RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: If two numbers are in the ratio 2:3. If 10 is added to both of the numbers then the ratio becomes 3:4 then find the smallest number?
A.10
B.20
C.25
D.30
Answer: B.20
Explanation: 2:3
2x + 10 : 3x + 10 = 3 : 4
4[2x + 10] = 3[3x + 10]
8x + 40 = 9x + 30
9x - 8x = 40 - 30
x = 10
Then smallest number is = 2
2x = 20
B)
Question: At what rate percent per annum will a sum of money double in 16 years
A.6 ¼ % p.a
B.6 % p.a
C.8¼ % p.a
D.3 ¼ % p.a
Answer: B.6 % p.a
Explanation: Let principal = P. Then, S.l. = P and T = 16 yrs.
Rate = (100 x P)/(P*16)% = 6 ¼ % p.a
Answer is B.
Question: If 4 girls can color 48 m long cloth in 2 days, then 6 girls can color 36 m long cloth in
A.1 1/5 days
B.1/5 day
C.1 day
D.2 days
Answer: C.1 day
Explanation: The length of cloth painted by one girl in one day = 48 / 4 × 2 = 6 m
No. of days required to paint 36 m cloth by 6 girls = 36/ 6 × 6 = 1 day.
C
Question: m and n are the x and y coordinates, respectively, of a point in the coordinate plane. If the points (m, n) and (m + p, n + 12) both lie on the line defined by the equation x = (y/4) - (2/5), what is the value of p?
A.1
B.2
C.3
D.4
Answer: C.3
Explanation: x = (y/4) - (2/5), and so y = 4x + 8/5. The slope is 4.
(n+12-n) / (m+p-m) = 3
p = 3
The answer is C.
Question: In a box of 10 pencils, a total of 2 are defective. If a customer buys 3 pencils selected at random from the box, what is the probability that neither pencils will be defective?
A.1/12
B.7/15
C.2/13
D.2/15
Answer: B.7/15
Explanation: First, there are 8C3 ways you can select 3 good pencils from 4 good ones.
Second, there are 10C3 ways you select 3 pencils from 6 ones in the box.
Then, the probability that neither pen will be defective is: 8C3/10C3=56/120 =7/15
Answer is B
Question: A class consists of 15 biology students and 10 chemistry students. If you pick two students at the same time, what's the probability that one is maths and one is chemistry ?
A.2/7
B.5/7
C.1/2
D.3/7
Answer: C.1/2
Explanation: P(1st b, 2nd c) = 15/25*10/24 = 150/600 = 1/4;
P(1st c, 2nd b ) = 10/25*15/24 = 150/600 = 1/4.
P = 1/4 + 1/4 = 1/2.
Answer: C.
Question: The top of a 15 m. high tower makes an angle of elevation of 60 degree with the bottom of an electric pole and an angle of 30 degree with the top of the pole. What is the height of the pole?
A.12 m.
B.10 m.
C.11 m.
D.5 m.
Answer: B.10 m.
Explanation: let distance between tower and pole be x & height of pole be y.
x=15/tan60 & (15-y)/x = tan 30
thus solving two equation gives y= 10m
ANSWER:B
Question: A farm used two harvesting machines, H and K, to harvest 100 acres of wheat. Harvesting machine H, working alone at its constant rate, harvested 40 acres of wheat in 8 hours. Then harvesting machine K was brought in, and harvesting machines H and K, working together at their respective constant rates, harvested the remaining acres of wheat in 4 hours. Harvesting machine K harvested how many acres of wheat per hour?
A. 7
B. 8
C. 11
D. 13
Answer: C. 11
Explanation: Rate of H = 4 acres/hr
Remaining land to be harvested = 100 - 40 = 60
Rate of H and K = 60/4 = 15 acres/hr
Rate of K = 15- 4 = 11
Answer: C
Question: In the new budget the price of wheat rose by 8%. By how much percent must a person reduce his consumption so that his expenditure on it does not increase?
