divelab/Sys2Bench huggingface dataset:
Question: Find the value of y from (12)^3 x 6^ 4 ÷ 432 = y?
Options:
A)3456
B)4567
C)4789
D)5678
E)y=5184
Rationale: Given Exp. = (12)3 x 64 = (12)3 x 64 = (12)2 x 62 = (72) 2 = 5184
432 12 x 62
E
Answer: E
Question: A car finishes a journey in nine hours at the speed of 80 km/hr. If the same distance is to be covered in six hours how much more speed does the car have to gain?
Options:
A)8 km/hr
B)40 km/hr
C)12 km/hr
D)16 km/hr
E)None of these
Rationale: Distance covered by the car = 80 × 9 = 720 km
\ Speed = 720⁄6 = 120 km/hr
\ Speed gain = 120 – 80 = 40 km/hr
Answer B
Answer: B
Question: How many times does the minute hand and the second hand make a straight line?
Options:
A)2844
B)2832
C)2855
D)2381
E)2831
Rationale: make a straight line 59 x 2 times = 118 times (both aligned, and in opposition) and there are 24 hours in a day, so in a day minutes and second hand make a straight line 24 x 118 times = 2832 times.
so answer is B
Answer: B
Question: A used-book dealer sells paperback books at 3 times dealer's cost and hardback books at 4 times the dealer's cost. Last week, the dealer sold a total of 140 books, each of which had cost the dealer $1. If the gross profit (sales revenue minus the dealer's cost) on the sale of all of these books was $400, how many of the books sold were paperbacks?
Options:
A)20
B)40
C)60
D)80
E)100
Rationale: The dealer earns a profit of $2 per paperback and $3 per hardback.
If all 140 books were paperbacks, the dealer would earn a profit of $280.
Since the actual profit was $400, the dealer must have sold 120 hardbacks.
Then the number of paperbacks sold was 140-120 = 20.
The answer is A.
Answer: A
Question: In how many ways can a group of 4 men and 2 women be made out of a total of 7 men and 3 women?
Options:
A)100
B)102
C)105
D)107
E)101
Rationale: We need to select 4 men from 7 men and 2 women from 3 women.
Number of ways to do this
= 7C4 × 3C2
= 7C4 × 3C1 [∵ nCr = nC(n-r)]
= 105
Ans- C
Answer: C
Question: In a certain year, the population of a certain town was 9000. If in the next year the population of males increases by 4% and that of the females by 8% and the total population increases to 9600, then what was the ratio of population of males and females in that given year?
Options:
A)1 : 2
B)5 : 4
C)2 : 3
D)Data inadequate
E)None of these
Rationale: Let the population of males = x; then the population of females = 9000 – x
Now, 4% of x + 8% of (9000 – x)
= (9600 – 9000 ) = 600
or 0.04x + 720 – 0.08x = 600
or 720 – 600 = 0.08x – 0.04x
or, 120 = 0.04x
x = 3000
Reqd ratio of population of males and females
3000/9000−3000=3000/6000=1:2
Answer A
Answer: A
Question: Average of 7 results is 121. If the average of first three results is 115 and average of last three results is 120 Then find the fourth result?
Options:
A)142
B)150
C)126
D)185
E)165
Rationale: Option 'A'
Answer: A
Question: In an election between two candidates, 70% of the voters cast their votes, out of which 4% of the votes were declared invalid. A candidate got 6552 votes which were 75% of the total valid votes. Find the total number of votes enrolled in that election.
Options:
A)13000
B)12500
C)14000
D)12000
E)None of these
Rationale: Explanation :
Solution: let the total number of votes enrolled be x. then, number of votes cast = 70% of x. valid votes = 96% of(70% of x). .'. 75% of(96% of (70% of of x)) = 6552.
(75/100 * 96/100 * 70/100 * x) = 6552.
