divelab/Sys2Bench huggingface dataset:
Question: The compound ratio of 2/3, 6/7, 1/3 and 1/8 is given by?
Options:
A)1/48
B)1/42
C)1/46
D)1/47
E)1/43
Rationale: 2/3 * 6/7 * 1/3 * 1/8 = 1/42
Answer: B
Answer: B
Question: By the how much is two-fifth of 200 greater than three -fifths of 25?
Options:
A)15
B)3
C)5
D)30
E)65
Rationale: Reqd no. = 2â„5 Ã— 200 - 3â„5 Ã— 25
= 80 - 15 = 65
Answer E
Answer: E
Question: What two-digit number is less than the sum of the square of its digits by 10 and exceeds their doubled product by 5?
Options:
A) 94
B) 99
C) 26
D) 73
E) None of the Above
Rationale: Let the digits be x and y. The number would be 10x + y.
We are given that 2xy + 5 = 10x +y = x^2 y^2 -10
Thus 2xy +5 = x^2 + y^2 - 10
x^2 + y^2 -2xy = 15
(x-y)^2 = 16
(x-y) = 4 or -4
Substituting the values of (x-y) in the equation 2xy +5 = 10x + y
x comes out to be 1 or 9... thus the two numbers can be 15 or 94
Thus the answer is A
Answer: A
Question: A can run 1.5 km distance in 2 min 20 seconds, while B can run this distance in 2 min 30 sec. By how much distance can A beat B?
Options:
A)90 m
B)100 m
C)120 m
D)180 m
E)190 m
Rationale: A takes time 2.20 minutes=140sec
B takes time 2.30 minutes=150sec
diffrence= 150-140=10sec
now we are to find distance covered in 10 sec by B
150sec=1500m
1sec=10m
10sec=10x10=100m
ANSWER:B
Answer: B
Question: subash can copy 50 pages in 10 hrs.subash and prakash together can copy 300 pages in 40 hours.in how much time prakash can copy 25 pages.
Options:
A)8
B)10
C)12
D)14
E)16
Rationale: subhas 's 1 hr copy page=50/10=5 page
(subhas+prakash)'s 1 hr copy page=300/40=7.5 page
from above prakash's 1 hr copy page= 2.5 page
so time taken in 30 page's copy =(25/2.5)=10 hrs
ANSWER:B
Answer: B
Question: In traveling from a dormitory to a certain city, a student went 1/5 of the way by foot, 2/3 of the way by bus, and the remaining 14 kilometers by car. What is the distance, in kilometers, from the dormitory to the city?
Options:
A)30
B)45
C)60
D)90
E)105
Rationale: Whole trip = distance by foot + distance by bus + distance by car
x = 1/5x + 2/3x + 14
x - 13/15x = 14
2/15x = 14 => so x = (15/2)*14 = 105Km
Answer E
Answer: E
Question: The radius of the two circular fields is in the ratio 3: 5 the area of the first field is what percent less than the area of the second?
Options:
A)24%
B)74%
C)69%
D)64%
E)54%
Rationale: r = 3 πr2 = 9
r = 5 πr2 = 25
25 π – 16 π
100 ---- ? => 64%
Answer: D
Answer: D
Question: If b is a positive integer, then 3^b + 3^(b) =
Options:
A)3^(b + 1)
B)2^(b + 1)
C)2(3^b)
D)2b^(b + 1)
E)3(2^b)
Rationale: If b is a positive integer,3^b+3^b=2(3^b)
option C is answer
Answer: C
Question: On a race track a maximum of 5 horses can race together at a time. There are a total of 25 horses. There is no way of timing the races. What is the minimum number Q of races we need to conduct to get the top 3 fastest horses?
Options:
A)5
B)7
C)8
D)10
E)11
Rationale: Q=7 is the correct answer.
Good solution Buneul.B
Answer: B
Question: The sequence a1, a2, a3, a4. a5 is such that an = a n-1 +5 for 2≤ n ≤ 5. If a5 = 33 what is the value of a1 ?
Options:
A)1
B)6
C)13
D)16
E)21
Rationale: Here, each value of an is the previous value plus 5
Since the numbers are less, the fastest way to solve this problem is to successively subtract 5 from a5 till you reach a1
a5 = 33
a4 = 29
a3 = 23
a2 = 18
a1 = 13 <<<< Ans C
Answer: C
Question: he average weight of 8 persons increases by 2.5 kg when a new person comes in place of one of them weighing 60 kg. What might be the weight of the new person ?
