RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: A researcher computed the mean, the median, and the standard deviation W for a set of performance scores. If 5 were to be added to each score, which of these three statistics would change?
A.The mean only
B.The median only
C.The standard deviation only
D.The mean and the median
Answer: D.The mean and the median
Explanation: If we add or subtract a constant to each term in a set the standard deviation W will not change..
If we add (or subtract) a constant to each term in a set the mean and the median will increase (decrease) by the value of that constant.
Answer: D.
Question: If 9 ministers are to be seated at a round table conference, then how many different ways can they be seated?
A.24
B.60
C.40320
D.720
Answer: C.40320
Explanation: Simple formula:
There are (n - 1)! ways to arrange n distinct objects in a circle.
so its (9-1)! = 8! = 40320=C
Question: If the productivity of a brigade grows by 12% when the number of the workers in the brigade is increased by one, then which of the following is closest to the ratio of the productivity of a 12-person brigade to that of a 10-person brigade?
A.0.21
B.0.82
C.1.2
D.1.232
Answer: D.1.232
Explanation: B = 10-men brigade
p = increase in the productivity = 12%
Solution: B x p = B x 1.12 = 1.12B -------> the productivity of 11 men brigade
1.12B x p = 1.12B x 1.1 = 1.232B -----> the productivity of 12 men brigade
The ratio of the productivity of a 12-men brigade to that of a 10-men brigade = 1.232B/B = 1.232
D
Question: A mixture containing 6% boric acid is to be mixed with 2 quarts of a mixture which is 15% acid in
order to obtain a solution which is 12% acid. How much of the 6% solution must be used?
A.1
B.2
C.3
D.4
Answer: A.1
Explanation: This is a mixture problem.
The question asks, “How much of the 6% solution”.
Let x the number of quarts of 6% solution needed.
Write the equation and solve.
0.06+0.15(2)=0.12(x+2)
0.06x+0.30=0.12x+0.24
6x+30=12x+24
6=6x
x=1
The answer: 1 qt of 6% boric acid solution must be used.
correct answer A
Question: In a basket of apples, 12% of them are rotten and 66 are in good condition. Find the total number of apples in the basket.
A.33
B.75
C.23
D.20
Answer: B.75
Explanation: Let the total number of apples in the basket be m
12 % of the apples are rotten, and apples in good condition are 66
Therefore, according to the question,
88% of m = 66
88/100 × m = 66
m = (66 × 100)/88
m = 3 × 25
m = 75
Therefore, total number of apples in the basket is 75.
Answer:B
Question: A train speeds past a pole in 15 seconds and a platform 140 meters long in 25 seconds. What is the length of the train (in meters)?
A.190
B.200
C.210
D.220
Answer: C.210
Explanation: Let the length of the train be x meters.
The speed of the train is x / 15.
Then, x + 140 = 25*(x / 15)
10x = 2100
x = 210 meters
The answer is C.
Question: (525 + 275) Ã— 4 Ã— (3 + 2) = ?
A.12000
B.24000
C.16000
D.14000
Answer: C.16000
Explanation: (525 + 275) Ã— 4 Ã— (3 + 2) = ?
or, ? = 800 Ã— 4 Ã— 5 = 16000
Answer C
Question: A luxury liner, Queen Marry II, is transporting several cats as well as the crew (sailors, a cook, and one-legged captain) to a nearby port. Altogether, these passengers have 15 heads and 43 legs. How many cats does the ship host?
A.4
B.5
C.6
D.7
Answer: D.7
Explanation: sa's +co +ca +cats = 15. sa's + 1 +1 +cats =15 or sa's +cats =13.
sa's(2) +2 +1 +cats*4 =43 sa's*2 +cats*4 = 40 or sa's +cats*2 =20 or 13-cats +cat*2 =20
then cats =7
D
Question: How long will a boy take to run round a square field of side 40 meters, if he runs at the rate of 9km/hr?
