divelab/Sys2Bench huggingface dataset:
Question: The expression (12.86 × 12.86 + 12.86 × p + 0.14 × 0.14) will be a perfect square for p equal to
Options:
A)0.28
B)0.26
C)1
D)0
E)2
Rationale: Explanation :
12.86 × 12.86 + 12.86 × p + 0.14 × 0.14 = (12.86)2 + 12.86 × p + (0.14)2
This can be written as (12.86 + 0.14)2 = 132, if 12.86 × p = 2 × 12.86 × 0.14
i.e., if p = 2 × 0.14 = 0.28
Hence, p = 0.28 . Answer : Option A
Answer: A
Question: 108.	Triangle A’s base is 7% greater than the base of triangle B, and A’s height is 7% less than the height of triangle B. The area of triangle A is what percent less or more than the area of triangle B?
Options:
A) 9 % less
B) 1 % less
C) Equal to each other
D) 1 % more
E) 2.1 % more
Rationale: Wish the question specified that we are talking about corresponding height.
Base of A = 8/7 * Base of B
Height of A = 6/7 * Height of B
Area of A = (1/2) * Base of A * Height of A = 8/7 * 6/7 * Area of B = 48/49 * Area of B
Area of A is 2.1% more than the area of B.
Answer (E)
Answer: E
Question: A, B and C are partners in a business. Their capitals are respectively, Rs.5000, Rs.6000 and Rs.4000. A gets 30% of the total profit for managing the business. The remaining profit is divided among three in the ratio of their capitals. In the end of the year, the profit of A is Rs.200 more than the sum of the profits of B and C. Find the total profit.
Options:
A)s.4500
B)s.5200
C)s.1800
D)s.Rs.3000
E)s.5000
Rationale: A:B:C = 5:6:4
Let the total profit = 100 - 30 = 70
5/15 * 70 = 70/3
A share = 70/3 + 30 = 160/3
B + C share = 100 - 160/3 = 140/3
A-(B+C) = 160/3 - 140/3 = 20/3
20/3 ---- 200
100 ---- ? => 3000
ANSWER:D
Answer: D
Question: John opened a shop investing Rs.40000. Joy joined him 4 months later, investing Rs.50000. They earned a profit of Rs.55000 after completion of one year. What will be Joy's share of profit?
Options:
A)23000
B)25000
C)24000
D)28000
E)29000
Rationale: SoL = ~s- So Joy's share = [5/11] x 55000 = 25000
Answer : B
Answer: B
Question: Find the largest 4 digit number which isexactly divisible by 88?
Options:
A)8765
B)9543
C)9944
D)1012
E)2465
Rationale: Largest 4 digit number is 9999
After doing 9999 ÷ 88 we get remainder 55
Hence largest 4 digit number exactly divisible by 88 = 9999 - 55 = 9944
C
Answer: C
Question: There were two candidates in an election. Winner candidate received 62% of votes and won the election by 336 votes. Find the number of votes casted to the winning candidate?
Options:
A)288
B)744
C)788
D)868
E)177
Rationale: W = 62% L = 38%
62% - 38% = 24%
24% -------- 336
62% -------- ? => 868
Answer: D
Answer: D
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)none
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] = (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 school having four classes only have student strength of 10, 40, 30 and 20 respectively. The pass percentages of these classes are 20%, 30%, 60% and 100% respectively. What is the pass percentage for the entire school?
Options:
A)56%
B)76%
C)52%
D)66%
E)46%
Rationale: 20% of 10+30% of 40+60% of 30+100% of 20
=2+12+18+20 =
now 52 of 100
= 52%
ANSWER:C
Answer: C
Question: Lottery balls numbered consecutively from one through one hundred are placed in a spinner. If one ball is drawn at random, what is the probability that it will have the number 1 on it exactly once?