Options:
A)75 kg
B)55 kg
C)80 kg
D)85 kg
E)25 kg
Rationale: Explanation:
Total weight increased = (8 x 2.5) kg = 20 kg.
Weight of new person = (60 + 20) kg = 80 kg.
Answer: C
Answer: C
Question: A train running at the speed of 60 km/hr crosses a pole in 30 sec. What is the length of the train?
Options:
A)535 m
B)178 m
C)186 m
D)168 m
E)500 m
Rationale: Speed = 60 * 5/18
= 50/3 m/sec
Length of the train
= speed * time
= 50/3 * 30
= 500 m
Answer:E
Answer: E
Question: During a car trip, Maria stopped to rest after she traveled 1/2 of the total distance to her destination. she stopped again after she traveled 1/4 of the distance remaining between her first stop and her destination, and then she drove the remaining 135 miles to her detination. What was the total distance, in miles from Maria's starting point to her destination?
Options:
A)280
B)320
C)360
D)420
E)480
Rationale: Easy 360 is the answer.
3/4 ( x/2) = 135
x = 135 * 8 /3 = 360.
Answer C
Answer: C
Question: A soccer team played 130 games and won 60 percent of them. How many games did it win?
Options:
A)84
B)94
C)100
D)125
E)78
Rationale: 60% of 130=x
0.60*130 = x
78=x
answer :E
Answer: E
Question: Among the employees of a certain company, 51 percent of the employees are male and 49 percent are female. In this company 70 percent of the male employees are married and 50 percent of the female employees are married. If one employee in the company is randomly selected, approximately what is the probability that he or she is NOT married?
Options:
A) 0.3
B) 0.6
C) 0.5
D) 0.4
E) 0.7
Rationale: Much faster: draw 4 quadrants
______________Male (51%)_____Female (49%)
Married :__________70%____________50%
Not Married:_______30%____________50%
Therefore: the probability of picking one random person Not Married (he or she) is: 0,51 x 0,30 + 0,50 x 0,50 = 0,15 + 0,25 (approx.)
Solution: approx. 0,4 (answer D)
Answer: D
Question: Set M contains numbers that satisfy the condition that, if integer x is in the set then x+2x will also be in the set M. If -4 is one of the value in the set, which of the following numbers must also be present in the set M.
I. -12
II. -1
III. 2
Options:
A)I only
B)II only
C)I and II only
D)II and III only
E)I, II and III
Rationale: Notice that we are askedwhich of the following numbers MUST also be present in the set MnotCOULD be in the set.
Now, if -4 is in the set, then -4-8=-12mustbe in the set. Could -1 or2 be in the set?sure no.
Answer: A.
Answer: A
Question: A man sold 20 articles for $60 and gained 20%. How many articles should he sell for $70 to incur a loss 20%?
Options:
A)45
B)35
C)40
D)50
E)48
Rationale: Production cost per article: $60*(100%-20%) / 20 = $2.40
Required production costs for a loss of 20%: $70*(100% + 20%) = $84
Number of articles to be sold for $84 to incur a 20% loss: $84 / $2.40 = 35
Thus, solution B is correct.
Answer: B
Question: J and M were each paid x dollars in advance to do a certain job together. J worked on the job for 12 hours and M worked for 4 hours less than J. If M gave J y dollars of her payment so that they would have received the same hourly wage, what was the dollar amount, in terms of y, that J was paid in advance?
Options:
A)a)4y
B)b)5y
C)c)6y
D)d)8y
E)e)9y
Rationale: J and M were both paid x dollars
If M gave Y dollars from her X to J then at the end
J will have X+Y dollars
M will have X- Y dollars
Now since the hourly wages have to be same then
Hourly wage of J = (X+Y) / 12 (Since J worked for 12 hrs)
Hourly wage of M = (X-y) /8 (Since M worked 4 hrs less than J)
Equating both
(X+Y)/12=(X-Y)/8
on simplifying X=5y
Answer B
Answer: B
Question: Find the simple interest on Rs. 70,400 at 16 2/3% per annum for 9 months.
Options:
A)s.8500
B)s.8000
C)s.7500
D)s.8800
E)s.6500
Rationale: P = Rs.70400,R = 50/3% p.a and T = 9/12 years = 3/4years.
S.I. = (P*R*T)/100 = Rs.(70,400*(50/3)*(3/4)*(1/100))
= Rs.8800
Answer is D.
Answer: D
Question: The C.P of 15 books is equal to the S.P of 18 books. Find his gain% or loss%?
