divelab/Sys2Bench huggingface dataset:
Question: In how many E ways can 4 white and 3 black chess pieces be arranged in a row such that they occupy alternate places? Assume that the pieces are distinct.
Options:
A)E=288
B)E=144
C)12
D)48
E)96
Rationale: 4 white chess pieces can be arranged in 4! ways and 4 black pieces can be arranged in 3 ! ways.
W_W_W_W
Number of ways = 4!*3! = 24 * 6 = 144
Answer B
Answer: B
Question: A train 120 m in length crosses a telegraph post in 12 seconds. The speed of the train is?
Options:
A)16 kmph
B)88 kmph
C)36 kmph
D)18 kmph
E)19 kmph
Rationale: S = 120/12 * 18/5
= 36 kmph
Answer: C
Answer: C
Question: How many ways could four cars can be parked at a parking lot with seven parking empty parking spots in which three of the seven spots will remain empty?
Options:
A)840
B)28
C)7
D)920
E)838
Rationale: ways in which 4 spots out 7 can be selected = 7C4
ways in which 4 cars can be arranged in 4 seats = 4!
Total ways of arrangement =7C4*4!
=(7*6*5/3*2)*24
=35*24
=840
Ans = A
Answer: A
Question: which number replaces the question mark and completes the puzzle ?
2 + 2 = 4,
3 + 3 = 18,
4 + 4 = 48,
6 + 6= ?
Options:
A)180
B)190
C)180
D)170
E)160
Rationale: Solution:
180
2 + 2 = 4 {2 * 2 * 1}
3 + 3 = 18 {3 * 3 * 2}
4 + 4 = 48 {4 * 4 * 3}
6 + 6 = 180 {6 * 6 * 5}
Answer A
Answer: A
Question: A mixture of 40 liters of milk and water contains 10% water. how much water should be added to this so that water may be 20% in the new mixture?
Options:
A)3
B)4
C)5
D)6
E)7
Rationale: 4 ltr - Water
36 ltr - milk
Let X water be added then the new mixture must have 20% water
Then
4 + X = 20/100 (40+X)
X=5
ANSWER:C
Answer: C
Question: what is the sum of the first 20 odd natural numbers
Options:
A)300
B)400
C)500
D)600
E)700
Rationale: sum of first n odd natural nuber is = n^2
so sum of the first 20 odd natural numbers=(20)^2=400
ans 400
ANSWER:B
Answer: B
Question: To fill a tank, 25 buckets of water is required. How many buckets of water will be required to fill the same tank if the capacity of the bucket is reduced to two-fifth of its present ?
Options:
A)65.5
B)63.5
C)60.5
D)61.5
E)62.5
Rationale: Let the capacity of 1 bucket = x.
Then, the capacity of tank = 25x.
New capacity of bucket = 2/5 x
Therefore, Required number of buckets = (25x)/(2x/5)
= (25x) x 5/2x
= 125/2
= 62.5
Answer is E.
Answer: E
Question: Two 6 faced dice are thrown together. The probability that both show the same number on them is ?
Options:
A)1/6
B)1/12
C)1/18
D)1/2
E)1/4
Rationale: It all 3 numbers have to be same basically we want doublets. 11, 22, 33, 44, 55 and 66. Those are six in number. Further the three dice can fall in 6 * 6 = 36 ways.
Hence the probability is 6/36 = 1/6
Answer:A
Answer: A
Question: If 4a = 16b and 9b = 14c, Find a:b:c?
Options:
A)52:13:7
B)13:7:52
C)7:13:52
D)64:14:9
E)None of these
Rationale: Explanation:
(4a = 16b ==> a/b = 16/4)
and (9b = 14c ==> b/c = 14/9)
==> a:b = 16:4 and b:c = 14:9
a:b:c = 64:14:9
Answer: Option D
Answer: D
Question: If Y > X and XM < YM, what must be true?
Options:
A)M >0.
B)M < Y.
C)X < 0.
D)M < 0.
E)Y < 0.
