RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: Working in a South Side studio at a constant rate, Kanye can drop a full-length platinum LP in 5 weeks. Working at his own constant rate, Common can drop a full-length platinum LP in x weeks. If the two emcees work together at their independent rates, they can drop a full-length platinum compilation LP in 2 weeks. Assuming no efficiency is lost or gained from working together, how many weeks would it take Common, working alone, to drop a full-length platinum LP?
A. 3 and 1/3 weeks
B. 3 weeks
C. 2 and 1/2 weeks
D. 2 and 1/3 weeks
Answer: A. 3 and 1/3 weeks
Explanation: VERITAS PREPOFFICIAL SOLUTION:
Now, while your instinct may be to Go! and speed through your initial read of this rate problem, remember: slow motion (is) better than no motion. As you read each sentence, you should start jotting down variables and relationships so that by the time you get to the question mark you have actionable math on your noteboard and you don’t have to read the question all over again to get started. You should be thinking:
Working in a South Side studio at a constant rate, Kanye can drop a full-length platinum LP in 5 weeks.
Rate (K) = 1 album / 5 weeks
Working at his own constant rate, Common can drop a full-length platinum LP in x weeks.
Rate (C) = 1 album / x weeks
If the two emcees work together…
I’m adding these rates, so their combined rate is 1/5 + 1/x
…they can drop a full-length platinum compilation LP in 2 weeks.
And they’re giving me the combined rate of 1 album / 2 weeks, so 1/5 + 1/x = 1/2
Assuming no efficiency is lost or gained from working together, how many weeks would it take Common, working alone, to drop a full-length platinum LP?
I’m using that equation to solve for Common’s time, so I’m solving for x.
Now by this point, that slow motion has paid off – your equation is set, your variable is assigned, and you know what you’ve solving for. Your job is to solve for x, so:
1/5 + 1/x = 1/2, so let’s get the x term on its own:
1/x = 1/2 – 1/5. and we can combine the two numeric terms by finding a common denominator of 10:
1/x = 5/10 – 2/10
1/x = 3/10, and from here you have options but let’s cross multiply:
10 = 3x, so divide both sides by 3 to get x alone:
10/3 = x, and that doesn’t look like the answer choices so let’s convert to a mixed number: 3 and 1/3 (there’s that number again), for answer choice A.
Question: A contractor undertook to do a piece of work in 10 days. He employed certain number of laboures but 5 of them were absent from the very first day and the rest could finish the work in only 13 days. Find the number of men originally employed ?
A.21.6
B.23.6
C.22.6
D.21.8
Answer: A.21.6
Explanation: Let the number of men originally employed be x.
10x = 13(x â€“ 5)
or x = 21.6
Answer A
Question: The ratio between the present ages of A and B is 5:3 respectively. The ratio between A's age 4 years ago and B's age 4 years hence is 1:1. What is the ratio between A's age 4 years hence and B's age 4 years ago?
A.3:9
B.3:7
C.3:1
D.3:2
Answer: C.3:1
Explanation: Let the present ages of A and B be 5x and 3x years respectively.
Then, (5x - 4)/(3x + 4) = 1/1
2x = 8 => x = 4
Required ratio = (5x + 4):(3x - 4) = 24:8 = 3:1
Answer: C
Question: If selling price is doubled, the profit triples. Find the profit percent.
A.66%
B.120%
C.105%
D.100%
Answer: D.100%
Explanation: Let C.P. be Rs. x and S.P. be Rs. y.
Then, 3(y - x) = (2y - x)
y = 2x.
Profit = Rs. (y - x) = Rs. (2x - x) = Rs. x.
Profit % =	x/x x 100% =100%
Answer is D.
Question: A train speeds past a pole in 15 seconds and a platform 100 m long in 25 seconds. Its length is?
A.886 m
B.787 m
C.876 m
D.150 m
Answer: D.150 m
Explanation: Let the length of the train be x meters and its speed be y m/sec.
They, x / y = 15 => y = x/15
x + 100 / 25 = x / 15
x = 150 m.
Answer:D
Question: Veena ranks 79rd from the top in a class of 182. What is her rank from the bottom if 22 students have failed the examination?
A.88
B.108
C.82
D.90
Answer: C.82
Explanation: total student=182
failed=22
paasd student=182-22=160
from bottom her rank is=160-79+1=82
ANSWER:C
Question: From a group of 6boys&4girls a Committee of 4 persons is to be formed. In how many different ways can it be done, so that the committee has at least 2 boys?
