RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: If n is a positive integer and n^2 is divisible by 72, then the largest positive integer T that must divide n is?
A.6
B.12
C.24
D.36
Answer: B.12
Explanation: Q: If n is a positive integer and n^2 is divisible by 72, then the largest positive integer T that must divide n is:
A 6, B 12, C 24, D 36, E 48
n^2 is divisible by 72, but it must also be greater than 72. If n is an integer, then n^2 must be a perfect square. The factorization of 72 is (8)(9), so if it is multiplied by 2, it will be (2)(8)(9) = (16)(9) = 144, a perfect square. So n^2 must be at least 144 or a multiple of 144, which means that n must be 12 or a multiple of 12.B
Question: A man leaves a point P at 6 a.m. and reaches the point Q at 10 a.m. another man leaves the point give at 8 a.m. and reaches the point P at 12 noon. At what time do they meet?
A.2 a.m
B.6 a.m
C.9 a.m
D.5 a.m
Answer: C.9 a.m
Explanation: 9 a.m.
Answer:C
Question: Mr. Hernandez, who was a resident of State X for only 10 months last year, had a taxable income of $22,500 for the year. If the state tax rate were 4 percent of the year’s taxable income prorated for the proportion of the year during which the taxpayer was a resident, what would be the amount of Mr. Hernandez’s State X tax for last year?
A. $900
B. $750
C. $600
D. $300
Answer: B. $750
Explanation: Total tax for the year = 22,500 x 4% = 900
As stated Annual tax is prorated as per the duration of stay.
Prorated Tax = 900 (10/12) = 750
Answer B
Question: Nicole cycles at a constant rate of 18 kilometers per hour, and is passed by Jessica, who cycles at a constant rate of 30 kilometers per hour. If Jessica cycles at her constant rate for x minutes after passing Nicole, then stops to wait for her, how many minutes will Jessica have to wait for Nicole to catch up to her?
A.x/3
B.2x/3
C.x
D.3x/2
Answer: B.2x/3
Explanation: In x minutes, Jessica travels (x/60)*30 = x/2 miles
The time it takes Nicole to travel x/2 miles is (x/2) / 18 = x/36 hours = 5x/3 minutes
Jessica needs to wait 5x/3 - x = 2x/3 minutes.
The answer is B.
Question: For the past n days, the average (arithmetic mean) daily production at a company was 50 units. If today's production of 115 units raises the average to 55 units per day, what is the value of n?
A.8
B.10
C.12
D.14
Answer: C.12
Explanation: The daily production was raised by 5 units for n days, which has a weighting of 5n.
5n = 115-55 = 60
n = 12
The answer is C.
Question: A certain company expects quarterly earnings of $0.80 per share of stock, half of which will be distributed as dividends to shareholders while the rest will be used for research and development. If earnings are greater than expected , shareholders will receive an additional $0.04 per share for each additional $0.10 of per share earnings. If quarterly earnings are $1.10 per share, what will be the dividend paid to a person who owns 100 shares of the company's stock?
A.$92
B.$96
C.$52
D.$120
Answer: C.$52
Explanation: EPS Actual> EPS expected.
each gets and additional .12 per share.
Thus .52*100 --> $52
answer is C
Question: How many integers from 0 to 48, inclusive, have a remainder of 1 when divided by 3 ?
A.15
B.16
C.17
D.18
Answer: B.16
Explanation: My ans is also C.17.
Explanation:
1 also gives 1 remainder when divided by 3, another number is 4, then 7 and so on.
Hence we have an arithmetic progression: 1, 4, 7, 10,..... 46, which are in the form 3n+1.
Now we have to find out number of terms.
tn=a+(n-1)d, where tn is the nth term of an AP, a is the first term and d is the common difference.
so, 46 = 1+(n-1)3
or, (n-1)3 = 45
or, n-1 = 15
or, n = 16
B
Question: If x^2 + 1/x^2 = 9, what is the value of x^4 + 1/x^4 ?