Options:
A)16 2/3% loss
B)66 2/3% loss
C)56 2/3% loss
D)26 2/3% loss
E)96 2/3% loss
Rationale: Explanation:
15 CP = 18 SP
18 --- 3 CP loss
100 --- ? => 16 2/3% loss
Answer: A
Answer: A
Question: City A to city B, David drove for 1 hour at 60 mph and for 3 hours at 90 mph. What was the average speed for the whole trip?
Options:
A)82.5
B)57.5
C)58.2
D)59
E)62
Rationale: The total distance is 1×60+3×90=330
And the total time is 4 hours. Hence,
Average Speed=(Total Distance/Total Time)=330/4=82.5
Answer : A
Answer: A
Question: The banker's discount on Rs. 1600 at 15% per annum is the same as true discount on Rs. 1680 for the same time and at the same rate. The time is:
Options:
A)3 months
B)4 months
C)5 months
D)6 months
E)7 months
Rationale: S.I. on Rs. 1600 = T.D. on Rs. 1680.
Rs. 1600 is the P.W. of Rs. 1680, i.e., Rs. 80 is on Rs. 1600 at 15%.
Time = (100x80)/(1600x15)= 1/3 year = 4 months
answer : B
Answer: B
Question: The H.C.F of two numbers is 8. Which one of the following can never be their L.C.M?
Options:
A)8
B)12
C)60
D)72
E)None
Rationale: Solution
H.C.F of two numbers divides their L.C.M exactly.
Clearly, 8 is not a factor of 60.
Answer C
Answer: C
Question: A 1200 m long train crosses a tree in 80 sec, how much time will I take to pass a platform 1000 m long?
Options:
A)288
B)146.66
C)188
D)180
E)12
Rationale: L = S*T
S= 1200/80
S= 15 m/Sec.
Total length (D)= 2200 m
T = D/S
T = 2200/15
T = 146.66Sec
Answer:B
Answer: B
Question: A loan has a variable interest rate that fluctuates between 8% and 10% of the base payment per month. If base payments remain at $350 each month and an additional monthly surcharge of 1% is added to the combined (base + interest), what would be the greatest possible payment due in any given month?
Options:
A)$385.35
B)$386.80
C)$387.50
D)$388.35
E)$388.85
Rationale: The maximum interest in one month is 10%*$350=$35.
The combined payment (base plus interest) is $350 + $35 = $385.
The greatest possible payment is: 1.01*$385=$388.85.
The answer is E.
Answer: E
Question: 12 buckets of water fill a tank when the capacity of each tank is 13.5 litres. How many buckets will be needed to fill the same tank, if the capacity of each bucket is 9 litres?
Options:
A)15 bukets
B)17 bukets
C)18 bukets
D)19 bukets
E)None of these
Rationale: Explanation:
Capacity of the tank = (12*13.5) litres
= 162 litres
Capacity of each bucket	= 9 litres.
So we can get answer by dividing total capacity of tank by total capacity of bucket.
Number of buckets needed = (162/9) = 18 buckets
Option C
Answer: C
Question: There are two inlets and one outlet to a cistern. One of the inlets takes 7/2 hours to fill up the cistern and the other inlet takes twice as much time to fill up the same cistern. Both of the inlets are turned on at 8:30 AM with the cistern completely empty, and at 10:30AM, the outlet is turned on and it takes 1 more hour to fill the cistern completely. How much time does the outlet working alone takes to empty the cistern when the cistern is full?
Options:
A)2 hours
B)2.5 hours
C)3 hours
D)3.5 hours
E)4 hours
Rationale: The combined inflow rate of the two inlets is 2/7 + 1/7 = 3/7 cistern/hour. Thus, working together, it takes 7/3 hours (time is reciprocal of rate) to fill the cistern.
From 8:30 AM to 10:30 AM, so in 2 hours, the inlet pipes will fill (time)*(rate) = 2*3/7 = 6/7 th of the cistern .
Then the outlet is turned on and the remaining 1/7 th of the cistern is filled in 1 hour.
Letting x to be the rate of the outlet, we would have: 3/7 - x = 1/7 --> x = 2/7 cistern/hour, which means that it takes 7/2 hours the outlet working alone to empty the cistern.
Answer: D.
Answer: D
Question: There are a lot of houses such that the numbers of their doorplates are odd numbers and the first number of the doorplates is 545, the last number of the doorplates is 715. How many houses are there?
Options:
A)86
B)71
C)81
D)91
E)101
Rationale: So it starts from 545 and goes like 547, 549,...... 715. and both first and last number are inclusive. Since every other number is odd, it's just 1/2 of the numbers and since it starts with an odd and ends with an odd inclusive add one to the result.
i.e., ([715-545][/2]+1 = 86
Ans A
Answer: A
Question: Set S is the prime integers between 0 and 50. If three numbers are chosen randomly from set S, what is the probability that the sum of these three numbers is odd?