A.145
B.198
C.185
D.210
Answer: C.185
Explanation: The committee of 4 persons is to be so formed that it has at least 2 men. The different ways that we can choose to form such a committee are:
(i) 2m. 2w in 6C2 x 4 C1=6X5 - 2X1 X 3X3 2X1 =n an (ii) 3m. 1w in 6C3 x 4C1 =6X5X4 3X2X1 X4 _n - a ''''
(iii) 4m in 6C4 -2x1 = 15 Total no. of different ways in which a committee of 4 persons can be formed so that it has at least 2 men. = 90 + 18 + 15 = 185
C
Question: How many positive 5-digit integers have the odd sum of their digits?
A.9*10^2
B.9*10^3
C.10^4
D.45*10^3
Answer: D.45*10^3
Explanation: We are looking at numbers between 10000 and 99999 both inclusive.
There are 90000 numbers.
Now for
10000 : sum of digits is odd;
10001 :sum of digits is even;
10002 : sum of digits is odd ; so on and so forth. So every alternate number is such that the sum of digit is odd.
(Exception for the above statement :
When it is 10009 the sum is even and for 10010 again the sum is even; But if you look at 10019 :sum is odd; 10020 : sum is odd
and this pattern continues so basically the number of odd sum of digits and even sum of digits are equal)
This means exactly half of the numbers will have odd sum of their digits. i.e 45000
Answer : D
Question: The function f is defined for all positive integers V by the following rule. f(V) is the number of positive integers each of which is less than V and has no positive factor in common with V other than 1. If Y is any prime, number then f(Y)=
A.Y-1
B.Y-2
C.(Y+1)/2
D.(Y-1)/2
Answer: A.Y-1
Explanation: If not the wording the question wouldn't be as tough as it is now. The GMAT often hides some simple concept in complicated way of delivering it.
This question for instance basically asks: how many positive integers are less than given prime number Y which have no common factor with Y except 1.
Well as Y is a prime, all positive numbers less than Y have no common factors with Y (except common factor 1). So there would be Y-1 such numbers (as we are looking number of integers less than Y).
For example: if Y=3 how many numbers are less than 3 having no common factors with 3: 1, 2, 3, --> 3-1=2.
Answer: A.
Question: Ajay can ride 50km in 1 hour. In how many hours he can ride 1250km?
A.10hrs
B.15hrs
C.20hrs
D.25hrs
Answer: D.25hrs
Explanation: 1 hour he ride 50km
he ride 1250km in = 1250/50 * 1 = 25hours
Answer is D
Question: To be considered for “movie of the year,” a film must appear in at least 1/4 of the top-10-movies lists submitted by the Cinematic Academy’s 795 members. What is the smallest number of top-10 lists a film can appear on and still be considered for “movie of the year”?
A.191
B.199
C.193
D.212
Answer: B.199
Explanation: Total movies submitted are 795.
As per question we need to take 1/4 of 795 to be considered for top 10 movies = 198.75
approximate the value we 199.
IMO option B is the correct answer...
Question: In a box, there are 10 red, 6 blue and 5 green balls. One ball is picked up randomly. What is the probability that it is neither red nor green?
A.4/51
B.10/21
C.7/12
D.11/31
Answer: B.10/21
Explanation: Total number of balls = 10+6+5 = 21
E = event that the ball drawn is neither red nor green
= event that the ball drawn is red
n(E) = 10
P(E) = 10/21
Answer is B
Question: John purchased some shirts and trousers for $1550. He paid $250 less for the shirts than he did for the trousers. If he bought 5 shirts and the cost of a shirt is $20 less than that of a trouser, how many trousers did he buy?
A.4
B.5
C.6
D.7
Answer: C.6
Explanation: Given that the total purchase of two items cost 1550.
So the average purchase of one item will cost 1550/2 =775.
Its given as total shirt cost 250$ less. Hence Total Shirt cost = 775 - 125 and Total trouser cost = 775 + 125
5 shirts =650$ ==> One shirt =130$
One trouser = 130 + 20 =150$
Total trousers = 900 / 150 =6.
C
Question: If (2^x)(3^y) = 324, where x and y are positive integers, then (2^x-1)(3^y-2) equals:
A.16
B.18
C.48
D.96
Answer: B.18
Explanation: So I would start attacking this problem by quickly performing the prime factorization of 288. With that it is easy to count the 5 twos and the 2 threes that are the prime factors. So x=2, y=4. now quickly 2^1(3^2)=18. Than answer should be number 2.