Options:
A)9/100
B)1/10
C)11/100
D)19/100
E)1/5
Rationale: Probability = No of balls with exactly one 1 / total number of balls
= {1,10,12 to 19, 21,31,41,51,61,71,81,91,100}/100
= 19/100
Answer is D
Answer: D
Question: The annual interest rate earned by an investment increased by 10 percent from last year to this year. If the annual interest rate earned by the investment this year was 11 percent, what was the annual interest rate last year?
Options:
A)1%
B)1.1%
C)9.1%
D)10%
E)10.8%
Rationale: Let us suppose the interest rate last year is X, This year the interest rate is increased by 10%. Hence this year interest rate would be 1.1*X.
Setting up the equation -----> 11=1.1*x
X=10%
ANSWER:D
Answer: D
Question: A basket contains 4 blue, 4 red and 4 yellow marbles. If 4 marbles are extracted from the basket at random, what is the probability that a marble of each color is among the extracted?
Options:
A)2/21
B)3/25
C)1/6
D)9/28
E)16/55
Rationale: 12/12*8/11*4/10 = 384/1320 = 16/55
the answer is (E)
Answer: E
Question: How many four digit numbers can be formed using the digits {1, 3, 4, 5, 7,9}(repetition of digits is not allowed)?
Options:
A)360
B)960
C)329
D)391
E)310
Rationale: The given digits are six.
The number of four digit numbers that can be formed using six digits is 6P4
= 6 * 5 * 4 * 3
= 360.
Answer: A
Answer: A
Question: The list price of an article is Rs.65. A customer pays Rs.56.16 for it. He was given two successive discounts, one of them being 10%. The other discount is?
Options:
A)9%
B)4%
C)2%
D)1%
E)6%
Rationale: 65*(90/100)*((100-x)/100) = 56.16
x = 4%
Answer: B
Answer: B
Question: ((-1.9)(0.6) – (2.6)(1.2))/5.0 = ?
Options:
A)-0.71
B)1.0
C)-0.852
D)1.71
E)2.71
Rationale: Dove straight into calculation
((-1.9)(0.6) – (2.6)(1.2))/7.0 = -0.852
Answer C
Answer: C
Question: Three friends are buying a gift for a friend. Declan contributes 4 dollars more than 1/4 the cost of the gift, Ed contributes 1 dollar less than 1/3 the cost of the gift, and Frank contributes the remaining 17 dollars. What is the cost of the gift?
Options:
A)48
B)54
C)60
D)66
E)72
Rationale: Declan = D, Ed = E, Frank = F
t = total
D + E + F = t
(t/4 + 4) + (t/3 - 1) + 17 = t
t = 20 + (7t/12)
12t = 20(12) + 7t
5t = 5*4(12)
t = 48
The correct answer is A.
Answer: A
Question: A began business with Rs.45000 and was joined afterwards by B with Rs.5400. When did B join if the profits at the end of the year were divided in the ratio of 2:1?
Options:
A)5
B)6
C)7
D)8
E)9
Rationale: 45*12 : 54*x = 2: 1
x = 5
12 -5 = 7
Answer:C
Answer: C
Question: A bag contains 4 white, 5 red and 6 blue balls. Three balls are drawn at random from the bag. The probability that all of them are red, is:
Options:
A)1/22
B)3/22
C)2/91
D)5/91
E)3/91
Rationale: Let S be the sample space.
Then, n(S)= number of ways of drawing 3 balls out of 15
= 15C3
=(15 x 14 x 13)/(3 x 2 x 1)
= 455.
Let E = event of getting all the 3 red balls.
n(E) = 5C3 = 5C2 =(5 x 4)/(2 x 1)= 10.
P(E) =	n(E)/n(S)=10/455=2/91.
Answer: E
Question: A person got Rs.48 more when he invested a certain sum at compound interest instead of simple interest for two years at 8% p.a. Find the sum?
Options:
A)7500 rupees
B)Rs.7000
C)Rs.8000
D)Rs.6500
E)None of these
Rationale: P = (d * 1002) / R2
=> (48 * 100 * 100) / 8 * 8 = Rs.7500
ANSWER:A
Answer: A
Question: x, y, a, and b are positive integers of V. When x is divided by y, the remainder is 6. When a is divided by b, the remainder is 9. Which of the following is NOT a possible value for y + b?