A.10
B.72
C.79
D.16
Answer: C.79
Explanation: IMPORTANT: I notice that if we SQUARE x², we get x⁴, and if we SQUARE 1/x², we get 1/x⁴, so let's see what happens if we take the equation x² + 1/x² = 9 andSQUAREboth sides:
(x² + 1/x²)²= 81
So, (x² + 1/x²)(x² + 1/x²) = 81
Expand to get: x⁴ + 1 + 1 + 1/x⁴ = 81
Simplify: x⁴ + 1/x⁴ = 79
Answer: C
Question: Which of the following must be subtracted from 2^96 so that the resulting integer will be a multiple of 3?
A.2
B.5
C.3
D.1
Answer: D.1
Explanation: {4^1} / 3 =4/3 remainder 1
{4^2} / 3 = 16/3 remainder 1
{4^3} / 3 = 64/3 remainder 1
{4^4} / 3 = 256/3 remainder 1
Actually the same remainder keeps repeating .....
Try with a diff no, say 2
{2^1}/3 = remainder 2
{2^2}/3 = remainder 1
{2^3}/3 = remainder 2
{2^4}/3 = remainder 1
Answer : D
Question: list of salaries of 8 employees are listed below. What is the median salary?
$40,000, $29,000, $35,500, $31,000, $43,000, $30,000, $27,000, $34,000
A.$28,000
B.$28,500
C.$32,500
D.$30,800
Answer: C.$32,500
Explanation: Ordering the data from least to greatest, we get:
$27,000, $29,000, $30,000, $31,000, $34,000, $35,500, $40,000, $43,000
Since there is an even number of items in the data set, we compute the median by taking the mean of the two middlemost numbers.
$31,000 + $34,000 = $65,000
The median salary is $32,500.
Answer : C
Question: A man saves a certain portion of his income during a year and spends the remaining portion on his personal expenses. Next year his income increases by 30% but his savings increase by 100%. If his total expenditure in 2 years is double his expenditure in 1st year, What %age of his income in the first year did he save?
A.21%
B.22.5%
C.25%
D.30%
Answer: D.30%
Explanation: 1st year Income= I
1st year savings= S
1st year Expense= E1
2nd year Income = 1.3I
2nd year savings= 2S (100% increase)
2nd Year expense= E2
E1+ E2= 2E1
E2=E1
That means Expenses are same during both years. With increase of 30% income the savings increased by 100%.
or S= .3I
or S= 30% of Income
D is the answer
Question: A bag contains 6 white and 4 black balls .2 balls are drawn at random. Find the probability that they are of same color?
A.7/15
B.7/17
C.8
D.8/15
Answer: A.7/15
Explanation: Let S be the sample space
Then n(S) = no of ways of drawing 2 balls out of (6+4) = \inline {\color{Black}10C_{2}} = =45
Let E = event of getting both balls of same colour
Then,n(E) = no of ways (2 balls out of six) or (2 balls out of 4)
=\inline {\color{Black}6C_{2}+4C_{2}} = = 15+6 = 21
Therefore, P(E) = n(E)/n(S) = 21/45 = 7/15
A)
Question: The average of seven numbers is 22. The average of first three numbers is 14 and the average of last three numbers is 19. What is the middle number?
A.27
B.55
C.31
D.34
Answer: B.55
Explanation: The total of seven numbers = 7X22 = 154
The total of first 3 and last 3 numbers is = 3 X 14+3 X 19 = 99
So, the middle number is (154 - 99 ) = 55
B
Question: Tough and Tricky questions: Absolute Values.
If |a| = 1/3 and |b| = 1/2, which of the following CANNOT be the result of a + b?
A.-5/6
B.-1/6
C.1/6
D.2/3
Answer: D.2/3
Explanation: |a| = 1/3
Absolute value of 'a' can have two values = 1/3 and -(1/3)
|b| = 1/2
Absolute value of 'b' can have two values = 1/2 and -(1/2)
Now different combinations of a + b are as follows:
a + b = (1/3) + (1/2) = 5/6
- a - b = -(1/3) - (1/2) = -5/6
a - b = (1/3) - (1/2) = -(1/6)
-a + b = -(1/3) + (1/2) = 1/6
Cross verifying with the given options, left over option is D.