B
Question: When positive integer a is divided by 6, the remainder is 1. Which of the following must be true?
I. a is a prime number
II. a is odd
III. a is divisible by 7
A.I only
B.II only
C.III only
D.I and II only
Answer: B.II only
Explanation: a=6q+1
Examine II) put q=0,1,2,3....... we have a=1,7,13,...25 so a must be odd
Examine III) 14/6 has reminder 249/7 has reminder 1 so not always true
Examine I) a= 7 true but while 2 is prime, it does not give reminder 1
Answer: B
Question: Find the area of a rhombus one side of which measures 20 cm and one diagonal is 23 cm.
A.100cm2
B.150cm2
C.300cm2
D.368cm2
Answer: D.368cm2
Explanation: Explanation: Let other diagonal = 2x cm.
Since diagonals of a rhombus bisect each other at right angles, we have:
(20)2 = (12)2 + (x)2 =>x =√(20)2 – (12)2= √256= 16 cm. _I
So, other diagonal = 32 cm.
Area of rhombus = (1/2) x (Product of diagonals) =(1/2× 23 x 32) cm2 = 368 cm2
Answer: Option D
Question: Mrs. Rodger got a weekly raise of $145. If she gets paid every other week, write an integer describing how the raise will affect her paycheck.
A.$ 130
B.$ 145
C.$ 115
D.$ 120
Answer: B.$ 145
Explanation: Let the 1st paycheck be x (integer).
Mrs. Rodger got a weekly raise of $ 145.
So after completing the 1st week she 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.
correct answer B
Question: The price of an article is cut by 10%. To restore it to the former value. The new price must be increased by ?
A.10%
B.9 1/11
C.11 1/9
D.11%
Answer: C.11 1/9
Explanation: Answer
Let original price = Rs. 100.
Then, new price = Rs. 90.
∴ Increased on Rs. 90 = Rs. 10
Required increase % = (10 x 100) / 90 % = 111/9%
Correct Option: C
Question: A committee has 4 men and 7 women. What are the number of ways of selecting 3 men and 4 women from the given committee?
A.110
B.120
C.130
D.140
Answer: D.140
Explanation: The number of ways to select three men and four women = 4C3 * 7C4 = 4 * 35 = 140
The answer is D.
Question: Each of three charities in Novel Grove Estates has 8 persons serving on its board of directors. If exactly 4 persons serve on 3 boards each and each pair of charities has 5 persons in common on their boards of directors, then how many distinct persons serve on one or more boards of directors?
A.8
B.13
C.16
D.24
Answer: B.13
Explanation: A intersect B intersect C = 4
A intersect B but not C = 1
B intersect C but not A = 1
C intersec A but not B = 1
A only is 2; B only is 2; C only is 2
Therefore, total 13 members serve on one or more boards of directors.
ANSWER:B
Question: Dropbox charges $3.10 for first 1/5 of a month for 500 GB storage, plus $0.40 for each additional 1/5 of a month. What would Dropbox charge for a data storage of 500 GB for 8 months ?
A.$15.60
B.$16.00
C.$17.80
D.$18.70
Answer: D.$18.70
Explanation: first 1/5 month charge = $3.10
rest of the months = 8 - (1/5) = 39/5
charge for the rest of the months = 39 *0.4 = 15.6
total charge = 3.10+15.6 = 18.7
Answer is D.
Question: A cistern of capacity 8000 litres measures externally 3.3 m by 2.6 m by 1.1 m and its walls are 5 cm thick. The thickness of the bottom is:
A.9
B.1
C.2
D.4
Answer: B.1
Explanation: Answer: B) 1 dm
Question: A box contains ELEVEN bulbs out of which 5 are defective. If four bulbs are chosen at random, find the probability that atleast one bulb is good?
A.325/330
B.325/420
C.369/430
D.546/558
Answer: A.325/330
Explanation: Required probability= 1-5C4/11C4= 1 - 5/330= 325/330Answer:A
Question: A certain gallery is hanging a series of 6 paintings. All the paintings will be exhibited in a row along a single wall. Exactly 2 of the paintings are on panel, the remainder are on canvas. In how many ways can the paintings be exhibited if the works on panel must be the second and sixth in the row?
OE
A.240
B.200
C.122
D.48
Answer: D.48
Explanation: We need to consider them separately because the question specifies:
1. Panel paintings have to be placed only at 2nd and 6th place.
2. Implies that Canvas has to be placed 1,3,4,5th place.
So we have two separatebucketsto consider.
