 in (x-1) hours = Speed ×Time = 75(x-1)
Total distance travelled = Distance travelled by train1 + Distance travelled by train2
=> 330 = 60x + 75(x-1)
=> 12x + 15(x-1) = 66
=> 12x + 15x - 15 = 66
=> 27x = 66 + 15 = 81
=> 3x = 9
=> x = 3
Hence the trains meet 3 hours after 8 a.m., i.e. at 11 a.m.
Answer: Option B
Answer: B
Question: If there are 9 horizontal lines and 9 vertical lines in a chess board, how many rectangles can be formed in the chess board?
Options:
A)1136
B)1268
C)1244
D)1296
E)1308
Rationale: Here m = 9, n = 9
Hence, number of rectangles that can be formed
= mC2 × nC2
= 9C2 × 9C2 = (9C2)^2
= 36^2
=1296
Ans-D
Answer: D
Question: Jessica can text 125 words per minute, while Maurice can text 10 words per minute. An abridged English translation of Tolstoy’s War and Peace contains 410,400 words. Working together, how many days will it take Jessica and Maurice to text the entire abridged translation of War and Peace?
Options:
A)0.3
B)2.1
C)3
D)9
E)11.3
Rationale: Since the answer choices are reasonably spaced out, we can approximate and save time
Combined words per day = 135*60*24 which should be 194400
410400/194400 will be 2.1,
So, Answer should be B.
Answer: B
Question: A certain manufacturer of cake, muffin, and bread mixes has 100 buyers, of whom 50 purchases cake mix, 40 purchase muffin mix, and 18 purchase both cake mix and muffin mix. If a buyer is to be selected at random from the 100 buyers, what is the probability that the buyer selected will be one who purchases neither cake mix nor muffin mix?
Options:
A)1/10
B)3/10
C)1/2
D)7/25
E)9/10
Rationale: C+M+B-CM-MB-CB-2CMB = 100
C - cake buyers, M - muffin and B - Bread buyers. CM,MB,CB and CMB are intersecting regions.
the question asks for people who have bought only bread mixes = B-CB-MB-2CMB has to be found out.
50 + 40 + B-CB-MB-18-2CMB = 100
B-CB-MB-2CMB = 28
hence the probability = 28/100 = 7/25.
D
Answer: D
Question: The cash difference between the selling prices of an article at a profit of 6% and 8% is Rs 3. The ratio of two selling prices is
Options:
A)51:52
B)52:53
C)53:54
D)54:55
E)None of these
Rationale: Explanation:
Let the Cost price of article is Rs. x
Required ratio = (106% of x) / (108% of x)
=106/108
=53/54 = 53:54.
Answer: C
Answer: C
Question: In how many years will a sum of money doubles itself at 5% per annum on simple interest?
Options:
A)22
B)20
C)99
D)88
E)76
Rationale: P = (P*5*R)/100
R = 20%
Answer: B
Answer: B
Question: Which of the following points is symmetric with y=x at (1,2)?
Options:
A)(-2,-1)
B)(-2,1)
C)(2,1)
D)(-1,-2)
E)(-1,2)
Rationale: We can think of line y = x as a mirror. Any point (x,y) becomes (y,x) when it isreflectedover the mirror. Reverse the coordinate and keep the same sign. These two points will be symmetric to the line y = x.
(1,2) would become (2,1).
Answer (C).
Answer: C
Question: A machine puts c caps on bottles in m minutes. How many seconds will it take to put caps on b bottles?
Options:
A)60bm/c
B)bm/60c
C)bc/60m
D)60b/cm
E)b/60cm
Rationale: A machine puts c caps on bottles in m minutes.
So, the machine puts 1 cap in m/c minutes
To put caps on b bottles, the machine will take bm/c minutes
In order to calculate the no. of hours taken , multiply the product by 60.
So, our answer is bm60/c
Answer : A
Answer: A
Question: Oak trees line both sides of a street for a length of 6/8 of a kilometer. If there is 12 meters of space between the trees, and each tree is 1 meter wide, how many trees are there along the street?
Options:
A)a)	59
B)b)	23
C)c)	24
D)d)	44
E)e)	46
Rationale: There is a gap of 16 m between every 2 trees , each tree is 1 m wide.