Rationale: X>Y, bus as soon as M is multiplied to both sides inequality sign changes.
This is only possible when -ve is multiplied on both sides. That means M is -ve
A is the answer
Answer: A
Question: A number when divided by a divisor leaves a remainder of 24.
When twice the original number is divided by the same divisor, the remainder is 11. What is the value of the divisor?
Options:
A)26
B)30
C)37
D)43
E)45
Rationale: Let the original number be 'a'
Let the divisor be 'd'
Let the quotient of the division of aa by dd be 'x'
Therefore, we can write the relation as a/d = x and the remainder is 24.
i.e., a=dx+24 When twice the original number is divided by d, 2a is divided by d.
We know that a=dx+24. Therefore, 2a = 2dx + 48
The problem states that (2dx+48)/d leaves a remainder of 11.
2dx2dx is perfectly divisible by d and will therefore, not leave a remainder.
The remainder of 11 was obtained by dividing 48 by d.
When 48 is divided by 37, the remainder that one will obtain is 11.
Hence, the divisor is 37.
C)
Answer: C
Question: It is being given that (232 + 1) is completely divisible by a whole number. Which of the following numbers is completely divisible by this number?
Options:
A)(216 + 1)
B)(216 - 1)
C)(7 x 223)
D)(296 + 1)
E)(296 + 3)
Rationale: Let 232 = x. Then, (232 + 1) = (x + 1).
Let (x + 1) be completely divisible by the natural number N. Then,
(296 + 1) = [(232)3 + 1] = (x3 + 1) = (x + 1)(x2 - x + 1), which is completely divisible by N, since (x + 1) is divisible by N.
Answer:D
Answer: D
Question: A military camp has a food reserve for 250 personnel for 40 days. If after 15 days 50 more personnel are added to the camp, find the number of days the reserve will last for?
Options:
A)25
B)67
C)26
D)29
E)18
Rationale: Explanation:
As the camp has a reserve for 250 personnel that can last for 40 days, after 10 days the reserve left for 250 personnel is for 30 days. Now 50 more personnel are added
in the camp.
Hence, the food reserve for 300 personnel will last for:
250:300::x:30 ……..(it is an indirect proportion as less men means more days)
x = (250*30)/300
x = 25 days
ANSWER: A
Answer: A
Question: The sum of all two digit numbers divisible by 4 is
Options:
A)1242
B)1542
C)1742
D)1610
E)1842
Rationale: Required numbers are 12,16,20 . . . . . 96
This is an A.P. in which a=12,d=4 and l=96.
Let the number of terms in it be n.Then t=96
So a+(n-1)d=96.
12+(n-1)*6=96,
12+4n-4=96
4+4n=96
4n=96-4
n = 92/4
then n=23.
Required sum
=n/2(a+l)
=23/2(12+96)
=1242
Answer is A
Answer: A
Question: Of the 90 electronics components that a factory must manufacture, 50 percent would be most e¢ ciently manufactured by Machine A and the remaining 50 percent would be most efficiently manufactured by Machine B, though either machine could manufacture any of the 90 components. If 50 percent of the components were manufactured by Machine A and the remainder were manufactured by Machine B, what is thehighest possible number of components that were manufactured by the machine that would manufacture them the most efficiently?
Options:
A) 80
B) 32
C) 90
D) 33
E) 36
Rationale: A can manufacture 50 % of 90 efficiently, which is 45.
B can manufacure 50 % of 90 efficiently, which is 45.
Now 50 % of 90 are produced by A. This means 45 parts. Since A can produce 45 efficiently, all 45 are produced efficiently. Rest (45) is produced by B, which can produce max. 45 parts efficiently.
Hence parts that were produced efficiently = 45+45 = 90. (C).
Answer: C
Question: The largest natural number which exactly divides the product of any four consecutive natural numbers is
Options:
A)6
B)12
C)24
D)120
E)none
Rationale: Sol.
Required number = 1 × 2 × 3 × 4 = 24.