Options:
A)24
B)21
C)20
D)17
E)15
Rationale: x, y, a, and b are positive integers of V. When x is divided by y, the remainder is 6. When a is divided by b, the remainder is 9.Answer: E.
Answer: E
Question: In a certain company, a third of the workers do not have a retirement plan. 30% of the workers who do not have a retirement plan are women, and 40% of the workers who do have a retirement plan are men. If 120 of the workers of that company are men, how many of the workers are women?
Options:
A)80
B)95
C)105
D)120
E)210
Rationale: Set up equation:
x = total number of workers
120 = 0,4 * 2/3 * x + 0,7 * 1/3 * x
120 = 15/30 x
x = 240
240 - 120 = 120
Answer D
Answer: D
Question: A woman takes certain sum of money at 10% p.a. simple interest. If she pays twice the amount takes, how many years has she been paying the interest?
Options:
A)5 years 7 months
B)10 years
C)15 years
D)6 years
E)20 years
Rationale: Solution: simple interest question
B=A[1+ (tr/100)]; where A is principal amount, B final amount, t time in years and r interest rate
after putting the values 10
3= [1+(10t/100)]
t= 20 which is 20 years
Answer is E
Answer: E
Question: Find large number from below question The difference of two numbers is 1365. On dividing the larger number by the smaller, we get 7 as quotient and the 15 as remainder
Options:
A)1235
B)1346
C)1590
D)1635
E)1489
Rationale: Let the smaller number be x. Then larger number = (x + 1365).
x + 1365 = 7x + 15
6x = 1350
x = 225
Large number = 225+1365 = 1590
C
Answer: C
Question: The value of 3Z + Z(ZZ)(ZZ) when Z = 5 is:
Options:
A)3150
B)3200
C)3140
D)3650
E)3104
Rationale: Solution:
3Z+ Z(ZZ)(ZZ)
Put the value of Z= 5 in the above expression we get,
15+ 5(55)(55)
= 15 + 5(5 Ã— 5)(5 Ã— 5)
= 15 + 3125
=3140
= 3140
Answer : C
Answer: C
Question: In the figure shown, the outer square has an area of
9 cm2, the inner square has an area of 1 cm2, and the
four rectangles are identical. What is the perimeter of
one of the four identical rectangles?
Options:
A)6 cm
B)8 cm
C)10 cm
D)9 cm
E)7 cm
Rationale: The outer square has an area of 9 cm2, so the sides of this outer
square have length 3 cm (since 3 3 = 9), and thus PN = 3 cm.
The inner square has an area of 1 cm2, so the sides of this inner
square have length 1 cm (since 1 1 = 1), and thus MR = 1 cm.
Since PN = 3 cm, then PS + SN = 3 cm and so QR + SN = 3 cm
(since QR = PS).
But QR = QM + MR, so then QM + MR + SN = 3 cm or
QM + 1 + SN = 3 cm (since MR = 1 cm).
From this last equation we get QM + SN = 2 cm.
P Q
R
S
M
N
Since each of QM and SN is the width of an identical rectangle, then QM = SN = 1 cm.
Using PS + SN = 3 cm, we get PS + 1 = 3 cm and so PS = 2 cm.
Since the rectangles are identical, then SN = PQ = 1 cm.
The perimeter of rectangle PQRS is 2 (PS + PQ) = 2x(2 + 1) = 2x3 = 6 cm.
correct answer A
Answer: A
Question: Difference between two numbers is 5, six times of the smaller lacks by 6 from the four times of the greater. Find the numbers?
Options:
A)12,7
B)12,8
C)12,9
D)13,2
E)14,5
Rationale: x â€“ y = 5
4x â€“ 6y = 6
x = 12 y = 7
ANSWER A
Answer: A
Question: In a diving competition, each diver has a 45% chance of a perfect dive. The first perfect dive of the competition, but no subsequent dives, will receive a perfect score. If Janet is the third diver to dive, what is her chance of receiving a perfect score? (Assume that each diver can perform only one dive per turn.)