A.64sec
B.45sec
C.1min
D.32sec
Answer: A.64sec
Explanation: Speed = 9 km/hr = 9*5/18 = 5/2 m/sec
Distance = 40*4 = 160m
Time taken = 160*2/5 = 64sec
Answer is A
Question: A triangle has a perimeter 17. The two shorter sides have integer lengths equal to x and x + 1. Which of the following could be the length of the other side?
A.4
B.5
C.6
D.7
Answer: D.7
Explanation: The SHORTER sides have integral lengths equal to x and x + 1
Let the longest side be 'a'
So, a + x + (x +1) = 17
a + 2x = 17.......eqn (1)
We know that the sum of the lengths of the shorter sides has to be more than the length of the longer one. i.e 2x+1> a
a =7
D
Question: For each month of a given year except December, a worker earned the same monthly salary and donated one-tenth of that salary to charity. In December, the worker earned N times his usual monthly salary and donated one-third of his earnings to charity. If the worker's charitable contributions totaled one-eighth of his earnings for the entire year, what is the value of N?
A.8/5
B.5/2
C.3
D.33/25
Answer: D.33/25
Explanation: Let monthly salary for each of the 11 months except December was x, then
11x*1/10 + Nx*1/3 = 1/8(11x + Nx);
11/10 + N/3 = 1/8(11 + N)
33+10N/30= 11+N/8 =>264+80N= 330+30N=>50N=66
N = 66/50=33/25
Answer: D.
Question: The average of first nine prime numbers is?
A.10
B.11.1
C.12.5
D.15.8
Answer: B.11.1
Explanation: Average = (2+3+5+7+11+13+17+19+23)/9= 100/9 = 11.1
Answer is B
Question: If an integer t is to be chosen at random from the integers 1 to 96, inclusive, what is the probability that t(t + 1)(t + 2) will be divisible by 8?
A.1/4
B.3/8
C.1/2
D.5/8
Answer: D.5/8
Explanation: for t Total numbers 8*12
There are 12 numbers divisible by 8 -> 3*12 (if 8 is an example - (6,7,8), (7,8,9), (8,9,10))
and 12 numbers divisible by 4 but not divisible by 8 -> 2*12 (if 4 is an example (2,3,4) and (4,5,6))
The answer 5/8 -> D
Question: If integers w and b are distinct factors of 30, which of the following CANNOT be a factor of 30?
I. wb + b^2
II. (w+ b)^2
III. w + b
A.I only
B.II only
C.III only
D.I and II only
Answer: B.II only
Explanation: Factors of 30 are: 1, 2, 3, 5, 6, 10, 15, and 30.
I. wb + b^2 --> if w=1 and b=2 then wb + b^2=6, which is a factor of 30. OK;
II. (w + b)^2 --> (w + b)^2 is a perfect square, no perfect square (but 1) is a factor of 30. DISCARD;
III. w + b --> if w=1 and b=2 then w + b=3, which is a factor of 30. OK.
Answer: B.
Question: Find the invalid no.from the following series 3, 6, 15, 31, 63, 127, 255
A.6
B.7
C.27
D.63
Answer: A.6
Explanation: Go on multiplying the number by 2 and adding 1 to it to get the next number.So, 6 is wrong.
A
Question: A certain university will select 1 of 7 candidates eligible to fill a position in the mathematics department and 3 of 10 candidates eligible to fill 3 identical positions in the computer science department. If none of the candidates is eligible for a position in both departments, how many different sets of 4 candidates are there to fill the 4 positions?
A.420
B.770
C.840
D.165
Answer: C.840
Explanation: 1 of 7 will be chosen for the math
3 of 10 will be chosen for the computer
None of the 4 chosen people can be in more than one departments.
We can choose any of the 7 candidates for the math dep., which gives as 7 selections.
We can choose 3 of the 10 candidates for the computer dep., which gives us 3 selections and 7 rejections.