Answer C
Answer: C
Question: An accurate clock shows 8 o'clock in the morning. Through how many degrees will the hour hand rotate when the clock shows 10 o'clock in the morning?
Options:
A)80°
B)60°
C)30°
D)10°
E)120°
Rationale: The angle traced by the hour hand in 12 hours is 360°, which is 30° per hour.
In 2 hours, the angle traced by the hour hand is 2×30° = 60°
The answer is B.
Answer: B
Question: Susan can type 10 pages in 5 minutes. Mary can type 5 pages in 10 minutes. Working together, how many pages can
they type in 30 minutes?
Options:
A)15
B)20
C)25
D)65
E)75
Rationale: susan can type 2 pages in 1 min
mary can type 0.5pages in 1 min
so, both of them work together they type 2.5 pages in 1 min
so,in 30 min they type (30*2.5)= 75 pages
ANSWER:E
Answer: E
Question: Mary works in a restaurant a maximum of 50 hours. For the first 20 hours, she is paid $8 per hour. For each overtime hour, she is paid at a rate which is 25% higher than her regular rate. How much Mary can earn in a week?
Options:
A)300
B)420
C)460
D)320
E)400
Rationale: Mary receives $8(20)=$160 for the first 20 hours.
For the 30 overtime hours, she receives $8(0.25) +$8 = $10 per hour, that is $10(30)=$300.
The total amount is $160+$300 = $460
Answer C 460.
Answer: C
Question: A certain sum of money at simple interest amounted Rs.698 in 7 years at 5% per annum, find the sum?
Options:
A)338
B)277
C)517
D)678
E)261
Rationale: 698 = P [1 + (7*5)/100]
P = 517
Answer:C
Answer: C
Question: The area of a triangle is with base 3m and height 10m?
Options:
A)88 m2
B)10 m2
C)66 m2
D)15 m2
E)31 m2
Rationale: 1/2 * 3 * 5 = 15 m2
Answer: C
Answer: C
Question: Angelo and Isabella are both salespersons. In any given week, Angelo makes $550 in base salary plus 8 percent of the portion of his sales above $5,000 for that week. Isabella makes 10 percent of her total sales for any given week. For what amount of weekly sales would Angelo and Isabella earn the same amount of money?
Options:
A) 7,500
B) 24,500
C) 25,500
D) 26,500
E) 27,500
Rationale: OFFICIAL SOLUTION:
The problem asks for the amount of weekly sales it takes for Angelo and Isabella to earn the same amount of money. You can write an equation that sets Angelo’s and Isabella’s weekly earnings equal to each other, with x representing weekly sales. Weekly earnings for each salesperson equal base salary plus commission. So Angelo’s earnings are 550 + (0.08)(x – 5,000), and Isabella’s are 0.10x. Set up the equation and solve:
550 + (0.08)(x – 5,000) = 0.10x
Distribute the 0.08:
550 + 0.08x – 400 = 0.10x
Combine terms and subtract 0.08x from both sides:
150 = 0.02x
Divide both sides by 0.02:
7,500 = x
Your answer is A.
Answer: A
Question: 101 Ã— 101 + 99 Ã— 99 = ?
Options:
A)10002
B)20004
C)20002
D)20102
E)20202
Rationale: Explanation :
(a + b)2 + (a âˆ’ b)2 = 2(a2 + b2)
(Reference : Basic Algebraic Formulas)
1012 + 992 = (100 + 1)2 + (100 âˆ’ 1)2 = 2(1002 + 12) = 2(10000 + 1) = 20002. Answer : Option C
Answer: C
Question: The lunch menu at a certain restaurant contains 4 different entrees and 5 different side dishes. If a meal consists of 1 entree and 2 different side dishes, how many different meal combinations T could be chosen from this menu?
Options:
A)10
B)20
C)40
D)80
E)100
Rationale: T=4C1 * 5C2
= 4 * (5*4*3!)/(3!2!)