A.7.5%
B.7.41%
C.10.9%
D.12.6%
Answer: B.7.41%
Explanation: Reduce in consumption = R/(100+R) *100% = 8/108 *100 = 7.41%
Answer is B
Question: Of the books standing in a row on a shelf, an atlas is the 30th book from the left and the 33rd book from the right. If 2 books to the left of the atlas and 7 books to the right of the atlas are removed from the shelf, how many books will be left on the shelf?
A.53
B.57
C.58
D.61
Answer: A.53
Explanation: 100%. There are total of 30+33-1=62 books and 2+7=9 books are removed, thus 62-9=53 books are left.
Answer: A.
Question: Evaluate:55- 12*3*2 =?
A.42
B.47
C.62
D.72
Answer: B.47
Explanation: According to order of operations, 12?3?2 (division and multiplication) is done first from left to right
12**2 = 4* 2 = 8
Hence
55 - 12*3*2 = 55- 8 = 47
correct answer B
Question: If x/y=4 and y is not '0' what % of x is 2x-y
A.150%
B.175%
C.200%
D.250%
Answer: B.175%
Explanation: let z be the percentt
x*z/100=2x-y
zx=7y*100
z=700y/4y
z=350/2
z=175%
ANSWER:B
Question: If x/y=4 and y is not '0' what % of x is 2x-y
A.150%
B.175percent
C.200%
D.250%
Answer: B.175percent
Explanation: let z be the percent
x*z/100= 2x-y
zx=7y* 100
z=700y/4y
z=350/2
z=175%
ANSWER:B
Question: Find the middle one when The sum of three consecutive even numbers is 21?
A.7
B.10
C.8
D.6
Answer: A.7
Explanation: 3 consecutive numbers can be a - 1, a, a + 1
So sum of numbers = 3a = 21.
Hence a = 7.
A
Question: In a class, there are 21 boys who are over 160 cm tall. If these constitute three–fourth of the boys and the total number of boys is one–fourth of the total number of students in the class. What is the total number of girls in the class
A.22
B.78
C.267
D.997
Answer: A.22
Explanation: Answer:A
Question: A cricketer has a certain average for 10 innings. In the eleventh inning, he scored 108 runs, thereby increasing his average by 6 runs. His new average is
A.42 runs
B.45 runs
C.48 runs
D.52 runs
Answer: C.48 runs
Explanation: Sol.
Let the average for 10 innings be x. Then,
10x + 108 / 11 = x+6 ⇔ 11x + 66 = 10x + 108 ⇔ x = 42.
∴ New average = (x+6) = 48 runs.
Answer C
Question: A radio station has to choose three days of the seven in a week to broadcast a certain program, and that set will repeat each week. The program can be broadcast equally on any of the seven weekdays —- weekdays vs. weekends don’t matter at all —- nor does it matter whether the days the program airs are adjacent or not. Absolutely any three of the seven weekdays can be chosen. How many different three-day combinations of the seven weekdays can be constructed?
A.9
B.15
C.21
D.35
Answer: D.35
Explanation: Behind the story, we are really being asked to evaluate 7C3. We could use the factorial formula, but above we conveniently happen to have Pascal’s Triangle written out to the seventh row. We see that 7C3, the third entry of the seventh row, is 35. Answer = D.
Question: At coffee factory, each employee working the second shift produced 2/3 as many widgets as each employee working the first shift. If the first shift has 3/4 as many employees, what fraction of the total widgets did the second shift produce?
A.8/17
B.1/2
C.8/9
D.9/8
Answer: A.8/17
Explanation: At coffee factory, Let the first shift have 3 employee and each produce 3 widgets, so the total number of widgets produced by the first shift is 3*3=9;
Then the second shift would have 4 employees and each second shift employee would produce 3*2/3=2 widgets, so the total number of widgets produced by the second shift employees would be 4*2=8;
The ratio of the second shift production to the total is 8/(9+8)=8/17.
Answer: A.