So, the way to find how many different selections of 2 candidates we can have for the computer dep., we do:
10! /3!*7!= 120
We are multiplying our individual selections: 7*120 = 840
In the bolded part, we don't have to multiply all of the numbers, as those in 8! are included in 10!, so we simplify instead.
Ans C
Question: Jo's collection contains US, Indian and British stamps. If the ratio of US to Indian stamps is 5 to 2 and the ratio of Indian to British stamps is 5 to 1, what is the ratio of US to British stamps?
A.10 : 5
B.15 : 2
C.20 : 2
D.25 : 2
Answer: D.25 : 2
Explanation: Indian stamps are common to both ratios. Multiply both ratios by factors such that the Indian stamps are represented by the same number.
US : Indian = 5 : 2, and Indian : British = 5 : 1. Multiply the first by 5, and the second by 2.
Now US : Indian = 25 : 10, and Indian : British = 10 : 2
Hence the two ratios can be combined and US : British = 25 : 2 Answer: D
Question: . A boy has five trousers and 11 shirts. In how many different ways can he select a trouser and a shirt?
A.45
B.55
C.65
D.75
Answer: B.55
Explanation: Explanation:
The boy can select one trouser in five ways.
The boy can select one shirt in 11 ways.
The number of ways in which he can select one trouser and one shirt is 5 * 11 = 55 ways.
Answer: Option B
Question: Jim is able to sell a hand-carved statue for $540 which was a 35% profit over his cost. How much did the statue originally cost him?
A.$400.00
B.$412.40
C.$455.40
D.$474.90
Answer: A.$400.00
Explanation: 540 = 1.35*X
X = 540/1.35 = 400
$400, which is (A).
Question: What sum of money will produce Rs.70 as simple interest in 4 years at 3 1/2 percent?
A.988
B.500
C.378
D.373
Answer: B.500
Explanation: 70 = (P*4*7/2)/100
P = 500
Answer: B
Question: In a car wheel, ten spokes cover 60 degrees. Then for the entire car,how many spokes are there?
A.120
B.140
C.240
D.320
Answer: C.240
Explanation: given, 10 spokes cover 60degrees,
so for 360 degrees.---->360*10/60=60..
so, for entire car, 4*60=240
ANSWER:C
Question: If y = x^2 + cx + d, y is minimum when x is:
A.c/d
B.-c/d
C.-c/2
D.-d/2
Answer: C.-c/2
Explanation: We're given the equation Y = X^2 + cX + d.
IF.. we use a simple Classic Quadratic....
c = 2
d = 1
Y = X^2 + 2X + 1
We can then go about finding the answer that yields the MINIMUM result when X = ...
Answer A: c/d = 2/1 = 2 --> 4+4+1 = +9
Answer B: -c/d = -2/1 = -2 --> 4-4+1 = +1
Answer C: -c/2 = -2/2 = -1 --> 1-2+1 = 0
Answer D: -d/2 = -1/2 -->(1/4)-1+1 = +1/4
Answer E: d/c = 1/2 --> (1/4)+1+1 = +2 1/4
From these results, we can see the minimum result:
C
Question: If two sides of a triangle are 12 and 4, which of the following could be the area of triangle?
1. 35
2. 48
3. 56
A.a) 1 only
B.b) 1 and 2 only
C.c) 1 and 3 only
D.d) 2 and 3 only
Answer: D.d) 2 and 3 only
Explanation: when two sides of a triangle are known , the maximum area occurs when the angle between those two sides is 90.
lets say base = 12 , height =8 (angle = 90)
maximum area = (1/2)*12*8 = 48 ( this is the same maximum area even when base is 8 and height is 12).
if we fix the base and keep lowering the angle, it will result in a lower height . hence the resulting area will always be < 48.
C,D and E are ruled out.
3 and 2 are possible areas as their areas are less than 48.
Hence the answer is D.