Options:
A)1/5
B)1/15
C)4/25
D)26/191
E)61/125
Rationale: Probability = Favourable Outcomes / Total Outcomes = 1 - (Unfavourable Outcomes / Total Outcomes)
Given:Probability of Perfect dive = 0.45 = 45/100 = 4/9
i.e. Probability of Non-Perfect dive = 0.55 = 55/100 = 5/9
The probability of Janet to dive and get a perfect score depends on that other other previous two dives must be Imperfect
Method-1:
i.e. Probability of First two being Imperfect and Third being Perfect dive = (5/9)*(5/9)*(4/9) =26/191
D
Answer: D
Question: Of the people who responded to a market survey, 240 preferred Brand X and the rest preferred Brand Y. If the respondents indicated a preference for Brand X over Brand Y by ratio of 6 to 1, how many people responded to the survey?
Options:
A)80
B)160
C)280
D)360
E)480
Rationale: Ratio = 6:1 => 6x respondents preferred Brand X and x preferred Brand Y
Since, no. of respondents who preferred Brand X = 240 => 6x=240 => x=40
Hence Total no. of respondents = 240 + 40 = 280
Hence C is the answer.
Answer: C
Question: Which of the following values of R gives the greatest value for the expression R/(R-2)?
Options:
A)5.5
B)4.5
C)3.5
D)2.5
E)1.5
Rationale: 5.5/(5.5 - 2) = 11/7 (~1.57)
4.5/(4.5 - 2) = 9/5 (1.8)
3.5/(3.5 - 2) = 7/3 (~2.33)
2.5/(2.5-2) = 5
1.5/(1.5 - 2) = -3
Thus, the answer is D.
Answer: D
Question: If the circumference of a circle is 200 units, Then what will the length of the arc described by an angle of 20 degree ?
Options:
A)11.11
B)11.89
C)11.1
D)11.18
E)11.19
Rationale: Explanation:
The angle formed by a circle is 360 degrees.
Length of the arc = θ360θ360 × Circumference of the circle.
So Length of the arc = 20360×20020360×200
So, the length of the arc described by 20 degree angle is 11.11 units.
Answer:A
Answer: A
Question: In a group of ducks and goats, the total number of legs are 32 more than twice the number of heads. Find the total number of goats.
Options:
A)A)14
B)B)12
C)C)6
D)D)8
E)E)16
Rationale: Explanation :
Let the number of ducks be d
and number of goats be c
Then, total number of legs = 2d + 4c = 2(d + 2c)
total number of heads = c + d
Given that total number of legs are 32 more than twice the number of heads
=> 2(d + 2c) = 32 + 2(c + d)
=> d + 2c = 16 + c + d
=> 2c = 16 + c
=> c = 16
i.e., total number of goats = 16
Answer : E
Answer: E
Question: You collect baseball cards. Suppose you start out with 17. Maria takes half of one more than the number of baseball cards you have. Since you're nice, you give Peter 1 baseball card. Since his father makes baseball cards, Paul decides to triple your baseball cards. How many baseball cards do you have at the end?
Options:
A)17
B)18
C)19
D)20
E)21
Rationale: Solution
Start with 17 baseball cards.
Maria takes half of one more than the number of baseball cards you have. So Maria takes half of 17 + 1 which is 9,
so you're left with 17 - 9 = 8.
Peter takes 1 baseball card from you: 8 - 1 = 7 baseball cards.
Paul triples the number of baseball cards you have: 7 Ã— 3 = 21 baseball cards.
So you have 21 at the end.
Correct answer : E
Answer: E
Question: Tourist purchased a total of 30 travelers checks in $50 and $100 denominations. The total worth of the travelers checks is $1800. How many checks of $50 denominations can he spend so that average amount (arithmetic mean) of the remaining travelers checks is $75?
Options:
A)4
B)18
C)15
D)20
E)24
Rationale: you could set-up a quick table and brute force the answer.