Question: Foodmart customers regularly buy at least one of the following products: milk, chicken, or apples. 60% of shoppers buy milk, 50% buy chicken, and 55% buy apples. If 10% of the customers buy all 3 products, what percentage of Foodmart customers purchase exactly 2 of the products listed above?
A. 5%
B. 10%
C. 15%
D. 45%
Answer: D. 45%
Explanation: Total = n(A) + n(B) - n(Exactly 2 products) -2 (AnBnC) + Neither.
Neither is zero.
Hence 100 = 60 + 50 + 55 - n (Exactly 2 products) - 2*10
100 = 145 - n (Exactly 2 products) => n (Exactly 2 products) = 45.
Answer: D
Question: In a rectangular coordinate system, what is the area of a rectangle whose vertices have the coordinates (-9, 1), (1, 1), (1, -8) and (-9, -8)?
A.72
B.180
C.70
D.90
Answer: D.90
Explanation: Length of side 1= 9+1=10
Length of side 2= 8+1= 9
Area of rectangle= 10*9= 90
D is the answer
Question: What will come in place of the x in the following Number series? 73205, 6655, 605, 55, x
A.64535
B.73205
C.79345
D.85463
Answer: B.73205
Explanation: (B)
5 x 11 = 55, 55 x 11 = 605, 605 x 11 = 6655, 6655 x 11 = 73205
Question: 10% of the inhabitants of a village having died of cholera, a panic set in, during which 25% of the remaining inhabitants left the village. The population is then reduced to 4050. Find the number of original inhabitants?
A.4500
B.5000
C.3000
D.6000
Answer: D.6000
Explanation: Let the total number of original inhabitants be x
Then, (100-25)% of (100-10)% of x = 4050
75/100 * 90/100 * x = 4050
x = 6000
Answer is D
Question: A watch passes through three hands and each gains 25%. If the 3rd sells it for Rs250, what did the 1st pay for it?
A.110
B.120
C.128
D.143
Answer: C.128
Explanation: First Purchased = 250 Wes= 128
C
Question: On her annual road trip to visit her family in Seal Beach, California, Traci stopped to rest after she traveled 1⁄3 of the total distance and again after she traveled 1⁄4 of the distance remaining between her first stop and her destination. She then drove the remaining 300 miles and arrived safely at her destination. What was the total distance, in miles, from Traci’s starting point to Seal Beach?
A. 600
B. 300
C. 350
D. 400
Answer: A. 600
Explanation: Let D = total distance
Traci traveled 1/3 = D/3
i.e. remaining distance = 2D/3
She traveled 1/4 th of 2D/3 = D/6
Thus:
D = (D/3) + (D/6) + 300
D = 600
ANSWER: A
Question: Nancy works 3 days per week at a rate of x dollars per day. If Nancy works more than 3 days per week, any extra days are paid at double her normal rate. Nancy worked 4 weeks with no overtime, and then worked 4 more weeks, each with y days of overtime. Which of the following represents Nancy’s total earnings over this period?
A.a) 3y(7x+2xy)
B.b) 3x+12y
C.c) 3xy(7x+2)
D.d) 8x(y+3)
Answer: D.d) 8x(y+3)
Explanation: Payment of a week for 3 days a week = $3x
Payment of 4 weeks for 3 days a week = $3x*4 = $12x
Payment of a week for y days overtime a week = $3x+$2xy
Payment of 4 weeks for y days overtime a week = ($3x+$2xy)*4
Total Earnings = $12x + ($3x+$2xy)*4 = 24x+8xy =8x(y+3)
Answer: option D
Question: The average of 5 consecutive odd numbers is 61. What is the difference between the highest and lowest numbers?