=> x = (6552*100*100*100)/(75*96*70) = 13000
Answer : A
Answer: A
Question: 100 oranges are bought at the rate of Rs. 350 and sold at the rate of 48 per dozen. The percentage of profit is
Options:
A)12 2/7%
B)13 2/7%
C)14 2/7%
D)15 2/7%
E)16 2/7%
Rationale: Explanation:
So before solving this question we will get the C.P. and S.P. of 1 article to get the gain percent.
C.P. of 1 orange = 350/100 = Rs 3.50
S.P. of one orange = 48/12 = Rs 4 [note: divided by 12 as 1 dozen contains 12 items]
Gain = 4 - 3.50 = Rs 0.50
Gain%=0.50/ 3.50∗100=100 /7%=14 2/7%
Option C
Answer: C
Question: The Kiljaro Highway is marked with Milestones denoting the distance to the town of Kiljaro. Tommy left kiljaro and drove the highway, passing the 30 km milestone at 8:30. Some time afterwards, Tommy got a phone call asking him to return home, and he made a U-turn at the 160 km milestone. At 09:A0 Tommy passed the milestone marking 70 km to Kiljaro. The variable A represents the tens digit of the minutes in 09:A0. Assuming Tommy maintained the same constant speed during the entire drive, how many kilometers did Tommy travel in one minute?
Options:
A)220/(30+10A)
B)220/(30+60A)
C)220/36A
D)220/(30+10A)
E)220/40A
Rationale: Since we are dealing with the variables in the answer choices,the best possible method according to me would besubstitution.
Substitute A with 3.meaning tommy would have travelled a distance of ((160-30) + (160-70)) in 60 minutes.
220 Kms in 60 minutes ==> 3.6km/hr.
Substitute A with 3 in the answer options.
Option A
Answer: A
Question: The compound ratio of 5:1, 3:1 and 2:5?
Options:
A)6:1
B)1:3
C)1:5
D)1:1
E)1:6
Rationale: 5/1 * 3/1 * 2/5 = 30/56:1Answer: A
Answer: A
Question: Mahesh can do a piece of work in 45days. He works at it for 20days and then Rajesh finished it in 30days. How long will Y take to complete the work?
Options:
A)54
B)25
C)37
D)41
E)30
Rationale: Work done by Mahesh in 45days = 20*1/45 = 4/9
Remaining work = 1 - 4/9 = 5/9
5/9 work is done by Rajesh in 30days
Whole work will be done by Rajesh is 30*9/5 = 54days
Answer is A
Answer: A
Question: A lemonade stand sold only small and large cups of lemonade on Tuesday. 5/9 of the cups sold were small and the rest were large. If the large cups were sold for 12/11 as much as the small cups, what fraction of Tuesday's total revenue was from the sale of large cups?
Options:
A)(a) 7/16
B)(b) 7/15
C)(c) 48/103
D)(d) 17/35
E)(e) 1/2
Rationale: A simpler way i guess would be to think that in total 9 cups were sold. Out of which 5 are small and 4 are large. Now let the small ones cost $11. so the large ones would cost $12.
So,
5*11=55 and 4*12=48.
Total revenue was 55+48=103
and Large cup sales as found above is 48
Therefore answer is 48/103
C
Answer: C
Question: A square, with perimeter 80, is inscribed in a circle. What is the area of the circle?
Options:
A)400π
B)200π
C)250π
D)300π
E)150π
Rationale: Area of circuscribed circle = pi/2*area of square
Area of square = (80/4)^2 = 20^2= 400
Area of circle = pi/2*400=200pi
Answer : B
Answer: B
Question: Ajit was driving down the country side when he saw a farmer tending his pigs and ducks in his yard. Ajit asked the farmer how many of each he had.The farmer replied that there were 60 eyes and 86 feet between them.How many ducks and how many pigs were there ?
Options:
A)13
B)14
C)15
D)16
E)17
Rationale: let the no of ducks be X and no of pigs be Y.
then,since there are 60 eyes in total and both ducks and pigs have 2 eyes we have : 2X+2Y=60 --(1)
and total no of legs are 86,ducks have 2 legs while a pig has four so.: 2X+4y=86 ---(2)
subtracting (1) from (2) ,we get
2Y=26. ie. Y =13
putting value in (1),
we get X=17
ANSWER:E
Answer: E
Question: In a can, there is a mixture of milk and water in the ratio 4 : 5. If it is filled with an additional 8 litres of milk the can would be full and ratio of milk and water would become 6 : 5. Find the capacity of the can?