Question: A boat goes 100 km downstream in 10 hours, and 200 Km upstream in 25 hours. The speed of the stream is?
A.1
B.22 1/7
C.2
D.22 1/2
Answer: A.1
Explanation: 100 --- 10 DS = 10
? ---- 1
200 ---- 30 US = 8
? ----- 1 S = (10 - 8)/2
= 1 kmph.
Answer:A
Question: The highest score in an inning was 3/11 of the total and the next highest was 3/11 of the reminder . If the score differ by 9, the total score was :
A.110
B.121
C.132
D.143
Answer: B.121
Explanation: Explanation:
Let the score be x. Then the highest score = 3x/11.
Reminder = (x - 3x/11) = 8x/11 .Next the highest score = 3/11 of 8x/11 = 24x/121.
3x/11 - 24x/11 = 9 <=> 33x - 24x = 9 × 121 <=> x = 121..
Answer: B
Question: Avg cost of 6 pencils and 8 pens is Rs. 70.The avg cost of 8 pencils and 10 pens is Rs.90. Find the total cost of 25 pencils and 25 pens?
A.100
B.125
C.130
D.80
Answer: B.125
Explanation: Avg cost of 6 pencils and 8 pens is Rs. 70
(6 pencil + 8 pens) 14=70
therefore 1 pencil cost is 70/14=5, so 6 pencil cost is 6x5=30 and 8 pens cost is 8x5=40
Again, avg cost of 8 pencils and 10 pens is Rs.90
(8 pencil + 10 pens) 18=90
therefore 1 pencil cost is 90/18=5, so 8 pencil cost is 8x5=40 and 10 pens cost is 10x5=50
So 25 pencil cost is (25/a)=125 and 25 pens cost is (25x5)=125
ANSWER:B
Question: In a certain store, the profit is 320% of the cost. If the cost increases by 25% but the selling price remains constant, approximately what percentage of the selling price is the profit?
A.30%
B.70%
C.100%
D.250%
Answer: B.70%
Explanation: Let C.P. = Rs. 100. Then, profit = Rs. 320, S.P. = Rs. 420
New C.P. = 125% of Rs. 100 = Rs. 125.
New S.P. = Rs. 420
Profit = 420 - 125 = Rs. 295
Required percentage = 295/420 * 100 = 1475/21 = 70%
ANSWER:B
Question: On the Richter scale, which measures the total amount of energy released during an earthquake, a reading of x-1 indicates one-tenth the released energy as is indicated by a reading of x. On that scale, the frequency corresponding to a reading of 7 is how many times as great as the frequency corresponding to a reading of 5?
A.10^2
B.10^3
C.10^4
D.10^5
Answer: A.10^2
Explanation: If Richter scale reading goes from X-1 to X it will be 10
if Richter scale reading goes from 5 to 6 it will be 10
Similarly if Richter scale reading goes from 6 to 7 it will be 10
so it will from 5 to 7 i.e 6,7 = 10*10 = 10^2
Answer is A
Question: In a group of 100 people,50 like reading books,20 like both reading books and listening songs. How many like listening songs?
A.40
B.50
C.70
D.60
Answer: C.70
Explanation: Make a Venn diagram, and enter your data.
Let the number of people who like Listening Songs be x
x + 20 + 30 = 100
x = 50
so number who like Listening Songs = 20+50 = 70
Answer C
Question: There are 6 baskets numbered from 1 to 6 and filled with apples . 10 children are asked to pick apples one by one from each basket such that the number of apples picked by each child from each basket is equal to the number marked on the basket. If there were 1000 apples in total and the baskets were filled in such a way that none of the basket became empty in the process, how many apples were left in the end?