So panels can be ordered in 2!
Canvas can be ordered in 4!
since relative position of panels to canvas is fixed (Panels 2nd and 6th) the answer is 2! x 4! = 48
D
Question: The time taken by a man to row his boat upstream is twice the time taken by him to row the same distance downstream. If the speed of the boat in still water is 42 kmph, find the speed of the stream?
A.76 kmph
B.17 kmph
C.14 kmph
D.18 kmph
Answer: C.14 kmph
Explanation: The ratio of the times taken is 2:1.
The ratio of the speed of the boat in still water to the speed of the stream = (2+1)/(2-1) = 3/1
= 3:1
Speed of the stream = 42/3 = 14 kmph.
Answer: C
Question: The roof of an apartment building is rectangular and its length is 3 times longer than its width. If the area of the roof is 588 feet squared, what is the difference between the length and the width of the roof?
A.28.
B.40.
C.42.
D.44.
Answer: A.28.
Explanation: Answer is A: 28
Let w be the width , so length is 3w. Therefore : w*3w = 588, solving for, w = 14 , so 3w-w = 2w = 2*14 = 28
Question: What value will replace the question mark in the following equation ? 5172.49 + 378.352 + ? = 9318.678
A.3767.836
B.3677.863
C.3767.863
D.3767.683
Answer: A.3767.836
Explanation: Let 5172.49 + 378.352 + x = 9318.678
Then , x = 9318.678 – (5172.49 + 378.352) = 9318.678 – 5550.842 = 3767.836
Answer is A.
Question: If n is a prime number greater than 11, what is the remainder when n^2 is divided by 12 ?
A.0
B.1
C.2
D.3
Answer: B.1
Explanation: There are several algebraic ways to solve this question, but the easiest way is as follows:since we cannot have two correct answers just pick a prime greater than 11, square it and see what would be the remainder upon division of it by 12.
n=17 --> n^2=289 --> remainder upon division 289 by 12 is 1.
Answer: B.
Question: A and B together can do a piece of work in 6 days and A alone can do it in 12 days. In how many days can B alone can do it?
A.11 days
B.15 days
C.12 days
D.21 days
Answer: C.12 days
Explanation: Explanation:
A and B can do work 1/6 in 1 day
A alone can do 1/12 work in 1 day
B alone can do (1/6 -1/12) =1/12 work in 1 day
=> complete work can be done in 12 days by B
Answer: Option C
Question: What is the smallest positive perfect square that is divisible by 9, 21, and 49?
A.225
B.324
C.441
D.529
Answer: C.441
Explanation: The number needs to be divisible by 3^2, 3*7, and 7^2.
The smallest such perfect square is 3^2*7^2 = 441
The answer is C.
Question: A box measuring 35 inches long by 20 inches wide by 10 inches deep is to be filled entirely with identical cubes. No space is to be left unfilled. What is the smallest number of cubes that can accomplish this objective?
A.17
B.18
C.54
D.56
Answer: D.56
Explanation: least number of cubes will be required when the cubes that could fit in are biggest.
5 is the biggest number that could divide all three, 35, 20 and 10.
Thus side of cube must be 5, and total number of cubes = 35/5 * 20/5*10/5 = 56
Ans D it is.
Question: A line that passes through (–1, –4) and (4, k) has a slope = k. What is the value of k?
A. 3/4
B. 1
C. 4/3
D. 2
Answer: B. 1
Explanation: Slope = (y2-y1)/(x2-x1)
=> k = (k+4)/(4+1)
=> 5k = k+4
=> k =1
Ans B it is!
Question: In how many different ways can the letters of the word 'OPTICAL' be arranged so that the vowels always come together?
A.520
B.720
C.890
D.870
Answer: B.720
Explanation: The word 'OPTICAL' contains 7 different letters.
When the vowels OIA are always together, they can be supposed to form one letter.
Then, we have to arrange the letters PTCL (OIA).
Now, 5 letters can be arranged in 5! = 120 ways.
The vowels (OIA) can be arranged among themselves in 3! = 6 ways.
Required number of ways = (120 x 6) = 720.
ANSWER B 72
Question: A, B and C started a business with capitals of Rs. 8000, Rs. 10000 and Rs. 12000 respectively. At the end of the year, the profit share of B is Rs. 1500. The difference between the profit shares of A and C is?
