RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: Last year, for every 100 million vehicles that travelled on a certain highway, 92 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)
A.288
B.320
C.2,760
D.3,200
Answer: C.2,760
Explanation: To solve we will set up a proportion. We know that “100 million vehicles is to 92 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:
100/92 = 3,000/x
Cross multiplying gives us:
100x = 3,000 * 92
x = 30 * 92 = 2,760
Correct answer is C.
Question: Using all the letters of the word "THURSDAY", how many different words can be formed?
A.8
B.8!
C.7!
D.7
Answer: B.8!
Explanation: Total number of letters = 8
Using these letters the number of 8 letters words formed is ⁸P₈ = 8!.
Answer:B
Question: Which of the following are/is prime?
I. 143
II. 145
III. 149
A. II only
B. III only
C. III
D. IIII
Answer: A. II only
Explanation: 1) 143 = 13*11 so we know it is not prime quickly eliminate all options having 1 as a choice
which leaves us with 2 ) and 3) as possible answers
From here on we find 147 = 3* 49 so we eliminate 147 which leaves us with 149 as the only possible solution
A
Question: In a school of 900 students, 44% wear blue shirts, 28% wear red shirts, 10% wear green shirts, and the remaining students wear other colors. How many students wear other colors (not blue, not red, not green)?
A.144
B.153
C.162
D.171
Answer: C.162
Explanation: 44 + 28 + 10 = 82%
100 – 82 = 18%
900 * 18/100 = 162
The answer is C.
Question: Irin, Ingrid and Nell bake chocolate chip cookies in the ratio of 9.18: 5.17: 2.05. If altogether they baked a batch of 148 cookies, what percent of the cookies did Ingrid bake?
A.0.125%
B.1.25%
C.31.33%
D.125%
Answer: C.31.33%
Explanation: 9.18x+5.17x+2.05x = 16.4x = 150 cookies
x= 150/16.4 = 9.14 (approx)
So, Ingrid baked 9.14*5.17 cookies or 47cookies (approx)
% share = 47/150 = 31.33 approx
Hence, answer is C.
Question: hoose the number pair/group which is different from others.
1. 40 : 50
2. 30 : 36
3. 8 : 10
4. 28 : 35
5. 16 : 20
A.30 : 36
B.30 : 39
C.30 : 332
D.30 : 37
Answer: A.30 : 36
Explanation: Explanation:
40 : 50 ==> 4 : 5
30 : 36 ==> 5 : 6
8 : 10 ==> 4 : 5
28 : 35 ==> 4 : 5
16 : 20 ==> 4 : 5
In each of the pair except 30 : 36, the ratio of the two numbers is 4 : 5.
ANSWER: A
Question: A can do a piece of work in 5 days of 9 hours each and B alone can do it in 5 days of 3 hours each.how long will they take it to do working together
2 1/4 hours a day?
A.2 days
B.3 days
C.4 days
D.5 days
Answer: D.5 days
Explanation: A's work per hour=1/45
B's work per hour=1/15
A & B's work per hour together=(1/45)+(1/15)=4/45
so a & B together complete the work in 45/4 hours...
if they work 2 1/4=9/4 hours a day,
it will take (45/4)/(9/4) days=5 days...
ANSWER:D
Question: The first year, two cows produced 8100 litres of milk. The second year their production increased by 15% and 10% respectively, and the total amount of milk increased to 9100 litres a year. How many litres were milked from each cow each year?
A.4370, 4730 liters and 3800, 4300 liters
B.4300, 3800 liters and 4730, 3800 liters
C.4730, 3800 liters and 4300, 3800 liters
D.3800, 4300 liters and 4370, 4730 liters
Answer: D.3800, 4300 liters and 4370, 4730 liters
Explanation: Let x be the amount of milk the first cow produced during the first year. Then the second cow produced (8100−x) litres of milk that year. The second year, each cow produced the same amount of milk as they did the first year plus the increase of 15% or 10%.