A.90
B.91
C.210
D.790
Answer: D.790
Explanation: Total number of apples in the basket initially = 1000
Each child picks up = 1+2+3+4+5+6 = 6*7/2 = 21
Total number of apples picked up by 10 children = 21*10 = 210
Number of apples left in the end = 1000-210 =790
Answer is D
Question: A man whose bowling average is 12.4, takes 3 wickets for 26 runs and there by decreases his average by 0.4. the number of wickets taken by him before his last match is?
A.23
B.24
C.25
D.26
Answer: C.25
Explanation: 12.4*x+26=(3+x)12
solve equation x=25
ANSWER:C
Question: Vishal invested 10% more than Trishul. Trishul invested 10% less than Raghu. If the total sum of their investments is Rs. 6358, how much amount did Raghu invest ?
A.1287
B.2200
C.2000
D.1129
Answer: B.2200
Explanation: Let money invested by Raghu = Rs. x
Money invested by Trishul = 9/10 x = 0.9x
Money invested by Vishal = 9/10x * 110/100 = 0.99x
Also, x+0.9x+0.99x = 6358
= x= 6358/2.89 = 2200
Therefore, amount invested by Raghu is Rs. 2200.
Answer: B
Question: For any integer p, *p is equal to the product of all the integers between 1 and p, inclusive. How many prime numbers are there between *7 + 3 and *7 + 7, inclusive?
A.None
B.One
C.Two
D.Three
Answer: A.None
Explanation: 7! = 720 * 7 = 5040
# in question = 5043, 5044, 5045, 5046, 5047
none of these are prime
Answer - A
Question: What is the ratio of 6/7 to the product 3*(7/3)?
A.3:7
B.1:3
C.3:21
D.6:49
Answer: D.6:49
Explanation: 6/7 / 21/3 = 6/49...
IMO option D.
Question: Mars travels around the Sun at an approximate speed of 14.4 miles per second. This speed is how many kilometers per hour? (1 km = 0.6 miles)
A.64,200
B.75,300
C.86,400
D.97,500
Answer: C.86,400
Explanation: The speed is 14.4 miles/s. Then 14.4/0.6 = 24 km/s
24*3600 = 86,400 kph
The answer is C.
Question: If -1 < h < 2, which of the following has the greatest value?
A.a) 1-h
B.b) 1+h
C.c) 1+h^2
D.d) 1-1/h
Answer: C.c) 1+h^2
Explanation: easiest way of solving this would be to substitute a value.
lets say h= - 1/2
a) 3/2
b) 1/2
c) 5/4
d) 3
e) - 3
the value you chose is wrong . h cannot be 0.9 as -1<h<0. if you chose -0.9 answer will still be D.
Answer is C.
Question: x =2.5 3.5 1.5
y= 25 49 9 then what is the relation between x and y
A.Y=(2*X)^2
B.Y=(2*X)^3
C.Y=(2*X)^4
D.Y=(3*X)^2
Answer: A.Y=(2*X)^2
Explanation: Y=(2*X)^2
25=(2*2.5)^2
ANSWER:A
Question: A certain manufacturer of cake, muffin, and bread mixes has 100 buyers, of whom 50 purchases cake mix, 40 purchase muffin mix, and 17 purchase both cake mix and muffin mix. If a buyer is to be selected at random from the 100 buyers, what is the probability that the buyer selected will be one who purchases neither cake mix nor muffin mix?
A.1/10
B.3/10
C.1/2
D.27/100
Answer: D.27/100
Explanation: C+M+B-CM-MB-CB-2CMB = 100
C - cake buyers, M - muffin and B - Bread buyers. CM,MB,CB and CMB are intersecting regions.
the question asks for people who have bought only bread mixes = B-CB-MB-2CMB has to be found out.
50 + 40 + B-CB-MB-17-2CMB = 100
B-CB-MB-2CMB = 27
hence the probability = 27/100
D
Question: How many paying stones, each measuring 2 1/2 m * 2 m are required to pave a rectangular court yard 30 m long and 16 1/2 m board?