Question: How many bricks each measuring 22cm x 10.25cm x 8cm, will be needed to build a wall 9m x 7m x 10.5m
A.5600
B.3066
C.3055
D.7200
Answer: B.3066
Explanation: Explanation:
no. of bricks= volume of the wall/volume of 1 brick = (900 x 700 x 10.5) / (22 x 10.25 x 8) = 3066
Answer: B
Question: Today is Sunday. After 36 days, what day of the week will it be?
A.Thursday
B.Monday
C.Tuesday
D.Saturday
Answer: B.Monday
Explanation: Each weekday is repeated every 7 days. 36 divided by 7 is 5 with a remainder of 1. So, after 35 days it will be a Sunday. After 36 days, it will be a Monday. Answer: B
Question: The LCM and HCF of two numbers are 60 and 2 respectively. Find the larger of the two numbers if their sum is 22.
A.12
B.2
C.4
D.54
Answer: A.12
Explanation: There are 2 approaches in solving this.
Methode 1.
HCF * LCM = The Actual Number.
60* 2= 120
So the answer which we are looking for has to be a factor of 120.
So among the options shortlist the answers by eliminating those numbers which is not divisible by 120. and then take the highest number as the answer as the question asks abt the highest number.
answer is A
Question: In Cliff’s impressive rock collection, there are half as many igneous rocks as sedimentary rocks. Of the igneous rocks, 4/5 are shiny and the rest are matte, while 1/5 of the sedimentary rocks are shiny. If there are 40 shiny igneous rocks, how many total rocks does Cliff have?
A.30
B.150
C.60
D.90
Answer: B.150
Explanation: We can start with the known quantity and then go on to find the others.
Shiny igneous ricks are 40. These are (4/5) of total igneous rocks.
(4/5)*Total igneous rocks = 40
Total igneous rocks = 40 * (5/4) = 50
Total sedimentary rocks = 2*Total igneous rocks = 2*50 = 100
Total number of rocks = 50 + 100 = 150
Answer (B)
Question: In a bag there are coins of 50 paisa, 25 paisa and one rupee in the proportion 10:6:5. If there are in all Rs.92, the number of 25 paisa coins is?
A.26
B.46
C.48
D.42
Answer: C.48
Explanation: 10x 6x 5x
50 25 100
500x + 150x + 500x = 9200
1150x = 9200
x = 8 => 6x = 48
Answer: C
Question: 1. Mrs. Ram got a weekly raise of $145. If he gets paid every other week, write an integer describing how the raise will affect her paycheck.
A.145
B.245
C.100
D.150
Answer: A.145
Explanation: Let the 1st paycheck be x (integer).
Mrs. Ram got a weekly raise of $ 145.
So after completing the 1st week he will get $ (x+145).
Similarly after completing the 2nd week she will get $ (x + 145) + $ 145.
= $ (x + 145 + 145)
= $ (x + 290)
So in this way end of every week her salary will increase by $ 145.
Answer :A
Question: Rs.900 amounts to Rs.920 in 3 years at simple interest. If the interest is increased by 3%, it would amount to how much?
A.Rs.1056
B.Rs.1001
C.Rs.2056
D.Rs.1026
Answer: B.Rs.1001
Explanation: (900*3*3)/100 = 81
920 + 81 = 1001
ANSWER:B
Question: If x > y, x < 6, and y > -3, what is the largest prime number that could be equal to x + y?
A.10
B.11
C.12
D.14
Answer: B.11
Explanation: Primes: 2, 3, 5, 7, 11, 13, 17, etc
If X is less than 6 and y is less than X, then 6+6 = 12 would be impossible. We know 13 and all the primes > 13 are out. Let's try 11.
5.9 + 5.1 = 11
5.9 < 6
5.1 < 5.9
everything checks out
Answer 11
ANSWER:B
Question: In a certain game there are 8 steps, referred to as step 1, step 2, and so on with the final step being step 8. The steps are played one after the other. In each step a score of 1, 2, 3, or 4 is obtained. Angel played the game, getting at least one score of each of 1, 2, 3, and 4, and never getting the same score in consecutive steps. What is the greatest possible score that Angel could have gotten?