Options:
A)15/56
B)3/8
C)15/28
D)4/5
E)3/4
Rationale: Total number of combinations=15C3=455................(1)
Total number of combinations including 2 and two other numbers=14C2=91......................(2)
Therefore the difference ie. (1)-(2) is the set of 3 primes without 2=(455-91)=364
So, probability=364/455=4/5
D
Answer: D
Question: A working mom wakes up every day at 7 am and goes to sleep at 11 pm. She works 8 hours a day. Spends 2 hours working out at the gym. She spends 1.5 hours cooking dinner and doing dishes. She spends .5 of an hour giving her daughter a bath. She spends 1 hour helping with homework and getting her daughter ready for bed. She spends another. 5 of an hour packing lunches for the family for the next day. She spends .5 of an hour cleaning the house and 2 hours taking a shower and reading or watching t.v. before she goes to sleep. What percent of her day does she spend at work?
Options:
A)60
B)50
C)70
D)55
E)40
Rationale: 8+2+1.5+.5+1+.5+.5+2=16= total number of hours
8/16=.05=50 percemt
The Answer is B
Answer: B
Question: How many integer values W are there for x such that 1 < 3x + 5 < 17?
Options:
A)Two
B)Three
C)Four
D)Five
E)Six
Rationale: 1 < 3x + 5 < 17
=> -4 < 3x < 12
=> -4/3 < x < 4
x can take integer values W -1,0 , 1 , 2 , 3
Answer D
Answer: D
Question: P and Q can complete a work in 15 days and 10 days respectively. They started the work together and then Q left after 2 days. P alone completed the remaining work. The work was finished in --- days.
Options:
A)12
B)16
C)20
D)24
E)28
Rationale: Explanation :
Work done by P in 1 day = 1/15
Work done by Q in 1 day = 1/10
Work done by P and Q in 1 day = 1/15 + 1/10 = 1/6
Work done by P and Q in 2 days = 2 × (1/6) = 1/3
Remaining work = 1 – 1/3 = 2/3
Time taken by P to complete the remaining work 2/3 = (2/3) / (1/15) = 10 days
Total time taken = 2 + 10 = 12 days
Answer : Option A
Answer: A
Question: If n ≠ 0, which of the following must be greater than n?
I. 2n
II. n^2
III. 2 - n
Options:
A)I only
B)II only
C)I and II only
D)II and III only
E)None
Rationale: n ≠ 0 => n = negative or n = positive
if n = negative:
2n < n (n = -1 then 2n = -2 => -2 < -1)
n^2 > n (n =-1 then n^2 = 1 => n^2 > n)
2 - n > n (n = -1 then 2--1 = 2+1=3 => 2-n > n)
but if n = positive:
n^2 > n (n = 2 then n^2 = 4 => n^2 > n) => II
2 - n < n(n =2 then 2-2 = 0)
=> only II
=>answer is B
Answer: B
Question: How many boxes do you need if you have to pack 240 pairs ornamental bangles into boxes that each hold 2 dozens of bangles?
Options:
A)40
B)35
C)20
D)25
E)30
Rationale: C
20
240 pairs of bangles = 480 bangles =40 dozens.
40 ÷ 2 = 20 boxes.
Answer: C
Question: Find the sum of first 26 natural numbers
Options:
A)470
B)468
C)465
D)351
E)485
Rationale: Explanation:
Sum of n natural numbers
=n(n+1)/2
=26(26+1)/2=26(27)/2=351
Answer: Option D
Answer: D
Question: What is the place value of 6 in the numeral 4634?
Options:
A)450
B)500
C)600
D)800
E)840
Rationale: Option 'C'
6 * 100 =600
Answer: C
Question: A man swims downstream 48 km and upstream 32 km taking 8 hours each time; what is the speed of the current?
Options:
A)1
B)2
C)3
D)4
E)5
Rationale: 48 --- 8 DS = 6
? ---- 1
32 ---- 8 US = 4
? ---- 1 S = ?
S = (6- 4)/2 = 1
Answer: A
Answer: A
Question: In a mixture 60 litres, the ratio of milk and water 2 : 1. If this ratio is to be 1 : 2, then the quanity of water to be further added is:
Options:
A)20
B)30
C)40
D)50
E)60
Rationale: Quantity of milk = (60 x 2/3) litres = 40 litres.
Quantity of water in it = (60- 40) litres = 20 litres.