A.99
B.18
C.16
D.10
Answer: A.99
Explanation: 30 * 33/2 = 5/2 * 2 * x => x
= 99
Answer:A
Question: A toy store sells small, medium, large, and super-large toy trucks in each of the colors red, blue, black, green, orange, and yellow. The store has an equal number of trucks of each possible color-size combination. If Paul wants a medium, red truck and his mother will randomly select one the trucks in the store, what is the probability that the truck she selects will have at least one of the two features Paul wants?
A.1/3
B.2/5
C.3/5
D.3/8
Answer: D.3/8
Explanation: Probability of NOT selecting medium out of 4 sizes = 3/4
Probability of NOT selecting red out of 6 colours = 5/6
Total probability of NOT selecting red and medium = (3/4)*(5/6) = 5/8
Required probability = 1 - 5/8 (this will select at least one of red and medium)
= 3/8
The answer is D.
Question: In honor of the year 2012, a donor has purchased 2016 books to be distributed evenly among the elementary schools in a certain school district. If each school must receive the same number of books, and there are to be no books remaining, which of the following is NOT a number of books that each school could receive?
A.18
B.36
C.42
D.51
Answer: D.51
Explanation: All options other than 'D' are factors of 2012. Hence, 'D' is the answer
Question: Find the number of square tiles to cover the floor of a room measuring 3.5 m * 9 m leaving 0.25 m space around the room. A side of square tile is given to be 25 cms?
A.408
B.476
C.472
D.471
Answer: A.408
Explanation: 3 * 8 1/2 = 1/4 * 1/4 * x => x
= 408
Answer:A
Question: A man covered a certain distance at some speed. Had he moved 3 kmph faster, he would have taken 40 minutes less. If he had moved 2 kmph slower, he would have taken 40 minutes more. The distance (in km) is
A.27
B.87
C.40
D.18
Answer: C.40
Explanation: Explanation:
Let distance = x km and usual rate = y kmph.
Then, x/y - x/(y+3) = 40/60 --> 2y (y+3) = 9x ----- (i)
Also, x/(y-2) - x/y = 40/60 --> y(y-2) = 3x -------- (ii)
On dividing (i) by (ii), we get:
x = 40 km.
Answer: C
Question: The function F(n) is defined as the product of all the consecutive positive integers between 3 and n^2, inclusive, whereas the function G(n) is defined as the product of the squares of all the consecutive positive integers between 1 and n, inclusive. The exponent on 2 in the prime factorization of F(3)/G(3) is
A.	1
B.	2
C.	3
D.	4
Answer: C.	3
Explanation: F(3)/G(3)
=product(1 to 3 ^2) / 1.2^2.3^2
=1.2.3.4.5.6.7.8.9/1.4.9
=1.2.3.(2^2).5.(2.3).7.(2^3).9/1.(2^2).9
=1.(2^7).3.5.7.9/1.(2^2).9
Loof for 2^7/2^2=2^5 ----Exponent 3
Answer: C
Question: The average of 7 consecutive numbers is 20. The largest of these numbers is
A.12
B.27
C.23
D.28
Answer: C.23
Explanation: Let the numbers be x, x + 1, x + 2, x + 3, x + 4, x + 5 and x + 6,
Then (x + (x + 1) + (x + 2) + (x + 3) + (x + 4) + (x + 5) + (x + 6)) / 7 = 20.
or 7x + 21 = 140 or 7x = 119 or x =17.
Latest number = x + 6 = 23.
Answer: C
Question: On the xy co-ordinate plane, point C is (5,-1) and point D is (-1,2.5). The point on line segment CD that is twice as far from C as from D is:
A.(1,-1)
B.(1,1)
C.(2,0.25)
D.(3,0.5)
Answer: C.(2,0.25)
Explanation: We want the point on the line that is twice as far from C as it is from D. We can examine the x and y coordinates separately since they are independent.