Options:
A)73
B)44
C)72
D)62
E)43
Rationale: Let the capacity of the can be T litres.
Quantity of milk in the mixture before adding milk = 4/9 (T - 8)
After adding milk, quantity of milk in the mixture = 6/11 T.
6T/11 - 8 = 4/9(T - 8)
10T = 792 - 352 => T = 44.
Answer: Option B
Answer: B
Question: A car takes 6 hours to cover a distance of 630 Km. how much should the speed in Kmph be maintained to cover the same direction in 3/2th of the previous time?
Options:
A)60
B)50
C)40
D)70
E)65
Rationale: Time = 6
Distance = 630
3/2 of 6 hours = 6 * 3/2 = 9 Hours
Required speed = 630/9 = 70 Kmph
Answer D.
Answer: D
Question: In a forest 150 deer were caught, tagged with electronic markers, then released. A week later, 50 deer were captured in the same forest. Of these 50 deer, it was found that 5 had been tagged with the electronic markers. If the percentage of tagged deer in the second sample approximates the percentage of tagged deer in the forest, and if no deer had either left or entered the forest over the preceding week, what is the approximate number of deer in the forest?
Options:
A)150
B)750
C)1,250
D)1,500
E)2,500
Rationale: Given 150 deers were caught and they are tagged in the first slot.
In the second slot , 50 were caught and 5 we tagged then 10% of them are tagged.
Given this 10% approximates the percentage of tagged deer in the forest..here number is 150..
then 100% is 1500.. is the number of deers population in the forest..
Answer: D is correct answer..
Answer: D
Question: At 9 am a car (A) began a journey from a point, traveling at 40 mph. At 10 am another car (B) started traveling from the same point at 60 mph in the same direction as car (A).
At what time will car B pass car A?
Options:
A)12 pm
B)1 pm
C)2 pm
D)3 pm
E)4 pm
Rationale: After t hours the distances D1 traveled by car A is given by
D1 = 40 t
Car B starts at 10 am and will therefore have spent one hour less than car A when it passes it. After (t - 1) hours, distance D2 traveled by car B is given by
D2 = 60 (t-1)
When car B passes car A, they are at the same distance from the starting point and therefore D1 = D2 which gives
40 t = 60 (t-1)
Solve the above equation for t to find
t = 3 hours
Car B passes car A at
9 + 3 = 12 pm
Answer A
Answer: A
Question: The balance of a trader weighs 8% less than it should. Still the trader marks up his goods to get an overall profit of 20%. What is the mark up on the cost price?
Options:
A)40%
B)8%
C)10.4%
D)16.66%
E)9%
Rationale: The most natural way to deal with 'weights' questions is by assuming values.
Say the trader's balance shows 100 gms. It is actually 92 gms because it weighs 8% less. Say, the cost price is $92 ($1/gm). Since he gets a profit of 20%, the selling price must be 92+(20/100)*92 = $110.4
Since the cost price is actually supposed to be $100 (for 100 gms) and the selling price is $110.4, the mark up is simply 10.4%.
Ans : C
Answer: C
Question: What are the unit's digits of 369, 6864, 4725 respectively ?
Options:
A)2
B)8
C)3
D)5
E)0
Rationale: Cyclicity of 3 is 4. 369 = (34)k.31(34)k.31 = (1)k.31(1)k.31 = 3
Power of 6 always gives units digit 6 only.
If power of 4 is odd, then we will get 4 as units digit, if power of 4 is even, then we get 6 as units digit.
Hence, Option 3 is correct.
Answer:C
Answer: C
Question: X and Y are positive two-digit integers such that the tens digit in X is the same as the units digit in Y, and the units digit in X is the same as the tens digit in Y. Which of the following can be the difference of X and Y ?