A.8
B.10
C.12
D.15
Answer: A.8
Explanation: Let the numbers be x, x+2, x+4, x+6, x+8
Then, (x+ x+2+ x+4+ x+6+ x+8)/5 = 61
x = 57
Required answer is = 57+8-57 = 8
Answer is A
Question: Arrange the following in a meaningful sequence :
1. Letter
2. Sentence
3. Word
4. Phrase
A.1, 2, 4, 3
B.2, 1, 3, 4
C.2, 4, 1, 3
D.1, 3, 4, 2
Answer: D.1, 3, 4, 2
Explanation: Explanation:
A group of letters makes a word. A group of words makes a phrase. A group of phrases makes a sentence.
Thus, correct order is 1, 3, 4, 2.
ANSWER D
Question: Brittany's income is 12 percent more than Tina's income, and Tina's income is 15 percent less than Jean's income. What percent of Jean's income is Brittany's income?
A.95.2%
B.91.2%
C.96.2%
D.94.2%
Answer: A.95.2%
Explanation: Jean's income = 100 (assume);
Tina's income = 85 (15 percent less than Jean's income);
Brittany's income = 95.2 (12 percent more than Tina's income).
Thus, Brittany's income (95.2) is 95.2% of Jean's income (100).
Answer: A
Question: Find the probability that the sum of dots appearing in two successive throws of two dice is every time 7
A.1/6
B.2/6
C.3/6
D.4/6
Answer: A.1/6
Explanation: No of sample space are n(s)=(6*6)=36
no of even aren n(E)={(1,6),(2,5),(3,4),(4,3),(5,2),(6,1)}=6
then Probability=n(e)/n(s)=6/36 =1/6
Ans is 1/6.
ANSWER:A
Question: P is a set containing 8 different positive odd numbers. Q is a set containing 7 different numbers, all of which are members of P. Which of the following statements CANNOT be true?
A.The range of Q is even.
B.The mean of P is even.
C.The mean of Q is even.
D.The range of P is equal to the range of Q.
Answer: C.The mean of Q is even.
Explanation: Given: P is a set containing 8 different positive odd numbers
Easily inferred: Q is a set containing 7 differentoddnumbers
(A) The range of Q is even. - Always even, since it is a difference of two odd numbers
(B) The mean of P is even. - can be. suppose 8 numbers consist of 4 pairs of (16n-1,16n+1) for different values of n. Adding these will give a multiple of 16, which when divided by 8 (to arrive at mean), will give an even number
(C) The mean of Q is even. - Cannot be. Mean = (sum of 7 odd numbers)/7 = Odd number/odd number thus cannot be even.
(D) The range of P is equal to the range of Q.
(E) The median of Q is equal to the mean of Q
Option C.
Question: Two trains 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 train to cross the faster train in seconds is?
A.54
B.62
C.48
D.62
Answer: C.48
Explanation: Relative speed = 60 + 90 = 150 km/hr.
= 150 * 5/18 = 125/3 m/sec.
Distance covered = 1.10 + 0.9 = 2 km = 2000 m.
Required time = 2000 * 3/125 = 48 sec.
Answer:C
Question: In five football games thus far this season, Barry has run for 98, 107, 85, 89, and 91 yards. At a minimum, how many yards F will he need to gain this Sunday if he wants to keep his season average above 100 yards?
A.101
B.116
C.130
D.F=131
Answer: D.F=131
Explanation: Sorry the answer F=131 is D.
Question: What percent of a day in 6 hours?
A.10%
B.15%
C.20%
D.25%
Answer: D.25%
Explanation: Required percentage = 6/24 * 100 = 100/4 = 25%
Answer is D
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 5 a.m.?
A.23 Minutes
B.24 Minutes
C.25 Minutes
D.27 Minutes
Answer: D.27 Minutes
Explanation: 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 =13*2=26 total=27
ANSWER:D
Question: The price of a T.V. set worth Rs. 10000 is to be paid in 20 installments of Rs. 1000 each. If the rate of interest be 6% per annum, and the first installment be paid at the time of purchase, then the value of the last installment covering the interest as well will be?