So 8100+15100⋅x+10100⋅(8100−x)=9100
Therefore 8100+320x+110(8100−x)=9100
120x=190
x=3800
Therefore, the cows produced 3800 and 4300 litres of milk the first year, and 4370 and 4730 litres of milk the second year, respectively.
So answer is D.
Question: one bottle is half-full of oil and another bottle with twice the capacity is one quarter full of oil. if water is added so that both the bottles are full and the contents of both are then poured into a third bottle that is empty and large enough to hold the contents of both, what fractions of the contents in the third bottle is oil?
A.1/4
B.1/3
C.3/8
D.2/3
Answer: B.1/3
Explanation: Let assume that 1st bottle capacity = 1Litre;
Therefore, it contain 1/2 litre Oil and 1/2 litre water .
(i.e) Water = 1/2 litre
Oil = 1/2 litre
2nd bottle is twice the capacity
i.e. 2 litre capacity
It means, 1/2litre filled with oil and 1(1/2)litre filled with water.
i.e. Oil = 1/2 liter
Water = 1(1/2)litre
In total the third bottle will contain,
1 litre oil and 2 litre water.
i.e., Oil = 1 litre
Water = 2 liter
Therefore, oil proportion is 1/3
ANSWER:B
Question: The perimeter of a semi circle is 144 cm then the radius is?
A.22
B.28
C.99
D.77
Answer: B.28
Explanation: 36/7 r = 144 => r = 28
Answer: B
Question: A furniture manufacturer has two machines, but only one can be used at a time. Machine E is utilized during the first shift and Machine B during the second shift, while both work half of the third shift. If Machine E can do the job in 12 days working two shifts and Machine B can do the job in 15 days working two shifts, how many days will it take to do the job with the current work schedule?
A.14
B.13
C.11
D.9
Answer: D.9
Explanation: machine E finish the job in 2*12 shifts = 24 shifts
machine B finish the job in 2*15 shifts = 30 shifts
Lets assume total work require 120 shifts
Therefore,
rate of E = 5 shifts/day
rate of B = 4 shifts/day
rate of (E+B) = 9 shifts/day
According to current schedule work complete in a day = 5+4+(9/2) =13.5 shifts/day
Therefore, Time required to finish 120 shifts = (120/13.5) = 8.88.. days ~ 9 days=D
Question: 9+2+2^2+2^3+2^4+2^5=？
A.(2^3-1)(2^3+1)
B.2^6+1
C.2^5-1
D.2^6+7
Answer: D.2^6+7
Explanation: From 9+2+2^2+2^3+2^4+2^5=71,
2^6+7=71
the correct answer is D.
Question: A salesmanâ€™s terms were changed from a flat commission of 5% on all his sales to a fixed salary of Rs.1000 plus 2.5% commission on all sales exceeding Rs. 4,000. If his remuneration as per new scheme was Rs. 800 more than that by the previous schema, his sales were worth?
A.s. 4,000
B.s. 12,000
C.s. 30,000
D.s. 40,000
Answer: A.s. 4,000
Explanation: [1000 + (X-4000) * (2.5/100)] - X * (5/100) = 800
X =4000
ANSWER:A
Question: A, B and C invested Rs.6300, Rs.4200 and Rs.10500 respectively, in a partnership business. Find the share of A in profit of Rs.12400 after a year?
A.3630
B.3637
C.3720
D.3631
Answer: C.3720
Explanation: 6300:4200:10500
3:2:5
3/10 * 12400 = 3720
Answer: C
Question: A man invested Rs.1552 in a stock at 97 to obtain an income of Rs.128. What is the dividend from the stock?