Options:
A)73
B)44
C)33
D)29
E)9
Rationale: X and Y are positive two-digit integers such that the tens digit in X is the same as the units digit in Y, and the units digit in X is the same as the tens digit in Y:
X = 10a + b
Y = 10a + b
X - Y = (10a + b) - (10a + b) = 9(a - b). As you can see the difference must be a multiple of 9. Only option E is a multiple of 9.
Answer: E.
Answer: E
Question: A bag contains 3 red, 4 black and 2 white balls. What is the probability of drawing a red and a white ball in two successive draws,each ball being put back after it is drawn?
Options:
A)2/27
B)1/9
C)1/3
D)4/27
E)2/9
Rationale: P=2∗39∗29=427P=2∗39∗29=427
We are multiplying by 2 as there are two possible wining scenarios RW and WR.
Answer: D.
Answer: D
Question: In Kaya's teacher's desk there are 10 pink highlighters, 15 yellow highlighters, and 8 blue highlighters. How many highlighters are there in all?
Options:
A)11
B)22
C)77
D)33
E)88
Rationale: Add the numbers of highlighters.
10 + 15 + 8 =33.
Answer is D.
Answer: D
Question: If m is an integer such that (-2)^2m=2^(21-m) then m=?
Options:
A)5
B)6
C)7
D)8
E)9
Rationale: 2m = 21-m
3m = 21
m = 7
The answer is C.
Answer: C
Question: In 1995, the Jossy spent $800 on the family’s water bills. Anticipating that water rates would increase in 1996 by 50%, the Jossy cut back their water usage. By how much must the Jossy have reduce their 1996 water usage to pay exactly the same amount in 1996 as they paid in 1995?
Options:
A)a)	33 1/3 %
B)b)	40 %
C)c) 50 %
D)d)	66 2/3 %
E)e)	100 %
Rationale: Let x be the water usage and c be the cost waterof Jossy
We have
xc =800, c=800/x
Y(1.5c)=800 where Y is the water usage in 1996
Y= 800/ (1.5*800/x)= 1/1.5x=2/3x
Thus reduction will be x-2/3x=1/3x=A
Answer: A
Question: If 6 years are subtracted from the present age of Arun and the remainder is divided by 18, then the present age of his grandson Gokul is obtained.If Gokul is 2 years younger to Madan whose age is 5 years, then what is the age of Arun?
Options:
A)48
B)60
C)84
D)96
E)69
Rationale: arun age x.
(x-6)/18=y
y is gokul age which is 3
x=60
ANSWER:B
Answer: B
Question: Rita bought 105 items from the market, and each item is either glass, cup, or spoon. If she ownsbought 5 more cups than glasses, and twice as many cups as glasses, how many glasses Rita did buy ?
Options:
A)20
B)25
C)30
D)40
E)50
Rationale: x = the number of glasses
y = the number of cups
z = the number of spoons
From the first sentence we have
Equation #1: x + y + z = 105
...she bought 5 more spoons than glasses...
Equation #2: z = 5 + x
...twice as many cups as glasses...
Equation #3: y = 2x
Now, we can replace y with x in Equation #1
x + 2x + z = 105
Equetion 4 : 3x + z = 105
by adding Equetion #2 and Equetion #4
4x = 100
x = 100/4
x = 25
There are 25 glasses. That's the answer. Just for check, this is 5 less than the number of spoons, so z = 30, y = 50, and 25 + 50 + 30 = 105.
Answer = 25,(B)
Answer: B
Question: If f(x) = -2x2 + 8x - 4, which of the follwoing is true?
Options:
A)The maximum value of f(x) is -4.
B)The graph of f opens upward.
C)The graph of f has no x-intercept
D)f is not a one to one function.
E)The maximum value of f(x) is 4.
Rationale: f(x) is a quadratic function and its graph is a parabola that may be intercepted by horizontal lines at two points and therefore is not a one to one function. The answer is D
correct answer D
Answer: D
Question: In an xy-coordinate plane, a line is defined by y = kx + 1. If (3, b), (a, 4), and (a, b+1) are three points on the line, where a and b are unknown, then k = ?