A.15
B.18
C.21
D.23
Answer: B.18
Explanation: There are two conditions:
1. Angel got at least one score of each of 1, 2, 3, and 4.
2. She never got the same score in consecutive steps.
Taking that into account, the greatest possible score that Angel could have gotten is 4 + 1 + 4 + 2 + 4 + 3 = 18.
Answer: B.
Question: The length of the room is 5.5m and width is 3.75m. Find the cost of paving the floor by slabs at the rate of Rs.800 per sq meter
A.Rs.16500
B.Rs.15500
C.Rs.17500
D.Rs.18500
Answer: A.Rs.16500
Explanation: l=5.5m w=3.75m
area of the floor = 5.5 x 3.75 = 20.625 sq m
cost of paving = 800 x 20.625 = Rs. 16500 Answer: A
Question: Look at this series: 83, 73, 93, 63, __, 93, 43, ... What number should fill the blank?
A.55
B.59
C.52
D.53
Answer: D.53
Explanation: D
53
This is a simple subtraction series in which a random number, 93, is interpolated as every third number. In the subtraction series, 10 is subtracted from each number to arrive at the next.
Question: 81,162,49,98,25,50,62
A.124
B.127
C.129
D.128
Answer: A.124
Explanation: 81*2=162
49*2=98
25*2=50
62*2=124
ANSWER:A
Question: The present ages of three persons are in the proportion of 4 : 7 : 9. Eight years ago, the sum of their ages was 116. Find their present ages.
A.20,35,45
B.28,49,63
C.16,28,36
D.16,28,46
Answer: B.28,49,63
Explanation: Let the present ages of three persons be 4K,7K and 9K respectively.
(4K - 8) + (7K - 8) + (9K - 8) = 116
20K = 140
K = 7
Therefore, then present ages are 28,49,63.
ANSWER:B
Question: Two teams are distributing information booklets. Team A distributes 60% more boxes of booklets than Team X, but each box of Team A’s has 60% fewer booklets than each box of Team X’s. Which of the following could be the total number of booklets distributed by the two groups?
A.2,000
B.3,200
C.4,100
D.4,800
Answer: C.4,100
Explanation: Let x be the no of booklets in each box that team X distributes. So, Team A has 60% fewer - 0.4x.
Let y be the no. of boxes distributed by team X. So, Team A distributes 60% more - 1.6y
Total booklets distributed by team A = xy
Total booklets distributed by team X=0.64xy
Total booklets distributed = xy+0.64xy=1.64xy
As no. of booklets can only be integer, plugging the answer choice equal to 1.64xy should give an integer.
Choice A - 1.64xy=2000; xy=2000/1.64 = doesn't provide an integer value.
Similarly all answer choices, except choice C, fail to provide an integer value.
Choice C = 4100/1.64= 2500 and is the correct answer.
Question: The mean of set P does not exceed mean of any subset of set P. Which of the following must be true about set P?
I. Set P contains only one element
II. All elements in set P are equal
III. The median of set P equals the mean of set P
A.of the three qualities is necessary
B.II only
C.III only
D.II and III only
Answer: D.II and III only
Explanation: The only necessary condition seems to be II.
If all nos are equal.... them mean of any subset is the same.
I is obviously ruled out ( e.g. P = {1,1,1} )
But III, what about 3?
It is not necessary in itself, rather, is automatically implied by II.
All sets that satsify II satisfy III=D
Question: If the sides of a cube are in the ratio 9:7. What is the ratio of their diagonals?
A.4:3
B.16:9
C.9:7
D.3:4
Answer: C.9:7
Explanation: Explanation:
Diagonal of a Cube=a√3 where a is side
a1:a2 = 9:7
d1:d2 = 9:7 where√3 cancelled both side
ANSWER:C
Question: If you roll a fair-sided die twice, what is the probability of getting a (2 ,2)?
A.1/4!
B.1/3!
C.1/2!
D.1/36
Answer: B.1/3!