= 4 * 10
= 40
Answer - C
Answer: C
Question: The two lines y = x and x = -6 intersect on the coordinate plane. If z represents the area of the figure formed by the intersecting lines and the x-axis, what is the side length of a cube whose surface area is equal to 6z?
Options:
A)16
B)3√2
C)8
D)2√2
E)(√2)/3
Rationale: 800score Official Solution:
The first step to solving this problem is to actually graph the two lines. The lines intersect at the point (-6, -6) and form a right triangle whose base length and height are both equal to 4. As you know, the area of a triangle is equal to one half the product of its base length and height: A = (1/2)bh = (1/2)(6 × 6) = 18; so z = 18.
The next step requires us to find the length of a side of a cube that has a face area equal to 18. As you know the 6 faces of a cube are squares. So, we can reduce the problem to finding the length of the side of a square that has an area of 18. Since the area of a square is equal to s², where s is the length of one of its side, we can write and solve the equation s² = 18. Clearly s = √18 =3√2 , oranswer choice (B).
Answer: B
Question: I remember during the school days , the teacher asked the class "can you tell me the sum of the first 50 odd numbers ?".
I ran quickly to the teacher and told her "the answer is 2500". The teacher replied "lucky guess".
She then asked me "can you tell me the sum of first 73 odd numbers ?".
I wait for approx 10 seconds and replied with the correct answer.
How can i answer so quickly and whats the correct answer ?
Options:
A)8715
B)0152
C)3581
D)5329
E)9126
Rationale: D
5329
n^1
73 * 73= 5329 (sum of first 73 odd numbers).
50 * 50 = 2500 (sum of first 50 odd numbers).
Answer: D
Question: An article is bought for Rs.1300 and sold for Rs.1250, find the loss percent?
Options:
A)3 11/13%
B)3 2/9%
C)3 5/3%
D)3 2/3%
E)3 7/3%
Rationale: 1300 ---- 50
50 ---- ? => 3 11/13%
Answer: A
Answer: A
Question: Solve : 0.6*0.6+0.6*0.6
Options:
A)0.46
B)0.56
C)0.64
D)0.65
E)None of them
Rationale: = 0.6*0.6+(0.6*6) = 0.36+0.1 = 0.46
Answer is A.
Answer: A
Question: During a trip on an expressway, Lon drove a total of x miles. His average speed on a certain 5-mile section of the expressway was 30 miles per hour, and his average speed for the remainder of the trip was 60 miles per hour. His travel time for the x-mile trip was what percent greater than it would have been if he had traveled at a constant rate of 60 miles per hour for the entire trip?
Options:
A)8.5%
B)50%
C)x/12%
D)60/x%
E)500/x%
Rationale: so Lon drove (x-5) miles at 60mph and 5 miles at 30mph:
(x-5)/60 + (10/60) = (X+5)/60 - current time to drive the whole distance
if the entire trip @60mph than time = x/60
so to get percent [(X+5)/60 ]/[x/60] x100
=(x+5)/x *100
=100+500/x
so increase of 500/x%[/u]=E
Answer: E
Question: If T persons take y days to complete z similar jobs, how long does it take y persons to complete 1 such job?
Options:
A)z
B)x
C)x/y
D)z/x
E)y/z
Rationale: the Q doesn't seem to be having the any correct answer as a choice..
since we are looking for days, lets keep days in end and work out a solution..
T person can do z jobs in y days..
so T person can do 1 job in y/z days..
and 1 person can do 1 job in y^2/z days..
so y person can complete 1 job in y^2/zy=y/z..
so the answer should be y/z=E
Answer: E
Question: A day-trader plans to invest a total of $23,300 into 15 separate investments. If each investment requires a minimum deposit of $1,400, then which of the following is the maximum amount that she could put into any one investment?
Options:
A)$2,800
B)$3,000
C)$3,700
D)$3,800
E)$3,900
Rationale: We can also just keep track of the HUNDREDS DIGITS(since the hundreds digit is different for each answer choice).