Options:
A) 1/2
B) 1
C) 3/2
D) 2/3
E) 5/2
Rationale: b=3k+1...(1)
b+1=ak+1...(2)
4=ak+1...(3)
Taking (2) and (3)
4=b+1
b=3
Taking (1)
3=3k+1
k=2/3
Answer : D
Answer: D
Question: There are 1400 jelly beans divided between two jars, Jar X and Jar Y. If there are 300 fewer jelly beans in jar X than three times the number of beans in jar Y, how many beans are in jar X?
Options:
A)925
B)950
C)975
D)1000
E)1025
Rationale: X+Y=1400 so Y=1400-X
X=3Y-300
X=3(1400-X)-300
4X=3900
X=975
The answer is C.
Answer: C
Question: A, B, C are three consecutive positive integers (A>B>C). What is the value of the expression 2A +B + C?
Options:
A)6A+7.
B)5A+1.
C)4A-3.
D)6A-5.
E)6A-7.
Rationale: B = A-1
C= A-2
Putting these values in 2A +B + C we get 4A-3
C is the answer
Answer: C
Question: Last year, for every 100 million vehicles that travelled on a certain highway, 90 vehicles were involved in accidents. If 3 billion vehicles travelled on the highway last year, how many of those vehicles were involved in accidents? (1 billion = 1,000,000,000)
Options:
A)288
B)320
C)2,700
D)3,200
E)28,800
Rationale: To solve we will set up a proportion. We know that “100 million vehicles is to 90 accidents as 3 billion vehicles is to x accidents”. To express everything in terms of “millions”, we can use 3,000 million rather than 3 billion. Creating a proportion we have:
100/90 = 3,000/x
Cross multiplying gives us:
100x = 3,000 * 90
x = 30 * 90 = 2,700
Correct answer is C.
Answer: C
Question: A hiker walked for 3 days. She walked 18 miles on the first day, walking 3 miles per hour. On the second day she walked for one less hour but she walked two mile per hour, faster than on the first day. On the third day she walked the same number of hours as on the first day, but at the same speed as on the second day. How many miles in total did she walk?
Options:
A)24
B)44
C)73
D)60
E)62
Rationale: She walked 18 miles on the first day, walking 3 miles per hour i.e. total time of walk on Day-1 = 18/3 = 6 Hours
Second day time of walk = 6-1 = 5 hours and Speed = 3+2=5 miles per hour i.e. Distance walked on second day = 5*5 = 25 miles
Third day time of walk = 6 hours and Speed = 5 miles per hour i.e. Distance walked on second day = 6*5 = 30 miles
Total Distance travelled on three days = 18+25+30 = 73
Answer: Option C
Answer: C
Question: What should come in place of the question mark (X) in the following equation ?
60% of X + 2/3 of 39 = 44
Options:
A)30
B)37
C)28
D)26
E)18
Rationale: Explanation:
60% of X + 2/3 of 39 = 44
i.e. 3/5 of X + 2/3 of 39 = 44 (60% = 3/5)
3/5 * X + 2/3 * 39 = 44
3/5 * X + 26 = 44
3/5 * X = 18
X = 18 * 5/3
X = 30
ANSWER: A
Answer: A
Question: The ratio of ducks and frogs in a pond is 35 : 39 respectively. The average number of ducks and frogs in the pond is 152. What is the number of frogs in the pond ?
Options:
A)160
B)152
C)156
D)144
E)None
Rationale: Solution:
Ratio of Ducks and Frogs in Pond,
= 35 : 39.
Average of Ducks and Frogs in Pond,
= 152.
So, total number of Ducks and Frogs in the Pond,
= 2* 152 = 304.
Therefore,
Number of Frogs, = (304 *39)/74 = 160.
Answer: Option A
Answer: A
Question: If x/(12p) is an even prime number, where x is a positive integer and p is a prime number, what is the least value of x?