A	4	*	50	200 1800	-200 1600	26 61.54
B	18	*	50	600 1800	-900 0900	12 75.00
C	15	*	50	750 1800	-750 1050	15 70.00
D	20	*	50	1000 1800	-1000	800	10 80.00
E	24	*	50	1200 1800	-1200	600	6 100.00
Answer is B
Answer: B
Question: Two trains of equal length, running with the speeds of 60 and 16 kmph, take 50 seconds to cross each other while they are running in the same direction. What time will they take to cross each other if they are running in opposite directions?
Options:
A)10.11
B)8.11
C)77.2
D)13.15
E)22.22
Rationale: RS = 60 -40 = 20 * 5/18 = 100/18
T = 50
D = 50 * 100/18 = 2500/9
RS = 60 + 16 = 76 * 5/18
T = 2500/9 * 18/380= 13.15 sec.Answer: D
Answer: D
Question: A can do a piece of work in 40 days; B can do the same in 30 days. A started alone but left the work after 10 days, then B worked at it for 10 days. C finished the remaining work in 10 days. C alone can do the whole work in?
Options:
A)21 days
B)24 days
C)23 days
D)25 days
E)26 days
Rationale: B
24 days
10/40 + 10/30 + 10/x = 1
x = 24 days
Answer: B
Question: Solve the given two equations and find the inequality of X and Y. (a) 3X^2+8X+4 = 0 and (b) 4Y^2-19Y+12= 0
Options:
A)If x>y
B)If x>=y
C)If x < y
D)If x<=y
E)x=y or relationship cannot be established
Rationale: Solution:-
Solving we get X= -2/3 or -2
Y= 3/4 or 4
C)
Answer: C
Question: (112 x 5^4) = ?
Options:
A)7000
B)700
C)70000
D)70
E)7
Rationale: (112 x 5^4) = 112 x(10/2)^4
=(112 x 10^4)/2^4
=1120000/16	= 70000
Answer is C.
Answer: C
Question: In the manufacture of a certain product, 7 percent of the units produced are defective and 5 percent of the defective units are shipped for sale. What percent of the units produced are defective units that are shipped for sale?
Options:
A)0.125%
B)0.35%
C)0.8%
D)1.25%
E)2.0%
Rationale: 0.07*0.05 = 0.0035 = 0.35%
The answer is B.
Answer: B
Question: A sum of money amounts to 9800 after 5 years and 12005 after 8 years at the same rate of simple interest. The rate of interest per annum is:
Options:
A)10
B)18
C)11
D)12
E)15
Rationale: D
12
S.I. for 3 years = (12005 - 9800) = 2205.
S.I. for 5 years = (2205/3)x 5 = 3675
Principal = (9800 - 3675) = 6125.
Hence, rate = (100 x 3675)/(6125x5)% = 12%
Answer: D
Question: In covering a distance of 30 km, Abhay takes 2 hours more than Sameer. If Abhay doubles his speed, then he would take 1 hour less than Sameer. Abhay's speed is:
Options:
A)5 kmph
B)6 kmph
C)6.25 kmph
D)7.5 kmph
E)7 kmph
Rationale: Let Abhay's speed be x km/hr.
Then,30/x	-30/2x = 3
6x = 30
x = 5 km/hr
Answer:A
Answer: A
Question: When a certain number X is divided by 66, the remainder is 14. What is the remainder when X is divided by 11?
Options:
A)2
B)3
C)7
D)9
E)10
Rationale: Let possible value of x is 80
least possible value of x/11 is 80/11 =>7 quotient with remainder 3
Thus answer is (B) 3
Answer: B
Question: Can you replace the question mark with the number to complete the series, provided the pair of numbers exhibits a similar relationship?