6/8 of 1 km = 750 m
Lets assume that x trees are planted So equation is
x*1 +(x-1)*12 = 750
Solve for x and we get x = 59, answer is A
Answer: A
Question: A can do a piece of work in 20 days. B in 15 days A and C in 12 days. In how many days can A finish the work if he is assisted by B on one day and C on the next, alternately?
Options:
A)2 days
B)8 days
C)6 days
D)8 days
E)9 days
Rationale: A + B = 1/20 + 1/15 = 7/60
A + C = 1/20 + 1/12 = 8/60
7/60 + 8/60 = 15/60 = 1/4
4 days * 2 = 8 days
Answer: B
Answer: B
Question: For any integer n greater than 1, n* denotes the product of all the integers from 1 to n, inclusive. How many prime numbers T are there between 6* + 2 and 6* + 6, inclusive?
Options:
A)None
B)One
C)Two
D)Three
E)Four
Rationale: Given that n* denotes the product of all the integers from 1 to n, inclusive so, 6*+2=6!+2 and 6*+6=6!+6.
Now, notice that we can factor out 2 our of 6!+2 so it cannot be a prime number, we can factor out 3 our of 6!+3 so it cannot be a prime number, we can factor out 4 our of 6!+4 so it cannot be a prime number, ... The same way for all numbers between 6*+2=6!+2 and 6*+6=6!+6, inclusive. Which means that there are no primes T in this range.
Answer: A.
Answer: A
Question: The ratio of males to females in a class is 2:3. The career preferences of the students in the class are represented in a circle graph. If the area of the graph allocated to each career preference is proportional to the number of students who have that career preference, how many degrees of the circle should be used to represent a career that is preferred by one-half of the males and three-fourths of the females in the class?
Options:
A)218
B)226
C)234
D)242
E)250
Rationale: 1/2*2/5 + 3/4*3/5 = 4/20 + 9/20 = 13/20
The number of degrees is 13/20 * 360 = 234 degrees
The answer is C.
Answer: C
Question: An article is bought for Rs.675 and sold for Rs.900, find the gain percent?
Options:
A)33 1/8%
B)33 1/9%
C)33 1/3%
D)33 8/3%
E)33 2/3%
Rationale: 675 ---- 225
100 ---- ? => 33 1/3%
Answer: C
Answer: C
Question: How many four digit numbers can be formed using the digits {1, 3, 4, 5, 7, 8, 9}(repetition of digits is not allowed)?
Options:
A)840
B)697
C)278
D)279
E)274
Rationale: The given digits are six.
The number of four digit numbers that can be formed using six digits is
7Pâ‚„ =7* 6 * 5 * 4
= 840.
Answer: A
Answer: A
Question: (1^2+2^2+3^2+.....+12^2)=?
Options:
A)330
B)345
C)365
D)385
E)650
Rationale: formula is (1^2+2^2+3^2+....+n^2=1/6 n(n+1)(2n+1)
n=12
=(1/6x12x13x25)
=650
Answer is E.
Answer: E
Question: A train speeds past a pole in 15 seconds and a platform 100 m long in 25 seconds. Its length is?
Options:
A)286 m
B)278 m
C)278 m
D)150 m
E)276 m
Rationale: Let the length of the train be x meters and its speed be y m/sec.
They, x / y = 15 => y = x/15
x + 100 / 25 = x / 15
x = 150 m.
Answer:D
Answer: D
Question: Two friends want to buy a snack. They combine their money and find they have $3.10, consisting of quarters, dimes, and nickels. If they have 28 coins and the number of quarters is half the number of nickels, how many quarters do they have?
Options:
A)3
B)4
C)5
D)6
E)7
Rationale: Let x be the number of quarters. Then 2x is the number of nickels.
(1) 25x + 10x + 10D = 310. Then 7x + 2D = 62
(2) 3x + D = 28. Then 6x + 2D = 56
Let's subtract equation (2) from equation (1).
x = 6
The answer is D.