A.Rs.628
B.Rs.629
C.Rs.629
D.Rs.600
Answer: D.Rs.600
Explanation: Ratio of investments of A, B and C is 8000 : 10000 : 12000 = 4 : 5 : 6
And also given that, profit share of B is Rs. 1500
=> 5 parts out of 15 parts is Rs. 1500
Now, required difference is 6 - 4 = 2 parts
Required difference = 2/5 (1500) = Rs.600'
Answer: D
Question: For a race a distance of 224 meters can be covered by P in 14 seconds and Q in 32 seconds. By what distance does P defeat Q eventually?
A.232m
B.288m
C.324m
D.231m
Answer: B.288m
Explanation: Explanation:
This is a simple speed time problem. Given conditions:
=>Speed of P= 224/14 = 16m/s
=>Speed of Q=224/32 = 7m/s
=>Difference in time taken = 18 seconds
Therefore, Distance covered by P in that time= 16m/s x 18 seconds = 288 metres
ANSWER: B
Question: The list price of an article is Rs.65. A customer pays Rs.56.16 for it. He was given two successive discounts, one of them being 10%. The other discount is?
A.1
B.4
C.5
D.6
Answer: B.4
Explanation: 65*(90/100)*((100-x)/100) = 56.16
x = 4%
Answer: B
Question: A sum of money invested at C.I. amounts to Rs. 800 in 3 years to Rs. 840 in 4 years. The rate of interest per annum is?
A.3
B.2
C.5
D.7
Answer: C.5
Explanation: Explanation:
S.I. on Rs. 800 for 1 year = (840 - 800) = Rs. 40 Rate = (100 * 40)/(800 * 1) = 5%
Answer:C
Question: How many seconds does a train 120 meters long, traveling at 54 km/h, take to completely cross a bridge of 180 meters in length?
A.18
B.20
C.22
D.24
Answer: B.20
Explanation: 54 km/h = 54000/3600 = 15 m/s
Time = 300 / 15 = 20 seconds
The answer is B.
Question: If x + 5 > 2 and x - 3 < 6, the value of x must be between which of the following pairs of numbers?
A. -3 and 10
B. -3 and 9
C. 2 and 7
D. 3 and 4
Answer: B. -3 and 9
Explanation: Let’s isolate x in each inequality.
x + 5 > 2
x > -3
Next we simplify x – 3 < 7.
x – 3 < 6
x < 9
We know that x is greater than -3 and less than 9.
The answer is B.
Question: In a stable there are men and horses. In all, there are 22 heads and 72 feet. How many men and how many horses are in the stable?
A.8 men and 14 horses.
B.7 men and 14 horses.
C.6 men and 14 horses.
D.5 men and 14 horses.
Answer: A.8 men and 14 horses.
Explanation: 8 men and 14 horses.
Let M = men and H = horses. We can come up with 2 equations.
M + H = 22
2M + 4H= 72
Solving the 2 equations will give 8 men and 14 horses.
Answer A
Question: A train running at the speed of 60 km/hr crosses a pole in 9 seconds. What is the length of the train?
A.120 metres
B.180 metres
C.324 metres
D.150 metres
Answer: D.150 metres
Explanation: Speed=(60 * 5/18) m/sec = (50/3) m/sec Length of the train = (Speed x Time) = (50/3 * 9) m = 150 m.
ANSWER:D
Question: How many of the positive factors of 19 are not factors of 29?
A.0
B.1
C.2
D.3
Answer: B.1
Explanation: Factors of 19 - 1, 19
factors of 29- 1, 29
Comparing both, we have three factors of 19 which are not factors of 29- 19,
The answer is B
Question: A train 130 m long crosses a platform with a speed of 70 kmph in 20 sec; find the length of the platform?
A.150
B.145
C.165
D.162
Answer: D.162
Explanation: D = 130 + x
T = 20
S = 130+x/15 * 18/5 = 70 kmph.
=> (130+x) * 18 = 5250
=> 130 + x = 292 => x= 162 m
Answer: D
Question: A shopkeeper forced to sell at cost price, uses a 850 grams weight for a kilogram. What is his gain percent?
A.17.65%
B.9%
C.11.11%
D.12 %
Answer: A.17.65%
Explanation: Shopkeeper sells 850g instead of 1000g.
So, his gain = 1000 - 850 = 150g.
Thus, %Gain = (150 *100)/850 = 17.65%.
answer : OPTION A
Question: A store sells chairs and tables. If the price of 2 chairs and 1 table is 60% of the price of 1 chair and 2 tables, and the price of 1 table and 1 chair is $72, what is the price, in dollars, of 1 table? (Assume that every chair has the same price and every table has the same price.)