A.None of these
B.9.7%
C.7.5%
D.8%
Answer: D.8%
Explanation: Explanation :
By investing Rs.1552, income = Rs.128
By investing Rs.97, income = 128×97/1552=8
ie, dividend = 8%
Answer : Option D
Question: I. a2 + 8a + 16 = 0,
II. b2 - 4b + 3 = 0 to solve both the equations to find the values of a and b?
A.If a < b
B.If a ≤ b
C.If the relationship between a and b cannot be established
D.If a > b
Answer: A.If a < b
Explanation: Explanation:
I. (a + 4)2 = 0 => a = -4
II.(b - 3)(b - 1) = 0
=> b = 1, 3 => a < b
Option A
Question: A certain fruit stand sold apples for $0.80 each and bananas for $0.70 each. If a customer purchased both apples and bananas from the stand for a total of $7.30, what total number of apples and bananas did the customer purchase?
A.9
B.10
C.11
D.12
Answer: B.10
Explanation: Let's start with 1 apple for $0.80.
Let's subtract $0.80 from $7.30 until we get a multiple of $0.70.
$7.30, $6.50, $5.70, $4.90 = 7*$0.70
The customer purchased 7 bananas and 3 apples.
The answer is B.
Question: A survey of employers found that during 1993 employment costs rose 3.5 percent, where employment costs consist of salary costs and fringe-benefit costs. If salary costs rose 3 percent and fringe-benefit costs rose 5.5 percent during 1993, then fringe-benefit costs represented what percent of employment costs at the beginning of 1993 ?
A.16.5%
B.20%
C.35%
D.55%
Answer: B.20%
Explanation: In my view easiest method would be, eliminating the percentage sign
Let 3.5 be 35
5.5 be 55
and 3 be 30
then first eq: S+F=E
130S+155F=135E
5s=20F
therefore, s=4F and then E=5F
F/E=F/5F=20%
Therefore, Answer is B
Question: In the coordinate plane, the points F (-2,1), G (1,6), and H (6,1) lie on a circle with center P. What are the coordinates of point P ?
A.(0,0)
B.(1,1)
C.(2,2)
D.(1,-2)
Answer: C.(2,2)
Explanation: I thought I need to find the 4th point that would lie on the circle
Hence my answer was D (1,-2)
But the the center of the circle will lie on (2,2)
C
Question: An outlet pipe can empty 2/3 rd of a cistern in 12 minutes. In 8 minutes, what part of the cistern will be emptied?
A.4/9
B.4/5
C.4/2
D.4/4
Answer: A.4/9
Explanation: 2/3 ---- 12
? ----- 8 ==> 4/9
Answer:A
Question: If 2x + y = 6 and x + 2y = 5, then (x + y)/3 =
A. 1
B. 4/3
C. 17/5
D. 11/9
Answer: D. 11/9
Explanation: We have two equations:
2x + y = 6
x + 2y = 5
Notice that something nice happens when we ADD them. We get:
3x + 3y = 11
Divide both sides by 3 to get:x + y =11/3
So, (x + y)/3 =11/9
Answer: D
Question: A is twice as good as workman as B and together they finish a piece of work in 18 days. In how many days will B alone finish the work.
A.27 days
B.54 days
C.56 days
D.68 days
Answer: B.54 days
Explanation: Explanation:
As per question, A do twice the work as done by B.
So A:B = 2:1
Also (A+B) one day work = 1/18
To get days in which B will finish the work, lets calculate work done by B in 1 day =
=(1/18∗1/3)=1/54
[Please note we multiplied by 1/3 as per B share and total of ratio is 1/3]
So B will finish the work in 54 days
Option B
Question: 30% loss on cost price in what percent loss on selling price?
A.28.44 %
B.38 %
C.40.35 %
D.42.85 %
Answer: D.42.85 %
Explanation: Sol.
Loss = 30% on CP i.e., 0.3CP ⇒ SP = 0.7CP Loss % on
SP = loss/SP * 100 = 0.3CP/0.7CP * 100 = 42.85%.
Answer D
Question: Five years ago, the average age of A, B, C and D was 45 yr. with E joining them now, the average of all the five is 42 yr. How old is E?