Answer: D
Question: Given a collection of points P in the plane a 1-set is a point in P that can be separated from the rest by a line; i.e the pint lies on one side of the line while the others lie on the other side. The number of 1-sets of P is denoted by n1(P) . The maximum value of n1(P) over all configurations P of 4 points in the plane is
Options:
A)1
B)2
C)3
D)4
E)5
Rationale: maximum no of 1-sets will be the no of points itself...as in even a simple configuration we can separate one point from others to make it 1-set
ANSWER:A
Answer: A
Question: John received a 10% raise each month for three consecutive months. What was his salary after the three raises if his starting salary was $1,000 per month?
Options:
A)$1,248
B)$1,300
C)$1,331
D)$1,410
E)$1,463
Rationale: 1,000 + 100 (10%) = 1,100
1,100 + 110 (10%) = 1,210
1,210 + 121 (10%) = 1,331
Answer: C
Answer: C
Question: The radius of a semi circle is 6.3 cm then its perimeter is?
Options:
A)32.5
B)32.4
C)32.1
D)32.9
E)32.3
Rationale: 36/7 r = 6.3 = 32.4
Answer:B
Answer: B
Question: In a survey about potential presidential candidates A and B, 39% of the public like A and 57% like B. If the percentage of the public who like one candidate only is twice the percentage of the public who like both candidates, then what is the percentage of the public that like neither?
Options:
A)28%
B)35%
C)43%
D)22%
E)61%
Rationale: Let x be the percentage of people who like both.
Then the percentage of people who like only 1 but not both is 2x.
39% + 57% = 2x + 2(x) because the percentage who like both are counted twice.
Then x = 24% and 2x = 48%
100% = 24% + 48% + Neither
Neither = 28%
The answer is A.
Answer: A
Question: A technician makes a round-trip to and from a certain service center by the same route. If the technician completes the drive to the center and then completes 40 percent of the drive from the center, what percent of the round-trip has the technician completed?
Options:
A)5%
B)70%
C)25%
D)40%
E)55%
Rationale: The complete round trip consists of driving to the service center and then back home again.
So, once the technician drives to the service center he/she has already competed 50% of the entire trip.
Since the technician completes a portion of the trip back home,the correct answer must be greater than 50%
so 0.5+0.5*0.4=0.70
Answer:
B
Answer: B
Question: What is the square root of 261,121?
Options:
A)476
B)489
C)497
D)511
E)524
Rationale: 1) Checking the last digits in the answer options A, C, E are out since last digit of the square is known to be 1.
2) B = 489^2 and D = 511^2
B = (500-11)^2 and D = (500 + 11)^2
Since we need the answer less than 250000 => B is out.
Thus we have D as the ans.
Answer: D
Question: B is 50% less efficient than A. How much time will they, working together, take to complete a job which A alone could have done in 15 days?
Options:
A)9 days
B)11 days
C)10 days
D)15 days
E)None of these
Rationale: Ratio of times taken by A and B = 100 : 150 = 2 : 3.
Suppose B takes x days to do the work.
Then, 2 : 3 : : 15 : x â‡’ x = (15Ã—3)/2 â‡’ x = 45â„2
A's 1 dayâ€™s work = 1â„15; Bâ€™s 1 days work = 2â„45
(A + B)â€™s 1 dayâ€™s work = (1â„15 + 2â„45) = 1â„9
âˆ´ A and B together can complete the job in 9 days.
Answer A
Answer: A
Question: 14 men can complete a piece of work in 25 days. In how many days can 20 men complete that piece of work?
Options:
A)27.5 days
B)15.5 days
C)17.5 days
D)16.5 days
E)18.5 days
Rationale: 14 * 25 = 20 * x => x = 17.5 days
ANSWER:C
Answer: C
Question: In a party there are 5 couples. Out of them 5 people are chosen at random. Find the probability that there are at the least two couples?
Options:
A)29.42
B)29.22
C)29.25
D)23.25
E)29.28
Rationale: Average of 9 = x
9x = 8 * 3 + x * 2 x = 3.25
Total = 9 * 3.25 = 29.25
Answer:C
Answer: C
Question: The average weight of a group of 30 friends increases by 10 kg when the weight of additional 30 friends was added. If average weight of the whole group after including the additional 30 members is 40 kg, what is the average weight of the additional friends?