Total of 14 minimized investments = (14)(1400) = $???600
The 15th investment + $???600 = $23,300
So, the HUNDREDS DIGITS of the 15th investment must be 7
Answer: C
Answer: C
Question: The C.P of 10 pens is equal to the S.P of 12 pens. Find his gain % or loss%?
Options:
A)16 2/3% profit
B)50/6% profit
C)16 2/3% loss
D)100/3% loss
E)None of these
Rationale: Explanation:
10 CP = 12 SP
12 --- 2 CP loss
100 --- ? => 16 2/3%
Answer IS C
Answer: C
Question: In how many different ways can the letters of the word 'OPTICAL' be arranged so that the vowels always come together?
Options:
A)728 ways
B)735 ways
C)767 ways
D)723 ways
E)720 ways
Rationale: The word 'OPTICAL' contains 7 different letters.
When the vowels OIA are always together, they can be supposed to form one letter.
Then, we have to arrange the letters PTCL (OIA).
Now, 5 letters can be arranged in 5! = 120 ways.
The vowels (OIA) can be arranged among themselves in 3! = 6 ways.
Required number of ways = (120 x 6) = 720.
Answer:E
Answer: E
Question: The maitre 'd at an expensive Manhattan restaurant has noticed that 60% of the couples order dessert and coffee. However, 20% of the couples who order dessert don't order coffee. What is the probability Q that the next couple the maitre 'd seats will not order dessert?
Options:
A) 20%
B) 25%
C) 40%
D) 60%
E) 75%
Rationale: could you use a venn diagram and just go with the number 100.
60 people order dessert and coffee... which is the union of D and C.
Q=2/10 of D aren't in D U C = so 8/10 of D are in DUC which means =60 =8/10D. So D in total=75, and 15 D's aren't in D union C. which means 25 people are in C only + Neither.
B 25%
Answer: B
Question: The profit earned after selling a T-shirt for Rs.575/- is the same as loss incurred after selling the same T-shirt for Rs.295/-. What is the cost price of the T-shirt?
Options:
A)Rs.425/-
B)Rs.435/-
C)Rs.415/-
D)Rs.245/-
E)None of these
Rationale: Explanation:
Let ‘x’ be the CP. Then 575-x = x-295
x = Rs.435
Answer: Option B
Answer: B
Question: Excluding stoppages, the speed of a bus is 50 km/hr and including stoppages, it is 36 km/hr. For how many minutes does the bus stop per hour?
Options:
A)118 min
B)10 min
C)18 min
D)16 min
E)15 min
Rationale: Due to stoppages, it covers 14 km less.
Time taken to cover 14 km = 14/50 * 60
= 16 min.
Answer:D
Answer: D
Question: Ajay bought a motor cycle for Rs. 50,000. 2 years later he sold it to Vijay at 10% less of the cost price. Vijay spend 5% of the purchasing price on its maintenance. Later Vijay displayed the sale price of his motorcycle Rs. 50,000. Chetan wanted to purchase it at 15% discount but Vijay gave him two successive discounts of 10% and 5% instead of 15% in one time. What is the actual discount availed by Chetan?
Options:
A)15%
B)15.5%
C)14.5	%
D)16.5%
E)Cannot determined
Rationale: Solution: 100 ----10%↓(1st discount)---> 90----5%↓---> 85.5
Net discount = 100-85.5 = 14.5%.
Answer: Option C
Answer: C
Question: A certain electric-company plan offers customers reduced rates for electricity used between 8 p.m. and 8 a.m. weekdays and 24 hours a day Saturdays and Sundays. Under this plan, the reduced rates Q apply to what fraction of a week?
Options:
A) 1/2
B) 5/8
C) 9/14
D) 16/21
E) 9/10
Rationale: Number of hours between 8 PM to 8 AM = 12
Number of hours with reduced rates = (12*5)+(24*2)
Hours with reduced rates Q /Total number of hours in a week = (12*5)+(24*2)/(24*7) = 108/(24*7) = 9/14
Answer: C
Answer: C
Question: If x and y are integers such that x^2= y and xy = 27, then x – y = ?