A.10 yr
B.40 yr
C.45yr
D.64 yr
Answer: A.10 yr
Explanation: Solution:
Total present age of A, B, C and D,
= (45*4)+(4*5) = 200 yr;
Total age present age of A, B, C, D and E,
= 42*5 = 210 yr.
So, age of E = 10 yr.
Answer: Option A
Question: How much interest can a person get on Rs. 8400 at 17.5% p.a. simple interest for a period of two years and six months?
A.3587.58
B.3587.59
C.3675
D.3587.52
Answer: C.3675
Explanation: I = (8400 * 2.5 * 17.5)/100 = (8400 * 5 * 35)/(100 * 2 * 2) = Rs. 3675.Answer: C
Question: A family consists of two grandparents, two parents and three grandchildren. The average age of the grandparents is 67 years, that of the parents is 35 years and that of the grandchildren is 6 years. What is the average age of the family?
A.28 4/7 years
B.31 5/7 years
C.32 1/7 years
D.None of these
Answer: B.31 5/7 years
Explanation: Required average
=((67 x 2 + 35 x 2 + 6 x 3)/(2 + 2 + 3))
=(134 + 70 + 18)/7
=222/7
= 31 5/7	years.
Answer : B
Question: A train leaves Delhi at 7 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?
A.229
B.840
C.600
D.888
Answer: B.840
Explanation: D = 30 * 7 = 210
RS = 40 – 30 = 10
T = 210/10 = 21
D = 40 * 21 = 840 km
Answer: B
Question: In how many possible ways can 5 people draw water from 5 taps if no tap can be used more than once?
A.120
B.700
C.300
D.150
Answer: A.120
Explanation: 1 - can draw from any of 5 taps
2 - draw remain 4
3rd - draw remain 3
4th -draw remain 2
5th - draw remain 1
so total possible = 5*4*3*2*1= 120
ANSWER A
Question: If a card is randomly drawn from a well shuffled pack of cards, what is the probability of drawing a black card or a heart?
A.15/26
B.7/13
C.2/3
D.3/4
Answer: D.3/4
Explanation: There are 26 black cards and 13 hearts.
P(black card or heart) = 39/52 = 3/4
The answer is D.
Question: Sreenivas sells a table to Shiva at 10% profit and Shiva sells it to Mahesh at 10% loss. At what price did Sreenivas purchase the table if Mahesh paid Rs. 2178?
A.Rs.2220
B.Rs.2229
C.Rs.2200
D.Rs.2297
Answer: C.Rs.2200
Explanation: Let the cost price of table for Sreenivas be Rs. x and given that, cost price of table for Mahesh = Rs. 2178.
=> (90%) of (110%) of x = Rs. 2178.
=> (90/100)(110/100)x = 2178
=> x = (2178 * 100)/(9 * 11)
=> x = Rs.2200
Answer:C
Question: When positive integer e is divided by 13, the remainder is 2. When n is divided by 8, the remainder is 5. How many such values are less than 180?
A. 0
B. 1
C. 2
D. 3
Answer: B. 1
Explanation: the equation that can be formed e is 13x+2=8y+5..
13x-3=8y...
as we can see x can take only odd values as the RHS will always be even..
Also x can take values till 13 as 13*14>180..
now we have to substitue x as 1,3,5,7,9,11,13...
once we find 7 fitting in , any other value need not be checked as every 4th value will give us answer so next value will be 15..
ans 1.. B
Question: Jim is able to sell a hand-carved statue for $750 which was a 35% profit over his cost. How much did the statue originally cost him?
A.$496.30
B.$512.40
C.$555.56
D.$574.90
Answer: C.$555.56
Explanation: 750 = 1.35*X
X = 750/1.35 = 555.5555556...
which rounds to $555.56, which is (C).
Question: A fruit seller had some oranges. He sells 40% oranges and still has 420 oranges. How many oranges he had originally?
A.500
B.700
C.750
D.900
Answer: B.700
Explanation: He sells 40% of oranges and still there are 420 oranges remaining.