Options:
A)50 kg
B)60 kg
C)61 kg
D)62 kg
E)91 kg
Rationale: let a=avg. wt. of additional 30 friends
original total weight=(30 friends)(30 kg avge)=900kg
(900+30a)/(30+30)=40 kg avge
a=50 kg
Answer - A
Answer: A
Question: If p^2 – 13p + 40 = h, and p is a positive integer between 1 and 10, inclusive, what is the probability that h < 0?
Options:
A)1/10
B)1/5
C)2/5
D)3/5
E)3/10
Rationale: p2 – 13p + 40 = h
so (p – 8)(p – 5) = h
For q to be negative, the expressions (p – 8) and (p – 5) must have opposite signs. Which integers on the number line will yield opposite signs for the expressions (p – 8) and (p – 5)? Those integers in the range 5 < p < 8 (notice 5 and 8 are not included because they would both yield a value of zero and zero is a nonnegative integer). That means that there are only two integer values for p, 6 and 7, that would yield a negative q. With a total of 10 possible p values, only 2 yield a negative q, so the probability is 2/10 or 1/5.
The correct answer is B.
Answer: B
Question: A man walks at a rate of 10 mph. After every ten miles, he rests for 5 minutes. How much time does he take to walk 50 miles?
Options:
A) 300
B) 318
C) 320
D) 324
E) 330
Rationale: To cover 50 miles the man needs (time) = (distance)/(rate) = 50/10 = 5 hours = 300 minutes. He will also rest 4 times (after 10, 20, 30 and 40 miles), so total resting time = 4*5 = 20 minutes.
Total time = 300 + 20 = 320 minutes.
Answer: C.
Answer: C
Question: A cyclist bikes x distance at 12 miles per hour and returns over the same path at 8 miles per hour. What is the cyclist's average rate for the round trip in miles per hour?
Options:
A)8.1
B)8.3
C)9.6
D)8.9
E)9.0
Rationale: Distance = d1 = x miles
Speed = s1 = 12 miles per hour
Time = t1 = Distance/ Speed = x/12
2. Going from B to A
Distance = d2 = x miles
Speed = s2 = 8 miles per hour
Time = t2 = Distance/ Speed = x/8
3. Average Speed = Total Distance/Total Time
Total Distance = x + x = 2x
Total Time = x/12 + x/8 = x (1/12 + 1/8) = =5x/24
Speed = 2x/(5x/24) = 48/5
= 9.6
Answer : C
Answer: C
Question: There are two bags, one of which contains 5 red and 7 white balls and the other 3 red and 12 white balls. A ball is to be drawn from one or other of the two bags ; find the chances of drawing a red ball.
Options:
A)7/120
B)17/120
C)27/120
D)37/120
E)47/120
Rationale: P(Getting a red ball from the first bag): (1/2)*(5/12)
P(Getting a red ball from the 2nd bag): (1/2)*(3/15)
P(Drawing a red ball):
(1/2)*(5/12)+(1/2)*(3/15)= 37/120
ANSWER:D
Answer: D
Question: The triplicate ratio of 1:3 is?
Options:
A)1:0
B)1:8
C)1:27
D)1:2
E)1:1
Rationale: 13: 33 = 1:27
Answer: C
Answer: C
Question: A man two flats for $675958 each. On one he gains 12% while on the other he loses 12%. How much does he gain or lose in the whole transaction?
Options:
A)1.44%
B)2.56%
C)3.12%
D)4.65%
E)5.12%
Rationale: In such a case there is always a loss
Loss% = (12/10)^2 = 36/25 = 1.44%
Answer is A
Answer: A
Question: Which is the middle even number between 4 and 12?
Options:
A)9
B)12
C)14
D)8
E)22
Rationale: 4+x = 12-x
2 x = 8
X = 4
Now 4+x = 8
ANSWER:D
Answer: D
Question: 3889 + 12.674 - ? = 3854.002
Options:
A)A)47.095
B)B)47.752
C)C)47.932
D)D)47.95
E)E)47.672
Rationale: Let 3889 + 12.674 - x = 3854.002.