Options:
A)-30
B)-20
C)-6
D)5
E)20
Rationale: here x and y are integers .
x^2=y xy =27.
substitute x^2=y in xy => x^3=27.
here X3 is positive ,
x is also positive.
x=3 then y=9.
x-y=-6
so option C is correct
Answer: C
Question: The two trains of lengths 400 m, 600 m respectively, running at same directions. The faster train can cross the slower train in 180 sec, the speed of the slower train is 48 km. then find the speed of the faster train?
Options:
A)85 Kmph
B)68 Kmph
C)103 Kmph
D)60 Kmph
E)90 Kmph
Rationale: Answer: Option B
Length of the two trains = 600m + 400m
Speed of the first train = X
Speed of the second train= 48 Kmph
1000/X - 48 = 180
1000/x - 48 * 5/18 = 180
50 = 9X - 120
X = 68 Kmph
Answer: B
Question: A 300m race is held between two players running 3m/s and 5m/s in swimming pool of 50m long. how many times the two player meet in opposite direction till the faster one completes the race.
Options:
A)3
B)4
C)5
D)6
E)7
Rationale: Every 10sec of time 1st will cover 30m
2nd will cover 50m,To complete total race by faster one i,e 2nd will take 50sec,
In that duration there are 4 crossings had been taken place,that's ans is 4
ANSWER:B
Answer: B
Question: 3*16 + 3*17 + 3*20 + 11 = ?
Options:
A)121
B)129
C)138
D)152
E)170
Rationale: 3*16 + 3*17 + 3*20 + 11 = 48 + 51 + 60 + 11 = 170
The answer is E.
Answer: E
Question: If a and b are positive integers and x = 7^a and y = 3^b, which of the following is a possible units digit of xy?
Options:
A)2
B)5
C)6
D)8
E)9
Rationale: The units digit of 7^a is either 7, 9, 3 or 1.
The units digit of 3^b is 3, 9, 7, or 1.
We can multiply the units digits together to see that the units digits of xy could be 1, 3, 7, or 9.
The answer is E.
Answer: E
Question: A toy store sells small, medium, large, and super-large toy trucks in each of the colors red, blue, black, green, and yellow. The store has an equal number of trucks of each possible color-size combination. If Paul wants a medium, red truck and his mother will randomly select one the trucks in the store, what is the probability that the truck she selects will have at least one of the two features Paul wants?
Options:
A)2/5
B)7/15
C)13/25
D)17/25
E)19/30
Rationale: Probability of NOT selecting medium out of 4 sizes = 3/4
Probability of NOT selecting red out of 5 colours = 4/5
Total probability of NOT selecting red and medium = (3/4)*(4/5) = 3/5
Required probability = 1 - 3/5 (this will select at least one of red and medium)
= 2/5
The answer is A.
Answer: A
Question: Sue's trail mix is 30% nuts and 70% dried fruit. Jane's trail mix is 60% nuts and 40% chocolate chips. If the combined mixture of Sue and Jane's trails mix contains 55% nuts, what percent of the combined mixture is dried fruit?
Options:
A)8.5%
B)11.7%
C)14.2%
D)17.6%
E)20.5%
Rationale: 55% is 25%-points above 30% and 5%-points below 60%.
So the ratio of Sue's mix to Jane's mix is 1:5.
1/6*70% = 11.7%
The answer is B.
Answer: B
Question: A person is traveling at 100 km/hr and reached his destiny in 5 then find the distance?
Options:
A)250km
B)300km
C)500km
D)450km
E)350km
Rationale: T = 5hr
S = 100km/hr
D= T*S = 100*5 = 500KM
Answer is C
Answer: C
Question: A set S = {x, -8, -5, -3, 3, 6, 9, y} with elements arranged in increasing order. If the median and the mean of the set are the same, what is the value of |x|-|y|?