=> 60% of oranges = 420
=> Total oranges
×
60
100
=
420
×60100=420
=> Total oranges
=
420
×
100
60
=
700
Option B
Question: The H.C.F of two numbers is 11 and their L.C.M is 7700. If one of the numbers is 275, then the other is
A.279
B.283
C.308
D.318
Answer: C.308
Explanation: Solution
Other number	= (11×7700 / 275)
= 308.
Answer C
Question: Fred and Sam are standing 55 miles apart and they start walking in a straight line toward each other at the same time. If Fred walks at a constant speed of 6 miles per hour and Sam walks at a constant speed of 5 miles per hour, how many miles has Sam walked when they meet?
A.5
B.9
C.25
D.30
Answer: C.25
Explanation: relative distance =55 miles
relative speed =6+5 =11 miles per hour
time taken =55/11=5 hours
distance travelled by sam =5*5=25 miles=C
Question: An bus covers a certain distance at a speed of 240 kmph in 5 hours. To cover the samedistance in 1hr, it must travel at a speed of?
A.700 km/hr
B.720 km/hr
C.870 km/hr
D.869 km/hr
Answer: B.720 km/hr
Explanation: Distance = (240 x 5) = 1200 km.
Speed = Distance/Time
Speed = 1200/(5/3) km/hr. [We can write 1 hours as 5/3 hours]
Required speed = 1200 x 3 km/hr = 720 km/hr.
B
Question: Two bullet train s are moving in opposite directions at 60 km/hr and 90 km/hr. Their lengths are 1.10 km and 0.9 km respectively. The time taken by the slower bullet train to cross the faster bullet train in seconds is:
A.58 sec.
B.78 sec.
C.68 sec.
D.48 sec.
Answer: D.48 sec.
Explanation: D
48 sec.
Relative speed = (60+ 90) km/hr
= 150x5/18
= 120/3 m/sec
Distance covered = (1.10 + 0.9) km = 2 km = 2000 m.
Required time = 2000 x 3/125 = 48 sec.
Question: Consider the word RMTMR. Whichever way you read it, from left to right or from right to left, you get the same word. Such a word is known as palindrome. Find the maximum possible number of 5 letter palindromes.
A.10987
B.11755
C.17576
D.19775
Answer: C.17576
Explanation: The first letter from the right can be chosen in 26 ways because there are 26 alphabets.
Having chosen this, the second letter can be chosen in 26 ways
The first two letters can chosen in 26 x 26 = 676 ways
Having chosen the first two letters, the third letter can be chosen in 26 ways.
All the three letters can be chosen in 676 x 26 =17576 ways.
It implies that the maximum possible number of five letter palindromes is 17576 because the fourth letter is the same as the second letter and the fifth letter is the same as the first letter.
C
Question: A bus starts from city X. The number of women in the bus is half of the number of men. In city Y, 16 men leave the bus and eight women enter. Now, number of men and women is equal. In the beginning, how many passengers entered the bus ?
A.15
B.30
C.36
D.72
Answer: D.72
Explanation: Explanation:
Originally, let number of women = x. Then, number of men = 2x.
So, in city Y, we have : (2x - 16) = (x + 8) or x = 24.
Therefore Total number of passengers in the beginning = (x + 2x) = 3x = 72.
Answer: D
Question: Find the amount for Rs. 6000 at 10% per annum, compounded semi-annually for 2 years.
A.1293
B.1283
C.1273
D.1263
Answer: A.1293
Explanation: Solution:
Semi annually means we have to compound the interest for every six months. So we have to calculate interest for 6 months. So R =
10/2= 5% (for half year)
Also, n = 2 years x 2 = 4 periods
Therefore, P = 6000, n = 4, r = 5%
A = 6,000(1+5/100)4 = Rs. 7,293
Interest = Rs.7293 - 6000 = 1293
Answer A
Question: The length of the bridge, which a train 130 metres long and travelling at 45 km/hr can cross in 30 seconds, is:
A.234
B.230
C.245
D.250
Answer: C.245
Explanation: Speed = [45 X 5/18] m/sec = [25/2] m/sec Time = 30 sec Let the length of bridge be x metres. Then, (130 + x)/30 = 25/2 => 2(130 + x) = 750 => x = 245 m.