*It should be noted that there are two solutions to this problem, one point between C and D, and another point with D in the middle of C and the point. We can quickly look at the answer choices and see that all the points are between C and D, therefore we can search for that point using the following method:
Taking the x-coordinate first, the distance between C and D is |(x-coordinate of C) - (x-coordinate of D)|= |5 - (-1)| = 6
The x-coordinate that is twice as far from C as it is from D (and in between C and D) will be 4 units from C and 2 units from D. So the x coordinate of the point we're looking for is 5-4 = 1, or (-1)+2 = 1.
Now looking at the y-coordinate, we do the same thing. The distance between C and D is |(-2) - 2.5| = 4.5
The y-coordinate that is twice as far from C as it is from D (and in between C and D) will be 3 units from C and 1.5 units from D. So the y coordinate of the point we're looking for is (-2)+3 = 1, or 2.5-1.5 = 1.
So now we have our coordinates of the point on the line that is twice as far from C as it is from D: (2,0.25)
Answer: C
Question: A ladies hostel had provision of food for 120 women for 35 days. After 10 days, 25 women left the hostel. The number of days for which the remaining food will last is:
A.39.47
B.39
C.39.23
D.39.74
Answer: A.39.47
Explanation: Explanation :
After 10 days : 120 women had food for 25 days.
Suppose 95 women had food for x days.
Now, Less women, More days (Indirect Proportion)
95 : 150 :: 25 : x
=> 95 x x = 150 x 25
=> x = 150 x 25 / 95
=> x = 39.47
Answer : A
Question: With out any halt a train travels a certain distance with an average speed of 75 km ph , and with halts it covers the same distance at an average speed of 60 kmph. When it is traveling with halts, how many
minutes/per hour does the train halt on an average ?
A.48 min
B.12min.
C.15min.
D.18min.
Answer: B.12min.
Explanation: With halt in 1 hour the train travels 60km
With out halt for traveling same distance it take 60/75 = 4/5 = 48 minutes
:. 12 minutes is the halting time per hour
Answer: B
Question: How many two-element subsets of {1,2,3,4} are there that do not contain the pair of elements 2 and 4?
A.One
B.Two
C.Four
D.Five
Answer: D.Five
Explanation: {1,2}, {1,3}, {1,4}, {2,3}, {3,4}.
Or: C24−1=5
Answer: D.
Question: 8 man's increases average weight by 2.5 kg when a new man comes in place of one of them weighing 65 kg. What might be the weight of the new man?
A.85 kg
B.70 kg
C.75 kg
D.90 kg
Answer: A.85 kg
Explanation: Total weight = (8 x 2.5) kg = 20 kg.
Weight - new man = (65 + 20) kg = 85 kg
ANSWER A
Question: During 2001, a stock lost 60 percent of its value. During the following year, the stock's value increased by 200 percent. Which of the following is the percent change in the stock's value during those two years?
A.60 percent decrease
B.40 percent decrease
C.20 percent increase
D.60 percent increase
Answer: C.20 percent increase
Explanation: Let the value of the stock in 2000 be 100, then in 2001 its value would be 100*(1-60/100)=100*0.4=40 and in 2002 its value would be 40*(1+200/100)=120. Hence during those two years the value of the stock increased from 100 to 120, so by 20%.
Answer: C.
Question: Two pipes can fill a tank in 18 minutes and 15 minutes. An outlet pipe can empty the tank in 45 minutes. If all the pipes are opened when the tank is empty, then how many minutes will it take to fill the tank?
A.1/15
B.1/16
C.1/11
D.1/10
Answer: D.1/10
Explanation: Part of the filled by all the three pipes in one minute
= 1/18 + 1/15 - 1/45 = (5 + 6 - 2)/90 = 9/90 = 1/10
So, the tank becomes full in 10 minutes.
Answer:D
Question: 6,61,212,507,_?
A.974
B.994
C.954
D.845
Answer: B.994
Explanation: (2)3-2=6
(4)^3-3=61
(6)^3-4=212
(8)^3-5=507
(10)^3-6=994
ANSWER:B
Question: John bought a 1-year, $20,000 certificate of deposit that paid interest at an annual rate of 8 percent compounded semiannually. What was the total amount of interest paid on this certificate at maturity?