Options:
A)2
B)0
C)-1
D)Cannot be determined
E)1
Rationale: Median of the set = (-3+3)/2 = 0
As per statement, Mean of the set = 0
Mean of the set
|y|- |x| +18-16 = 0 (where x is negative n y is positive)
|y|- |x| = -2
So the absolute difference between two numbers is 2
Answer A
Answer: A
Question: A rectangular football field is fenced on all four sides. The length of the football field is twice the length of its breadth. The cost of fencing the field was $360. The football management has decided to change the dimensions of field by decreasing the breadth by 50% of its original value and increasing the length by 25% of its original value and fence the field again.. What will be the cost of the new fencing?
Options:
A)$360
B)$180
C)$425
D)$405
E)$415
Rationale: Let's take x to be the breadth. Then the length of the football field is 2x.
The perimeter of the old football field is x + 2x + x + 2x = 6x.
Now, for the new football field:
The new breadth = 0.5 times old breadth = 0.5x
The new length is 1.25 times old length = (1.25)2x = 2.5x
So the new perimeter is 0.5x + 2.5x + 0.5x + 2.5x = 6x.
The new perimeter is the same as the older perimeter! So presumably the cost is the same at $360.
Ans - A
Answer: A
Question: If the price of 23 toys is 230, then what will the price of 18 toys ?
Options:
A)144
B)361
C)180
D)287
E)112
Rationale: One toy price = 230/23 = 10
18 toy price = 18 * 10 = 180
Answer : C
Answer: C
Question: Given a spinner with four sections of equal size labeled Q, B, C, and D, what is the probability of NOT getting an Q after spinning the spinner two times?
Options:
A)15/16
B)9/16
C)1/2
D)1/4
E)1/8
Rationale: The probability of NOT getting an Q after spinning the spinner two times is 3/4*3/4=9/16 (so getting any of the remaining 3 letters out of 4).
Answer: B.
Answer: B
Question: If |20x-10| = 190, then find the product of the values of x?
Options:
A)-45
B)50
C)-62
D)35
E)-90
Rationale: |20x-10| = 190
20x-10 = 190 or 20x-10 = -190
20x = 200 or 20x = -180
x = 10 or x = -9
product = -9*10 = -90
Answer is E
Answer: E
Question: What is the product of all the prime factors of 13?
Options:
A)12
B)11
C)13
D)15
E)18
Rationale: factors :1 , 13
1*13 = 13
Answer : C
Answer: C
Question: If nine persons sit in a row, then the probability that three particular persons are always together is?
Options:
A)1/5
B)1/4
C)1/9
D)1/6
E)1/12
Rationale: Nine persons can be arranged in a row in 9! ways.
Treat the three persons to sit together as one unit then there six persons and they can be arranged in 6! ways.
Again three persons can be arranged among them selves in 3! ways.
Favourable outcomes = 3!6!
Required probability = 3!6!/9! = 1/12
Answer:E
Answer: E
Question: If 0 < g< 1 < h, which of the following must be true?
Options:
A)1 < 1/g< 1/h
B)1/g< 1 < 1/h
C)1/g< 1/h< 1
D)1/h< 1 < 1/g
E)1/h< 1/g < 1
Rationale: 0<x<1<y. Let g=1/2 and h=2
Substituting values:
A. 1<2<1/2 ---Wrong
B. 2<1< 1/2 ---Wrong
C. 2<1/2<1 ---Wrong
D. 1/2<1<2 ---Correct
E. 1/2<2<1 ---Wrong
Hence answer is D
Answer: D
Question: In how many different ways can the letters of the word "CLAIM" be rearrangement?
Options:
A)110
B)120
C)125
D)130
E)140
Rationale: The total number of arrangements is
5P5 = 5! = 120
B
Answer: B
Question: Convert the 1/3 m/s into kilometers per hour?
Options:
A)2.9 kmph
B)9.9 kmph
C)1.3 kmph
D)1.2 kmph
E)5.7 kmph
Rationale: 1/3 m/s = 1/3 * 18/5 = 12/10
= 1.2 kmph.
Answer: D
Answer: D