? : 4623 :: 9 : 647
Options:
A)16
B)17
C)18
D)19
E)20
Rationale: Solution:
17
Explanation :
The relationship holds for below formula :
pow(x,3) - pow(x,2) - 1
=> 9*9*9 - 9*9 - 1
=> 729 - 81 - 1
=> 647
Similarly,
17*17*17 - 17*17 - 1
=> 4913 - 289 - 1
=> 4623
Answer B
Answer: B
Question: A hare and a jackal are running a race. Three leaps of the hare are equal to four leaps of the jackal. For every two leaps of the hare, the jackal takes three leaps. Find the ratio of the speed of the hare to the speed of the jackal.
Options:
A)64:25
B)8:9
C)5:8
D)25:64
E)4:7
Rationale: The hare takes 2 leaps and the jackal takes 3 leaps.
1 hare leap = 4/3 jackal leaps
Thus the hare's 2 leaps = 2*(4/3) = 8/3 jackal leaps.
The ratio of their speeds is 8/3:3 = 8:9.
The answer is B.
Answer: B
Question: The sum of first five prime numbers is:
Options:
A)10
B)15
C)69
D)28
E)65
Rationale: Explanation:
Required sum = (2 + 3 + 5 + 7 + 11) = 28.
ANSWER D
Answer: D
Question: Two machines, Y and Z, work at constant rates producing identical items. Machine Y produces 23 items in the same time Machine Z produces 21 items. If machine Y takes 21 minutes to produce a batch of items, how many minutes does it take for machine Z to produce the same number of items?
Options:
A)6
B)9
C)9 1/2
D)12
E)23
Rationale: rate z/rate y=21/23
time z/time y=23/21
(23/21)*21=23 minutes
E
Answer: E
Question: When tossed, a certain coin has equal probability of landing on either side. If the coin is tossed 3 times, what is the probability that it will land twice on heads and once on tails?
Options:
A)1/16
B)1/3
C)1/6
D)1/2
E)1/8
Rationale: Must be once on twice and once on tails
1/2*1/2*1/2 = 1/8
Answer: E
Answer: E
Question: In Cliff’s impressive rock collection, there are half as many igneous rocks as sedimentary rocks. Of the igneous rocks, 2/3 are shiny and the rest are matte, while 1/5 of the sedimentary rocks are shiny. If there are 40 shiny igneous rocks, how many total rocks does Cliff have?
Options:
A)180
B)45
C)60
D)90
E)135
Rationale: We can start with the known quantity and then go on to find the others.
Shiny igneous ricks are 40. These are (2/3) of total igneous rocks.
(2/3)*Total igneous rocks = 40
Total igneous rocks = 40 * (3/2) = 60
Total sedimentary rocks = 2*Total igneous rocks = 2*60 = 120
Total number of rocks = 60 + 120 = 180
Answer (A)
Answer: A
Question: 12.5 * 3.2 * 7.8 = ?
Options:
A)312
B)435
C)224
D)646
E)742
Rationale: A
312
? = 12.5 * 3.2 * 7.8 = 312
Answer: A
Question: From an island, it is possible to reach the mainland by either Ferry P or Ferry Q. Ferry P travels for 2 hours at 8 kilometers per hour, while Ferry Q takes a route that is three times longer. If Ferry P is slower than Ferry Q by 4 kilometers per hour, how many hours longer is the journey of Ferry Q compared with the journey of Ferry P?
Options:
A)1
B)2
C)3
D)4
E)5
Rationale: The distance traveled by Ferry P is 16 km.
Then the distance traveled by Ferry Q is 48 km. Ferry Q travels at a speed of 12 kph. The time of the journey for Ferry Q is 48/12 = 4 hours, which is 2 hours more than Ferry P. The answer is B.
Answer: B
Question: A reduction of 20% in the price of salt enables a lady to obtain 10kgs more for Rs.200, find the original price per kg?
Options:
A)s.7
B)s.4
C)s.5
D)s.1
E)s.9
Rationale: 100*(20/100) = 20 --- 10
? --- 1 => Rs.2
200 --- 80
? --- 2 => Rs.5
Answer:C
Answer: C
Question: How many different groups of 3 people can be formed from a group of 5 people?
Options:
A)5
B)6
C)8
D)9
E)10
Rationale: Choosing 3 distinct objects out of 5 when order of the selection is not important 3C5=5!/(3!(5−3)!)=10 .