A.9000
B.26699
C.96000
D.19000
Answer: A.9000
Explanation: Money paid in cash = Rs. 1000
Balance payment = (10000 - 1000) = Rs. 9000
Answer: A
Question: If n is the product of three consecutive integers, and n is divisible by 11, which of the following is not necessarily a divisor of n ?
A.990
B.1210
C.1716
D.0
Answer: D.0
Explanation: IF ONE NO. IS 11 THEN OTHER CONSEQUTIVE NO. ARE 9*10*11=990 ,10*11*12 =1210 , 11*12*13 =1716
N IS NOT DIVISOR ANY ABOVE NO =0
D
Question: The cost price of 5 oranges equal to the selling price of 8 oranges. Calculate the % profit or loss.
A.38.5%
B.37.5%
C.73.5%
D.32.5%
Answer: B.37.5%
Explanation: Let the cost price of 1 orange is Rs 1
Cost of 8 orange = Rs 8
Selling price of 8 orange = 5
Gain/loss = 8 - 5 = 3
%=3/8âˆ—100= 37.5
Answer: B
Question: In a certain game, you perform three tasks. You flip a quarter, and success would be heads. You roll a single die, and success would be a three. You pick a card from a full playing-card deck, and success would be picking a ace with heart card.
If exactly one of these three tasks is successful, then you win the game. What is the probability of winning?
A.61/312
B.13/624
C.325/624
D.181/312
Answer: D.181/312
Explanation: Event(1): Probability of getting head in a flip of coin = 1/2
Event(2): Probability of getting three in a roll of dice = 1/6
Event(3): Probability of getting ace with heart in a pack of card = 1/52
Probability of winning is having exactly one successful event is:
P(success 1)* P(Fail 2)* P(Fail 3) + P(Fail 1)* P(Success 2)* P(Fail 3) + P(Fail 1)* P(Fail 2)* P(Success 3)
= 1/2*5/6*51/52 +1/2*1/6*51/52 +1/2*5/6*1/52
=255/624 + 102/624 +5/624
=362/624
= 181/312
Answer :D
Question: In a certain game, you pick a card from a standard deck of 52 cards. If the card is a clever, you win. If the card is not a clever, the person replaces the card to the deck, reshuffles, and draws again. The person keeps repeating that process until he picks a clever, and the point is to measure how many draws did it take before the person picked a clever and won. What is the probability that there will be at least four draws involved in a win, i.e. someone picking her clever on the fourth draw or later?
A. 1/2
B.27/64
C. 11/16
D. 13/16
Answer: B.27/64
Explanation: Probability of picking a clever on any draw = 1/4
Probability of NOT picking a heart on the first draw AND on the second draw And 3rd draw = [1-(1/4)] X [1-(1/4)] X [1-(1/4)]= 3/4 X 3/4 X 3/4 = 27/64
Answer : B
Question: Kareem is three times as old as his son. After ten years, the sum of their ages will be 76 years. Find their present ages.
A.13
B.14
C.15
D.16
Answer: B.14
Explanation: Sol. Let the present age of Kareem’s son be x years.
Then, Kareem’s age = 3x years
After 10 years, Kareem’s age = 3x + 10 years
and Kareem’s son’s age = x + 10 years
∴ (3x + 10) + (x + 10) = 76
=> 4x = 56 => x = 14
∴ Kareem’s present age = 3x = 3 × 14 = 42 years
Kareem’s son’s age = x = 14 years.
Answer B
Question: Anand starts from a point P towards point Q, where PQ = 70 km. After 1 hour, Ram starts from P and catches up with Anand after 2 more hours. After meeting they continue to travel towards Q. On reaching Q, Ram reverses his direction and meets Anand 6 hours after the first meeting. Find Anand's speed.
A.(45/7) kmph
B.(60/7) kmph
C.(40/7) kmph
D.(20/3) kmph
Answer: D.(20/3) kmph
Explanation: Let the first meeting point be at a distance of x km from P, the remaining distance until Q would be (70-x) km
Anand traveled this x kms in 3 hours, making his speed x/3 kmph
Ram traveled the same x kms in 2 hours, making his speed x/2 kmph
So, in 6 hours:
Anand will cover=6x/3=2x km
Ram will cover=6x/2=3x km
And between their first meeting point and second, they both together covered a distance of 2(90-x) km.