Explanation: total no. in two dice (1,1) ,(2,2) .....(6,)
Total number of events= 6*6
Total events of getting same pair(2, 2) = 6
Probability= 6/6*6= 1/6=1/3!
B
Question: What is the difference between the largest number and the least number written with the digits 7, 3, 1, 4?
A.6084
B.6184
C.5084
D.6048
Answer: A.6084
Explanation: 1347
7431
------------
6084
ANSWER:A
Question: The game of blackjack is played with a deck consisting of 13 cards (one of each of the numbers 2-10, one jack, one queen, one king, and one of ace) in each of four suits: clubs, diamonds, hearts, and spades.
In a game of blackjack, if your first card is a spade, what are the odds that it is a 9?
A.1/13
B.1/26
C.5/13
D.1/4
Answer: A.1/13
Explanation: The question should ask about the probability not the odds.
There are 13 spades, the probability that the spade we already have is 9 is therefore 1/13.
Answer: A.
Question: Each shelf of a bookcase contains 20 books. If the librarian took out 42 books and rearranged the remaining books so that all shelves but the last one contained 16 books and the last shelf contained 22 books, how many shelves does the bookcase have?
A.A)4
B.B)12
C.C)6
D.D)8
Answer: B.B)12
Explanation: Denoting x the number of the shelves,
we can build an equation: 20x=16(x−1)+22+42
Solving the equation, we get x=12
Answer: B
Question: A fair 2 sided coin is flipped 3 times. What is the probability that tails will be the result at least twice, but not more than 3 times?
A.5/8
B.3/4
C.3/8
D.7/4
Answer: C.3/8
Explanation: at least twice, but not more than 3 timesmeans exactly 2 times, 3 times
The probability of getting exactly k results out of n flips is nCk/2^n
3C2/2^3=3/8
Option: C
Question: A library has an average of 510 visitors on Sundays and 240 on other day. The average number of visitors in a month of 30 days starting with sunday is
A.280
B.285
C.290
D.295
Answer: B.285
Explanation: Explanation:
As the month begin with sunday, so there will be five sundays in the month. So result will be:
=(510×5+240×25 / 30)=(8550 / 30)=285
Option B
Question: Jim and Renee will play one game of Rock, Paper, Scissors. In this game, each will select and show a hand sign for one of the three items. Rock beats Scissors, Scissors beat Paper, and Paper beats Rock. Assuming that both Jim and Renee have an equal chance of choosing any one of the hand signs, what is the probability that Jim will win or draw?
A.5/6
B.2/3
C.1/2
D.5/12
Answer: B.2/3
Explanation: There are 3*3=9 combinations (cases) possible. In 3 cases there will be a tie (rock-rock, scissors/scissors, paper/paper). Now, out of 6 cases left Jim and Renee have equal chances of winning, so in 3 cases Jim will win and in other 3 Renee will win. So the probability Jim winning the game is (favorable outcomes)+Drawing the game / (total # of outcomes) = 6/9 = 2/3.
Or: no matter what sign Renee will select Jim can select 1 sign to win, 1 sign to get tie and 1 sign to loose, so the probability Jim winning the game or drawing is 2/3.
Answer: B
Question: If 2 cards are selected (with replacement) at random from the deck of 52 cards then what is the probability that one of the selected cards will be a heart and the other will be a club?
A deck of cards has a total of 52 cards, consisting of 4 suits: spades (black), hearts(red), diamonds (red), and clubs (black). In each suit, there are 13 cards including 1 king, 1 queen, and 1 jack.
A.1/8
B.1/16
C.1/32
D.1/64
Answer: A.1/8
Explanation: P(1 heart and 1 club) = 2(1/4*1/4) = 1/8
The answer is A.
Question: A jogger running at 9 kmph alongside a railway track in 240 metres ahead of the engine of a 120 metres long train running at 45 kmph in the same direction. In how much time will the train pass the jogger?