Answer: Option C
Question: A and B r 2 men who enter into business and they invest Rs 1000, Rs 2000respectively. How will they divide the income of Rs 5000
A.3336,1667
B.3339,1667
C.3333,1666
D.3333,1668
Answer: C.3333,1666
Explanation: they invested in the ratio 1:2
a's share =1/3*5000=1666
b's share=2/3*5000=3333
ANSWER:C
Question: How many positive integers less than 50 are there such that they are multiples of 9?
A.5
B.6
C.4
D.8
Answer: A.5
Explanation: Number of multiples of 9 => 45-9/9+1= 5
Answer is A
Question: For which of the following functions does f(−u)=−f(u) for all real number values of x?
A.u^8
B.−u^6
C.u^5
D.u^9/(u^5+1)
Answer: C.u^5
Explanation: f(-u) = (-u)^5 = -u*u^4
-f(u) = -u^5
C
Question: The average of first 10 odd numbers is?
A.11
B.10
C.88
D.176
Answer: B.10
Explanation: Sum of 10 odd no. = 100
Average = 100/10 = 10
Answer: B
Question: Of the 11 temporary employees in a certain company, 4 will be hired as permanent employees. If 5 of the 11 temporary employees are women, how many of the possible groups of 4 employees consist of 3 women and one man?
A.22
B.35
C.60
D.70
Answer: C.60
Explanation: another approach :
one scenario : [WWWM]
now we have 5 ways for the first women , 4 ways for the 2nd women and , 3 ways for the third women.
and 6 ways to select one man
so 5*4*3*6 = 360
now the three women are same so combinations with win them are irrelevant the 3 women can we arranged in 3! ways
hence 360/3!= 360/6= 60
C
Question: The probability that a visitor at the mall buys a pack of candy is 30%. If three visitors come to the mall today, what is the probability R that exactly two visitors will buy a pack of candy?
A.0.343
B.0.147
C.0.189
D.0.063
Answer: C.0.189
Explanation: 3C2 * (3/10)^2 * 7/10
= 3 * 9/100 * 7/10
= 189/1000
= 0.189=R
Answer - C
Question: The difference between a two-digit number and the number obtained by interchanging the digits is 36. What is the difference between the sum and the difference of the digits of the number if the ratio between the digits of the number is 1 : 2 ?
A.4
B.8
C.16
D.20
Answer: B.8
Explanation: Since the number is greater than the number obtained on reversing the digits, so the ten's digit is greater than the unit's digit.
Let ten's and unit's digits be 2x and x respectively.
Then, (10 x 2x + x) - (10x + 2x) = 36
9x = 36
x = 4.
Required difference = (2x + x) - (2x - x) = 2x = 8.
Answer = B
Question: The area of a rectangular field is equal to 300 square meters. Its perimeter is equal to 70 meters. Find the length and width of this rectangle.
A.W = 35 and L = 31
B.W = 15 and L = 20
C.W = 25 and L = 42
D.W = 27 and L = 37
Answer: B.W = 15 and L = 20
Explanation: L * W = 300 : area , L is the length and W is the width.
2 L + 2 W = 70 : perimeter
L = 35 - w : solve for L
(35 - W) * W = 300 : substitute in the area equation
W = 15 and L = 20 : solve for W and find L using L = 35 - w.
correct answer B
Question: A man buys 50 pens at marked price of 46 pens from a whole seller. If he sells these pens giving a discount of 1% , what is the profit percent?