A.$1650
B.$1660
C.$2632
D.$1632
Answer: D.$1632
Explanation: 8 percent compounded semiannually --> 4% in 6 moths.
For the first 6 moths interest was 4% of $20,000, so $800;
For the next 6 moths interest was 4% of $20,800, so $832
Total interest for 1 year was $800+$832=$1632
Answer : D
Question: The average weight of a group of boys is 20 kg. After a boy of weight 35 kg joins the group, the average weight of the group goes up by 1 kg. Find the number of boys in the group originally ?
A.12
B.14
C.18
D.24
Answer: B.14
Explanation: Let the number off boys in the group originally be x.
Total weight of the boys = 20x
After the boy weighing 35 kg joins the group, total weight of boys = 20x + 35
So 20x + 35 = 21(x + 1) = > x = 14.
ANSWER:B
Question: A wholeseller has $329,864 in her savings account. What is the least amount of money (in whole number of dollars) that he must add to his account if she wants to split this money evenly among his 9 debters?
A.$1
B.$2
C.$3
D.$4
Answer: D.$4
Explanation: To find the least amount the wholeseller should add to her saving account to split the money evenly among his 9 debtors,
he needs to make the total divisible by 9
Simply add the individual digits of the total = 3+2+9+8+6+4 = 32
If you add 4 , the number is divisible by 9 (32+ 4)
Correct Option : D
Question: The altitude drawn to the base of an isosceles triangle is 8 cm and the perimeter is 32 cm. The area of the triangle is
A.72 cm2
B.60 cm2
C.66 cm2
D.65 cm2
Answer: B.60 cm2
Explanation: Let ABC be the isosceles triangle and AD be the altitude.
Let AB = AC = x. Then, BC = (32 – 2x).
Since, in an isosceles triangle, the altitude bisects the base. So, BD = DC = (16 – x).
In ΔADC, AC2 = AD2 + DC2
⇒ x2 = (8)2 + (16 – x)2
⇒ 32x = 320 ⇒ x = 10.
∴ BC = (32 – 2x) = (32 – 20) cm = 12 cm.
Hence, required area = (1⁄2 × BC × AD)
= (1⁄2 × 12 × 10) cm2 = 60 cm2
Answer B
Question: A salt manufacturing company produced a total of 2500 tonnes of salt in January of a particular year. Starting from February its production increased by 100 tonnes every month over the previous months until the end of the year. Find its average monthly production for that year?
A.2060
B.3050
C.5550
D.2889
Answer: B.3050
Explanation: Total production of salt by the company in that year = 2500 + 2600 + 2700 + .... + 3600 = 36600.
Average monthly production of salt for that year = 36600/12 = 3050.
Answer: B
Question: A train 110 m long is running with a speed of 60 km/hr. In what time will it pass a man who is running at 6 km/hr in the direction opposite to that in which the train is going?
A.6
B.7
C.9
D.5
Answer: A.6
Explanation: Speed of train relative to man = 60 + 6 = 66 km/hr.
= 66 * 5/18 = 55/3 m/sec.
Time taken to pass the men = 110 * 3/55
= 6 sec.
Answer: A
Question: A man can do a piece of work in 7days, but with the help of his son, he can finish it in 3days. In what time can the son do it alone?
A.5
B.4 1/5
C.7 1/2
D.6
Answer: B.4 1/5
Explanation: Son's 1day work = 1/3 - 1/7 = 5/21
Son alone can do the work in 21/5days = 4 1/5 days
Answer is B
Question: A man can row downstream at 22 kmph and upstream at 14 kmph. Find the speed of the man in still water and the speed of stream respectively?
A.13, 3
B.18, 4
C.15, 3
D.14, 4
Answer: B.18, 4
Explanation: Explanation:
Let the speed of the man in still water and speed of stream be x kmph and y kmph respectively.
Given x + y = 22 --- (1)
and x - y = 14 --- (2)
From (1) & (2) 2x = 36 => x = 18, y = 4.
Answer: Option B