A.3.6 sec
B.18 sec
C.36 sec
D.72 sec
Answer: C.36 sec
Explanation: Speed of train relative to jogger = (45 - 9) km/hr = 36 km/hr.
= 36 x	5/18	m/sec
= 10 m/sec.
Distance to be covered = (240 + 120) m = 360 m. Answer: Option C
Time taken = 360/10	sec	= 36 sec.
Question: A policeman noticed a criminal from a distance of 180 km. The criminal starts running and the policeman chases him. The criminal and the policeman run at the rate of 8 km and 9 km per hour respectively. What is the distance between them after 3 minutes ?
A.100 m
B.120 m
C.130 m
D.150 m
Answer: C.130 m
Explanation: Explanation :
Solution: Relative speed = (9 - 8) = 1 km/hr.
Distance covered in 3 minutes = (1 * 3/60) km = 1/20 km = 50 m.
.'. Distance between the criminal and policeman = (180 - 50) m = 130 m.
Answer : C
Question: What percent of 500 is 125?
A.0.25%
B.4%
C.25%
D.40%
Answer: C.25%
Explanation: 500*x /100 = 125
x = 125/5
x = 25
Ans: C
Question: Tough and Tricky questions: Word Problems.
Micheal , Saren and Donald decided to club together to buy a present. Each of them gave equal amount of money. Luckily Saren negotiated a 20% discount for the present so that each of them paid 4 dollars less. How much did they pay for a present?
A.20
B.36
C.48
D.60
Answer: C.48
Explanation: Answer C.
We know that Saren negotiated a discount of 20%, so each of them paid $4 less. Since there are three people, the 20% of the original price amounts to $12. 5 times 12$ is 60$, so the original price, before Saren negotiated the discount, had been $60. They paid $12 less than the base price, so they spent $48.
Question: The profit earned by selling an article for Rs. 832 is equal to the loss incurred when the same article is sold for Rs. 448. What should be the sale price for making 80% profit?
A.1152
B.230
C.960
D.780
Answer: A.1152
Explanation: C.P. = Rs. x.
Then, 832 - x = x - 448
2x = 1280 => x = 640
Required S.P. = 180% of Rs. 640 = 180/100 * 640 = Rs. 1152.
A
Question: How many meters are there in 550 centimeters?
A.550 meters
B.5.5 meters
C.100 meters
D.2.5 meters
Answer: B.5.5 meters
Explanation: Solution:
1 meter = 100 centimeters
Just divide 550 by 100
550 Ã· 100 = 5.5, so there are 5.5 meters in 550 centimeters
Option B
Question: The length of a rectangle is 5 more than the width. What are the dimensions of the rectangle if the perimeter is 34?
A.11
B.12
C.13
D.14
Answer: A.11
Explanation: Pretend width = 1, then length = 6 ( 1 + 5)
2 × 1 + 2 × 7 = 2 + 14 = 16. Notice that 16 is far from a perimeter of 34
Try much bigger number.
How about if we...
Pretend width = 4, then length = 9 ( 4 + 5)
2 × 4 + 2 × 9 = 6 + 18 = 24. We are getting closer to a perimeter of 34
Pretend width = 5, then length = 10 ( 5 + 5)
2 × 5 + 2 × 10 = 10 + 30 = 30.
Pretend width = 7, then length = 12 ( 7 + 5)
2 × 7 + 2 × 12 = 14 + 24 = 38. This is higher than a perimeter of 34. So width should be higher than 5 and smaller than 7. May be a width of 6 will work.
Pretend width = 6, then length = 11 ( 6 + 5)
2 × 6 + 2 × 11 = 12 + 22 = 34.
Use of algebra:
Let width = x
Let length = x + 5
P = 2 × L + 2 × W
34 = 2 × ( x + 5) + 2 × x
34 = 2x + 10 + 2x
34 = 4x + 10
34 - 10 = 4x + 10 - 10
24 = 4x
24/4 = 4x/4
6 = x
Therefore, width = 6 and length = x + 5 = 6 + 5 = 11
Answer A