Options:
A) 22
B) 33
C) 44
D) 48
E) 99
Rationale: x/(12p) = even prime number
x = even prime number * 11p
Least value of x = Lowest even prime number * 12 * Lowest value of p
= 2 * 12* 2 = 48
Answer D
Answer: D
Question: What number has a 5:1 ratio to the number 10?
Options:
A)88
B)50
C)66
D)2881
E)11
Rationale: 5:1 = x: 10
x = 50
Answer: B
Answer: B
Question: A clock shows the time as 3:30 P.m. If the minute hand gains 2 minutes every hour, how many minutes will the clock gain by 1 a.m.?
Options:
A)23 Minutes
B)19 Minutes
C)25 Minutes
D)26 Minutes
E)None of these
Rationale: if the minute hand gains 2 minutes in 1 hour the from 3:30 p.m-4:00 p.m it gains 1 min
then from 4:00p.m-4:00 a.m =9*2=18 total=19
ANSWER:B
Answer: B
Question: A can do a job in 15days and B in 20days. If they work on it together for 4 days, then the fraction of the work that is left is?
Options:
A)2/15
B)8/15
C)3/11
D)1/12
E)6/13
Rationale: A's 1 day work = 1/15
B's 1day work = 1/20
A+B 1day work = 1/15 + 1/20 = 7/60
A+B 4days work = 7/60*4 = 7/15
Remaining work = 1 - 7/15 = 8/15
Answer is B
Answer: B
Question: Two trains are moving at 80 kmph and 70 kmph in opposite directions. Their lengths are 150 m and 100 m respectively. The time they will take to pass each other completely is?
Options:
A)4 sec
B)5 sec
C)6 sec
D)7 sec
E)8 sec
Rationale: 70 + 80 = 150 * 5/18 = 125/3 mps
D = 150 + 100 = 250 m
T = 250 * 3/125 = 6 sec
Answer:C
Answer: C
Question: The radius of a cylindrical vessel is 5cm and height is 3cm. Find the whole surface of the cylinder?
Options:
A)251.4 sq cm
B)220 sq cm
C)440 sq cm
D)132 sq cm
E)138 sq cm
Rationale: r = 5 h = 3
2πr(h + r) = 2 * 22/7 * 5(8) = 251.4
ANSWER:A
Answer: A
Question: In a apartment, 30% of the people speak English, 20% speak Hindi and 13% speak both. If a people is selected at random, what is the probability that he has speak English or Hindi?
Options:
A)1/30
B)2/30
C)10/27
D)2/90
E)13/27
Rationale: P (E) = 30 / 100 , P (H) = 20 / 100 and P (E âˆ© H) = 13 / 100 =
P (E or H) = P (E U H)
= P (E) + P (H) - P (E âˆ© H)
= (30 / 100) + (20/100 - (13 / 100) = 37/100 = 10/27
C
Answer: C
Question: If 36 men can do a piece of work in 25 hours, in how mwny hours will15 men do it?
Options:
A)22
B)38
C)60
D)88
E)72
Rationale: Explanation:
Let the required no of hours be x. Then
Less men , More hours (Indirct Proportion)
\inline \fn_jvn \therefore 15:36 ::25:x \inline \fn_jvn \Leftrightarrow (15 x X)=(36 x 25) \inline \fn_jvn \Leftrightarrow \inline \fn_jvn x=\frac{36\times 25}{15}=60
Hence, 15 men can do it in 60 hours.
Answer: C) 60
Answer: C
Question: A bookshop had science and art books in the ratio of 2:5. By the end of the week, 20% of both type of books were sold and 2240 books were unsold. How many art books were there at the starting?
Options:
A)1355
B)1350
C)1450
D)1600
E)2000
Rationale: science books sold = 2x × 0.2 = 0.4x
science books unsold = 2x – 0.4x = 1.6x
art books sold = 5x × 0.2 = x
art books unsold = 5x – x = 4x
total books unsold = 1.6x + 4x = 5.6x
5.6x = 2240
x = 400
2x science = 800
and 5x art books = 2000
E
Answer: E
Question: In the xy-plane, a line has slope 3 and x-intercept 4. What is the y-intercept of the line?