2x+3x=2(70-x)
5x=140-2x
7x=140
x=140/7 km
Anand's speed=x/3=140/(3*7)=20/3 kmph
Ans:D
Question: A particular parking garage is increasing its rates by 40 percent per month. Bob decides to reduce the number of days he uses the garage per month so that the amount he spends at the garage per month remains unchanged. Which of the following is closest to Bob’s percentage reduction in the number of days he uses the garage each month?
A.20%
B.25%
C.29%
D.33%
Answer: C.29%
Explanation: Let x be the original number of days that Bob used the garage.
Let P be the original cost per day.
Let N*x be the new number of days that Bob uses the garage.
N*x*1.4P = x*P
N*x = x/1.4 which is about 0.71x, thus a 29% reduction.
The answer is C.
Question: Danny and Steve are running towards each other, each one from his own house. Danny can reach Steve's house in 29 minutes of running, which is half the time it takes Steve to reach Danny's house. If the two started to run at the same time, how much time longer will it take Steve to reach the halfway point between their houses than Danny to reach the halfway point between their houses?
A.14.5 minutes
B.29 minutes
C.35 minutes
D.58 minutes
Answer: A.14.5 minutes
Explanation: Danny's time is 29 minutes. The time to reach halfway is 14.5 minutes.
Steve's time is 58 minutes. The time to reach halfway is 29 minutes.
The time difference is 29 - 14.5 = 14.5 minutes
The answer is A.
Question: In how many ways can the letters D, I, T , K , T be arranged so that the two I's are not next to each other?
A.36
B.48
C.72
D.96
Answer: A.36
Explanation: 1 D
1 I
1 G
2 T
Number of ways these letters can be arranged = 5!/2! (2! to account 2 same Is) = 60
Consider 2 Is as 1 entity and thus the number of arrangements for (TT)DGI = 4! = 24
Total allowed cases = 60-24 =36
A is the correct answer.
Question: The bankers gain of a certain sum due 2 years hence at 10% per annum is Rs 24 .The percent worth is
A.387
B.238
C.278
D.600
Answer: D.600
Explanation: Explanation:
T.D = (B.G * 100) / (Rate * Time)
(24*100) / (10 * 2)
= 120.
P.W = (100 *T.D) / (Rate * Time)
= (100 * 120) /(10 * 2)
= 600
Answer: D) 600
Question: The area of a square field 3136 sq m, if the length of cost of drawing barbed wire 3 m around the field at the rate of Rs.1.50 per meter. Two gates of 1 m width each are to be left for entrance. What is the total cost?
A.736
B.988
C.999
D.729
Answer: C.999
Explanation: Explanation:
a2 = 3136 => a = 56
56 * 4 * 3 = 672 – 6 = 666 * 1.5 = 999
Answer: Option C
Question: The length of a rectangle is twice its breadth. If its length is decreased by 5 cm and breadth is increased by 5 cm, the area of the rectangle is increased by 75 sq. cm. Find the length of the rectangle.
A.10 cm
B.15 cm
C.20 cm
D.18 cm
Answer: C.20 cm
Explanation: Explanation:
Let breadth = x. Then, length = 2x. Then,
(2x - 5) (x + 5) - 2x * x = 75 => 5x - 25 = 75 => x = 20.
Length of the rectangle = 20 cm.
Answer: Option C
Question: The length of a train and that of a platform are equal. If with a speed of 90 k/hr, the train crosses the platform in one minute, then the length of the train (in meters) is?
A.729
B.720
C.718
D.750
Answer: D.750
Explanation: Speed = [90 * 5/18] m/sec = 25 m/sec; Time = 1 min. = 60 sec.
Let the length of the train and that of the platform be x meters.