Then x = (3889 + 12.674) - 3854.002
= 3901.674 - 3854.002
= 47.672.
Answer = E
Answer: E
Question: It takes John 20 minutes to walk to the car park and 45 to drive to work. At what time should he get out of the house in order to get to work at 9:00 a.m.?
Options:
A)7:50
B)7:45
C)6
D)5
E)4
Rationale: The time it takes John to get to work: time to walk to car park + time to drive
20 + 45 = 70 minutes = 1 hour and 10 minutes
John needs to get out of the house 1 hour and 10 minutes before 9:00 am at
9:00 - 1:10 = 7:45 a.m.
B
Answer: B
Question: The length of the bridge, which a train 160 metres long and travelling at 45 km/hr can cross in 30 seconds, is?
Options:
A)245
B)777
C)282
D)266
E)215
Rationale: Speed = [45 X 5/18] m/sec = [25/2] m/sec Time = 30 sec Let the length of bridge be x metres. Then, (160 + x)/30 = 25/2 => 2(160 + x) = 750 => x = 215 m.
Answer: E
Answer: E
Question: A cyclist rides a bicycle 9 km at an average speed of 12 km/hr and again travels 12 km at an average speed of 9 km/hr. What is the average speed for the entire trip?
Options:
A)9.5
B)9.8
C)10.1
D)10.6
E)11.2
Rationale: distance = 21 km
time = 9/12 + 12/9 = (81 + 144) / 108 = 225 / 108 = 25/12 hours
average speed = (21 * 12) / 25 = 10.1 km/h
The answer is C.
Answer: C
Question: A train leaves Delhi at 9 a.m. at a speed of 30 kmph. Another train leaves at 2 p.m. at a speed of 40 kmph on the same day and in the same direction. How far from Delhi, will the two trains meet?
Options:
A)229
B)277
C)600
D)275
E)221
Rationale: D = 30 * 5 = 150
RS = 40 – 30 = 10
T = 150/10 = 15
D = 40 * 15 = 600 km.,Answer: C
Answer: C
Question: For how many values of B, is |||B - 5| -10| -5| = 2?
(Those ls are mods)
Options:
A) 0
B) 2
C) 4
D) 8
E) More than 8
Rationale: I think its 8
|||B-5|-10|-5| =2
let |B-5| = a which makes above
||a-10|-5| =2
let |a-10| = b which makes
|b-5| = 2
now for the above b can take 3, 7
for every b =3 a can have 13, 7
and for b = 7 a can have 17 and 3
so 'a' has four solutions 13, 7, 17 and 3
for a = 13; x has 18 or -8 thus has 2 for every combination hence 4x2 = 8
answer D
Answer: D
Question: A certain club has 10 members, including Harry. One of the 10 members is to be chosen at random to be the president, one of the remaining 9 members is to be chosen at random to be the secretary, and one of the remaining 8 members is to be chosen at random to be the treasurer. What is the probability that Harry will be the member chosen to be the secretary ?
Options:
A) 1/720
B) 1/80
C) 1/10
D) 1/9
E) 1/5
Rationale: This question is much easier than it appears.
Each member out of 10, including Harry, has equal chances to be selected for any of the positions (the sequence of the selection is given just to confuse us). The probability that Harry will be selected to be the secretary is 1/10 .
Answer: C
Answer: C
Question: Of the five numbers in a sequence, the first term is 10,000, and each of the following terms is 20% of the previous term. What is the value range of the five numbers?
Options:
A)9,375
B)9,750
C)9,975
D)9,984
E)10,736
Rationale: 1st number= 10,000
2nd number = 20% of 10,000= 2000
3rd number= 20% of 2000= 400
4th number = 20% of 400= 80
5th number= 20% of 80= 16
Range = 10,000-16= 9984
D is the answer
Answer: D
Question: A, B and C rents a pasture for Rs.870. A put in 12 horses for 8 months, B 16 horses for 9 months and 18 horses for 6 months. How much should C pay?
Options:
A)270
B)289
C)267
D)255
E)552
Rationale: 12*8 :16*9 = 18*6
8: 12: 9
9/29 * 870 = 270
Answer: A
Answer: A