A.55
B.84
C.63
D.75
Answer: C.63
Explanation: LET C= CHAIR ; T =TABLE
2C+1T = 0.6 (1C + 2T) OR C( 2-0.6) = 1.2T -1T OR 1.4C = 0.2 T THEREFORE C= 0.2/1.4 T = 1/7 T
IC +1T =72 OR 1/7T + 1T =60 THEREFORE T= 72*7/8 =63
C
Question: Raja sold two cycles, each for Rs.990. If he made 10% profit on the first and 10% loss on the second, what is the total cost of both cycles?
A.2000
B.6700
C.3400
D.7800
Answer: A.2000
Explanation: A
(10*10)/100 = 1%loss
100 --- 99
? --- 1980 => Rs.2000
Question: 90 percent of the members of a study group are women, and 60 percent of those women are lawyers. If one member of the study group is to be selected at random, what is the probability that the member selected is a woman lawyer?
A.0.34
B.0.44
C.0.54
D.0.64
Answer: C.0.54
Explanation: Say there are 100 people in that group, then there would be 0.9*0.60*100=54 women lawyers, which means that the probability that the member selected is a woman lawyer is favorable/total=54/100.
Answer: C
Question: In a group of 5 boys and 5 girls, four children are to be selected. In how many different ways can they be selected such that at least one boy should be selected?
A.100
B.110
C.179
D.205
Answer: D.205
Explanation: Number of ways to select four children is 10C4 = 210
Number of ways to choose only girls is 5C4 = 5
Number of ways that at least one boy is selected is 210 - 5 = 205
The answer is D.
Question: Ms. Lopez deposits $ 140 in an account that pays 20% interest, compounded semiannually. How much money will there be in the account at the end of one year?
A.$118.00
B.$120.00
C.$169.40
D.$122.00
Answer: C.$169.40
Explanation: Using Formula - A = P(1+r/n)^nt
Given
P=140
n=2
t=1
r=0.2
Substituting value in formula
A = 140(1+0.2/2)^2
A= 169.40$=C
Question: Two vessels P and Q contain 62.5% and 87.5% of alcohol respectively. If 2 litres from vessel P is mixed with 4 litres from vessel Q, the ratio of alcohol and water in the resulting mixture is?
A.19:1
B.19:4
C.19:8
D.19:5
Answer: D.19:5
Explanation: Quantity of alcohol in vessel P = 62.5/100 * 2 = 5/4 litres
Quantity of alcohol in vessel Q = 87.5/100 * 4 = 7/2 litres
Quantity of alcohol in the mixture formed = 5/4 + 7/2 = 19/4 = 4.75 litres
As 6 litres of mixture is formed, ratio of alcohol and water in the mixture formed
= 4.75 : 1.25 = 19:5.
Answer: D
Question: Three candidates contested an election and received 1136, 7636 and 11628 votes respectively. What percentage of the total votes did the winning candidate get?
A.45%
B.57%
C.34%
D.90%
Answer: B.57%
Explanation: B
57%
Total number of votes polled = (1136 + 7636 + 11628) = 20400.
Required percentage = (11628/20400 x 100)% = 57%.
Question: How many numbers between 100 and 630 are divisible by 2, 3, and 7 together?
A.112
B.77
C.267
D.13
Answer: D.13
Explanation: Explanation:
As the division is by 2, 3, 7 together, the numbers are to be divisible by: 2*3*7 = 42
The limits are 100 and 600
The first number divisible is 42*3 = 126
To find out the last number divisible by 42 within 630:
630/42 = 13
Hence, 42*15 = 630 is the last number divisible by 42 within 630
Hence, total numbers divisible by 2, 3, 7 together are (15 â€“ 2) = 13
ANSWER: D
Question: Jack and Jill collect ladybugs. Jack only collects the ones with 2 spots,
and Jill only collects the ones with 7 spots. Jack has 5 more ladybugs
than Jill. The total number of spots found on all of their ladybugs is 100.
How many ladybugs do they have in their combined collection?
A.17
B.21
C.23
D.25
Answer: D.25
Explanation: If x is the number of ladybugs that Jack has and y is the number of ladybugs that Jill has, then
x − y = 5 and 2x + 7y = 100. Multiplying the first of these equations by 5 and the second by 2
and adding gives 9(x + y) = 225. Hence, x + y = 25.
correct answer D