Options:
A)-12
B)-3
C)0
D)3
E)9
Rationale: Let the line be represented by a general equation y=mx+b, where m = slope (3) and b=y intercept. We are also given the value of x-intercept 4.
Theory : y intercept represents the point on the line where the x=0, and x intercept represents the point on the line where the y=0.
Putting these values in the equation : 0 = 3*4 + b => b = -12. Hence A.
Answer: A
Question: The income of a company increases 20% per annum. If its income is 2664000 in the year 1999 what was its income in the year 1997?
Options:
A)2220000
B)2850000
C)2121000
D)1855000
E)None of these
Rationale: Let income in 1997 = x
According to the question,
Income in 1998 = x + x⁄5 = 6x⁄5
Income in 1999 = 6x⁄5 + 6x⁄25 = 36x⁄25
But given, income in 1999 = 2664000
∴ 36x⁄25 = 2664000 ⇒ x = 1850000
Answer E
Answer: E
Question: 5 men and 5 women participated in a interview. If two people get the job, how many chances there will be at least a man is
selected?
Options:
A)30
B)32
C)35
D)31
E)40
Rationale: 5 women and 5 men. Two people is slelected
It is always better to subtract the total from none in case of at least one problems.
Total ways = 10C2 = 45
Total ways without any man = 5C2 = 10
Hence ways in which at least one man will be present = 45 - 10 = 35
Correct option: C
Answer: C
Question: A right triangle PQR has sides such that the longest side PR is twice the length of side PQ and thrice the length of side QR. If PR = 6, what is the area of the triangle?
Options:
A)6
B)36
C)3
D)2
E)4
Rationale: Since PR is twice of PQ, so PQ=3 and QR=2 since PR is thrice of QR. Area of right triangle equals PQ*QR/2. So the correct answer is C.
Answer: C
Question: An isosceles triangle has a perimetre of 37 centimetres and its base has a length of 9 centimetres. The other two sides will each have a length of
?
Options:
A)14 cm
B)15 cm
C)16 cm
D)17 cm
E)18 cm
Rationale: Solution:
The isosceles triangle has two equal sides. The sum of the equal sides will be 37 - 9 = 28 cm . Thus, one of them will be 28 ÷ 2 = 14 cm
Answer A
Answer: A
Question: Of the employees in a company, 30 % are female who have a master degree. If 20 % of the female employees do not have a master degree, what percent of the employees in the company are female?
Options:
A)25 %
B)30 %
C)32.5 %
D)37.5 %
E)45 %
Rationale: No. of female employees with Masters = 0.3 x E (From the question)
No. of female employees without masters = 0.2 x F (From the question)
Therefore No. of female employees with masters = F - 0.2 F = 0.8 F
The 2 expressions equal each other therefore 0.8F = 0.3E; F/E = 0.3/0.8 = 37.5%
Ans: D
Answer: D
Question: If a coin has an equal probability of landing heads up or tails up each time it is flipped , what is the probability that the coin will land Tails up exectly twice in 3 consecutive flips ?
Options:
A)0.375
B)0.25
C)0.325
D)0.5
E)0.666
Rationale: Total number of ways in which H or T can appear in 3 tosses of coin is
= 2 * 2 * 2 = 8 ways
For 2 T and 1 TH
Thus probability is
= P(HTT) + P(TTH) + P(THT)
= 1/8 + 1/8 + 1/8
= 3/8
= .375
Answer :A
Answer: A
Question: Find the no.of ways of arranging the boy and 4 guests at a circular table so that the boy always sits in a particular seat?
Options:
A)7!
B)4!
C)9!
D)10!
E)11!
Rationale: Ans.(B)
Sol. Total number of persons = 5 Host can sit in a particular seat in one way. Now, remaining positions are defined relative to the host. Hence, the remaining can sit in 4 places in 4P4 = 4! Ways ... The number of required arrangements = 4! x 1= 4! = 4! ways
Answer: B