A.5.3 %
B.7.6 %
C.10.6 %
D.12 %
Answer: B.7.6 %
Explanation: Explanation:
Let Marked price be Re. 1 each
C.P. of 50 pens = Rs. 46
S.P. of 50 pens = 99% of Rs. 50 = Rs. 49.50
Profit % = (Profit /C.P.) x 100
Profit% = (3.50/46) x 100 = 7.6 %
ANSWER B
Question: The sum of all consecutive odd integers from −23 to 31, inclusive, is
A.96
B.112
C.158
D.192
Answer: B.112
Explanation: The sum of the odd numbers from -23 to +23 is 0.
Let's add the remaining numbers.
25+27+29+31 = 112
The answer is B.
Question: Jack's toy box contains 13 toy soldiers, 7 model airplanes and 5 dolls. What is the probability that a randomly chosen toy from the box will be either a model airplane or a doll?
A.35/252
B.12/25
C.(7/25)+(5/24)
D.20/25
Answer: B.12/25
Explanation: Probability of selecting either a model airplanes or a doll = 1 - ( Probability of Selecting a Toy )
Probability of selecting either a model airplanes or a doll = 1 - 13C1/ 25C1
Probability of selecting either a model airplanes or a doll = 1 - 13/25
Probability of selecting either a model airplanes or a doll = 12/25
Hence answer will be (B)
Question: If -2<= x <= 2 and 3 <= y <= 5, which of the following represents the range of all possible values of y-x?
A. 5 <= y-x <= 6
B. 1 <= y-x <= 7
C. 1 <= y-x <= 6
D. 5 <= y-x <= 10
Answer: B. 1 <= y-x <= 7
Explanation: Maximum value of y-x= 5 - (-2)= 7
Minimum value of y-x= 3-2= 1
B mentions the correct range
Question: For what value of x between −8 and 8, inclusive, is the value of x^2 − 10x + 16 the greatest?
A.− 8
B.− 2
C.0
D.2
Answer: A.− 8
Explanation: we can see from the statement that two terms containing x, x^2 will always be positive and -10x will be positive if x is -ive..
so the equation will have greatest value if x is -ive, and lower the value of x, greater is the equation.
so -8 will give the greatest value..
ans A
Question: Donovan and Michael are racing around a circular 500-meter track. If Donovan runs each lap in 45 seconds and Michael runs each lap in 40 seconds, how many laps will Michael have to complete in order to pass Donovan, assuming they start at the same time?
A.9
B.10
C.11
D.12
Answer: A.9
Explanation: One way of approaching this question is by Relative speed method
1. Speed/ Rate of Donovan = Distance/ time => 500/45 =>100/9
2. Speed/ Rate of Michael = Distance/ time => 500/40 => 50/4
Relative Speed between them = 50/4 -100/9 => 25/36 (We subtract the Rates if moving in the same direction and add the rates if moving in the opposite direction)
In order to pass Donovan-
Distance to be covered = 500, Relative Rate = 50/36
Total Time taken by Micheal to surpass Donovan = Distance / rate => 500*36/ 50=> 3600/10 => 360
No. of laps taken by Michael = Total time / Michael's rate => 360/40 => 9
Hence correct answer is 9 Laps.
A
Question: A committee of 3 people is to be chosen from the chairman and vice chairman of four different companies. What is the number of different committees that can be chosen if two people who work for the same company cannot both serve on the committee?
A.16
B.24
C.32
D.34
Answer: C.32
Explanation: Each company can send only one representative to the committee. Let's see in how many ways we can choose 3 companies (as there should be 3 members) to send only one representatives to the committee: 4C3=4.
But these 3 chosen companies can send two persons (either chairman or vice chairman ): 2*2*2=2^3=8.
Total # of ways: 4C3*2^3=32.
Answer: C.
Question: There are 26 girls in hostel whose average age is decreased by 2 months, when one girl 18 yrs is replaced by a new boy.Find the age of new girl.
A.1 year
B.1 year 2 months
C.4 years 4 months
D.3 years
Answer: C.4 years 4 months
Explanation: Total decrease = 26 * 2 = 52 monthS
= 4 years 4 months
C