Answer: E.
Answer: E
Question: If x-y=9, which of the following must be true?
I. Both x and y are positive
II. If x is negative, y must be negative
III.If x is positive, y must be positive
Options:
A)I only
B)II only
C)III only
D)I and II
E)II and III
Rationale: The best way to approach such questions is to plug in values for x and y
Given: x-y=9
I. Both x and y are positive:
Let x=10 and y=2
x-y=9
But,
Let x=6 and y=-3
x-y=8
Therefore, NOT TRUE
III. If x is positive, y must be positive
Let x=10 and y=2
x-y=9
But,
Let x = 6 and y=-3
x-y=8
Therefore, NOT TRUE
II. If x is negative, y must be negative
If x is negative, for the expression x-y=9 to be true, y must be a -ve number. Otherwise, the sum of two negative numbers will yield another negative number!
Therefore, TRUE
Ans: 'B'
Answer: B
Question: What percent of the different arrangements of the letters of the word AJICUX are those in which the vowels appear together?
Options:
A)25%
B)30%
C)40%
D)20%
E)50%
Rationale: let's determine the number of total possibilities in arranging the letters. There are six spaces, so the total number of arrangements is 6!, or 360.
Next, we need to figure out how to determine the number of ways that we can arrange the 3 vowels together - simply place them together (as in AAU) and call that a single place.
Next, we must determine the number of ways to arrange the now 4 units (i.e., AAU, B, C, S). Like above, there are 4 units and 4 places so the number of arrangements is 4!, or 24.
Finally, we need to account for the number of ways we can arrange AAU. We can either write out each unique iteration (AAU, AUA and UAA) or calculate as 3!/2! and get 3.
Putting this all together, we get the number of ways to arrange the letters so that the vowels are together is 4! x 3 ==> 72
the number of total arrangements of all the letters is 6! ==> 360
72/360 = 1/5, or 20% Correct answer is D
Answer: D
Question: Difference between the length &breadth of a rectangle is 23 m. If its perimeter is 206 m, then its area is?
Options:
A)2400 m^2
B)2500 m^2
C)2520 m^2
D)2560 m^2
E)2580 m^2
Rationale: Solving the two equations, we get: l = 63 and b = 40.
Area = (l x b) = (63 x 40) m2 = 2520 m^2
C
Answer: C
Question: 575.104 x 15.98 Ã· 9.001 + 21.25 = ?
Options:
A)983.578
B)1043.65
C)1033.65
D)656.112
E)456.512
Rationale: Explanation:
? = 575.104 x 15.98 Ã· 9.001 + 21.25
â‰ˆ (575.104 x 16/9) + 21.25 â‰ˆ 1022.40 + 21.25 â‰ˆ 1043.65
Answer: Option B
Answer: B
Question: By selling 45 books, a shopkeeper gains the price of 12 books. His gain per cent is
Options:
A)35.35%
B)37.37%
C)38.38%
D)36.36%
E)39.39%
Rationale: Suppose S.P of 45 books = Rs 45
Therefore, Gain = Rs 12 => C.P = Rs 33
Gain % = 12/33 x 100 = 36.36%
Gain = 36.36%
ANSWER:D
Answer: D
Question: Two cars are traveling in the same direction along the same route. The red car travels at a constant speed of 40 miles per hour, and the black car is traveling at a constant speed of 50 miles per hour. If the red car is 30 miles ahead of the black car, how many hours will it take the black car to overtake the red car?
Options:
A)0.1
B)0.6
C)1
D)1.2
E)3
Rationale: Option E
20+40t=50t
t=3
Answer: E
Question: The side of a square is increased by 25% then how much % does its area increases?
Options:
A)56.28 %
B)56.25 %
C)56.75 %
D)52.25 %
E)56.25 %
Rationale: a = 100 a2 = 10000
a = 125 a2 = 15625
----------------
10000 --------- 5625
100 -------? => 56.25 %
Answer: B
Answer: B