Then, 2x/60 = 25 è x = 25 * 60 / 2
=750
Answer:D
Question: A man bought 40 shares of Rs. 60 at 5 discount, the rate of dividend being 12%The rate of interest obtained is
A.13.09%
B.15.5%
C.14%
D.14.25%
Answer: A.13.09%
Explanation: Explanation :
Face Value of a share = Rs.60
He bought each share at Rs.60 - Rs.5 = Rs.55
Number of shares = 40
Dividend = 12 %
Dividend per share = 60×12×100=Rs.7 1/5
Total dividend = (40 × 7 1/5)
ie, He got a dividend of (40 × 7 1/5) for an investment of Rs.(40 × 55)
Interest obtained = 40×7 1/5×100/40×55=13.09%
Answer : Option A
Question: Which of the following is equal to the average (arithmetic mean) of (x+1)^2 and (x-1)^2?
A.x^2
B.x^2+1
C.x^2 +4
D.x^2+2x
Answer: B.x^2+1
Explanation: Avg = [(x+1)^2 + (x-1)^2] / 2
Expanding and simplifying, (x^2 + 2x + 1 + x^2 -2x + 1 ) / 2 = x^2 + 1
Answer B.
Question: The ratio of the present ages of Giri and Hari is 5 : 8. 12 years hence, the ratio of their ages will be 11 : 14. Find the difference in their present ages?
A.5 years
B.6 years
C.3 years
D.9 years
Answer: B.6 years
Explanation: Let the present ages of Giri and Hari be 5x and 8x years respectively.
(5x + 12) / (8x + 12) = 11/14
70x + 168 = 88x + 132 => x= 2
Difference in their ages will be the same at all times.
This difference = Difference of their present ages
= 8x - 5x = 3x = 6 years.
Answer:B
Question: Three candidates contested an election and received 3644 votes, 7636 votes, and 12720 votes respectively. What percentage of the total votes did the winning candidate receive?
A.53%
B.55%
C.57%
D.59%
Answer: A.53%
Explanation: The total number of votes polled = (3644 + 7636 + 12720) = 24000
The winner's percentage = 12720/24000 * 100 = 53%
The answer is A.
Question: What will be the fraction of 10%
A.1/4
B.1/5
C.1/10
D.1/8
Answer: C.1/10
Explanation: Explanation:
It will 10*1/100 = 1/10
Answer: Option C
Question: The length of a rectangle is increased by 40% while its width is halved. What is the % change in area?
A.25%
B.30%
C.50%
D.65%
Answer: B.30%
Explanation: The original area is L*W
The new area is 1.4L*0.5W = 0.7*L*W = L*W - 0.3*L*W
The area decreased by 30%.
The answer is B.
Question: 3x^2 + 10x - 8 =
A.(3x-4)(x-1)
B.(3x-4)(x+2)
C.(3x-4)(x-2)
D.(3x-2)(x+4)
Answer: D.(3x-2)(x+4)
Explanation: 3x^2 - 10x - 8
= 3x^2 + 12x - 2x - 8
= 3x (x + 4) - 2 (x+4)
= (3x-2) (x+4)
Option D
Question: Let x < 0, 0 < y < 1, z > 1. Which of the following may be false?
A.(x^2– z^2) has to be positive.
B.yz can be less than one.
C.xy can never be zero.
D.(y^2– z^2) is always negative.
Answer: A.(x^2– z^2) has to be positive.
Explanation: Explanation :
Let's take any random value satisfying the given condition i.e x < 0, 0 < y < 1, z > 1.
Take x = -1, and z = 2
x2 - z2 -> (-1)2 - (2)2 = -3 .
Take y= 0.1,
then , yz -> (1/10)*2 = 1 /5 i.e less than 1.
According to the given condition, x and y both are non zero, so there product can't be zero.
Since, value of z will always be greater than 2 and y will always be less than 1, So, y2 - z2 will always result into a negative value.
Hence, only first option is false.
Answer : A