New ratio = 1 : 2
Let quantity of water to be added further be x litres.
Then, milk : water = (40/(20 + x))
Now, (40/(20 + x))= 1/2
= 20 + x = 80
= x = 60.
Therefore, Quantity of water to be added = 60 litres.
Answer is E.
Answer: E
Question: If it is assumed that 60 percent of those who receive a questionnaire by mail will respond and 300 responses are needed, what is the minimum number of questionnaires that should be mailed?
Options:
A)400
B)420
C)480
D)500
E)600
Rationale: Minimum no of mail to be sent for getting 300 responses at 60%
= 300/0.6 = 500
Option D
Answer: D
Question: In a 1000 m race, A beats B by 50 m and B beats C by 100 m. In the same race, by how many meters does A beat C?
Options:
A)145
B)772
C)552
D)288
E)132
Rationale: By the time A covers 1000 m, B covers (1000 - 50) = 950 m.
By the time B covers 1000 m, C covers (1000 - 100) = 900 m.
So, the ratio of speeds of A and C =
1000/950 * 1000/900 = 1000/855 So, by the time A covers 1000 m, C covers 855 m.
So in 1000 m race A beats C by 1000 - 855 = 145 m.
AnswerA
Answer: A
Question: Sum of two numbers prime to each other is 20 and their L.C.M. is 99. What are the numbers?
Options:
A)8 and 12
B)14 and 6
C)19 and 1
D)11 and 9
E)12 and 9
Rationale: As two numbers are prime, only two options satisfy ie option C and D.
but option C will not make the product of numbers i.e 99
ANSWER:D
Answer: D
Question: Of the 600 residents of Clermontville, 35% watch the television show Island Survival, 40% watch Lovelost Lawyers and 50% watch Medical Emergency. If all residents watch at least one of these three shows and 18% watch exactly 2 of these shows, then how many Clermontville residents C watch all of the shows?
Options:
A) 150
B) 108
C) 42
D) 21
E) -21
Rationale: OA is D.
100= A+B+C-AB-AC-BC+ABC, which is the same as the following formula
100= A+B+C+(-AB-AC-BC+ABC+ABC+ABC)-2ABC.
The term between parantheses value 18% so the equation to resolve is
100=35+40+50-18-2ABC
therefore the value of ABC is 3.5% of 600,C is 21. D is the correct answer
Answer: D
Question: n a fort, there are 1200 soldiers. If each soldier consumes 3 kg per day, the provisions available in the fort will last for 30 days. If some more soldiers join, the provisions available will last for 25 days given each soldier consumes 2.5 kg per day. Find the number of soldiers joining the fort in that case?
Options:
A)289
B)528
C)273
D)279
E)270
Rationale: Assume x soldiers join the fort. 1200 soldiers have provision for 1200 (days for which provisions last them)(rate of consumption of each soldier)
= (1200)(30)(3) kg.
Also provisions available for (1200 + x) soldiers is (1200 + x)(25)(2.5) k
As the same provisions are available
=> (1200)(30)(3) = (1200 + x)(25)(2.5)
x = [(1200)(30)(3)] / (25)(2.5) - 1200 => x = 528.
Answer: B
Answer: B
Question: A chemical supply company has 60 liters of a 35% HNO3 solution. How many liters of pure undiluted HNO3 must the chemists add so that the resultant solution is a 50% solution?
Options:
A)18
B)15
C)20
D)24
E)30
Rationale: 60 liters of a 35% HNO3 solution means HNO3 = 21 liters in 60 liters of the solution.
Now, let x be the pure HNO3 added.
As per question,
21 + x = 50% of (60 + x)
or x =18 Hence, A
Answer: A
Question: Given that a “24-inch pizza” means circular pizza with a diameter of 12 inches, changing from an 8-inch pizza to a 24-inch pizza gives you approximately what percent increase in the total amount of pizza?
Options:
A)330
B)500
C)670
D)800
E)125
Rationale: area of 8 inch pizza= 4*4*pi=16 pi
area of 24 inch pizza =12*12*pi=144 pi
128/16*100=800 increase
hence answer is D
Answer: D
Question: If c ≠ 1 and if dc/(d - c) = 1, what is the value of d in terms of c?
Options:
A)(c-1)/c
B)c/(1-c)
C)c/(c + 1)
D)(c + 1)/c
E)(1 - c)/c
Rationale: This question comes with a particular 'quirk' (one that you probably won't see on Test Day). The GMAT won't test you on the concept of undefined numbers (re: numbers divided by 0), so any time that this concept is a possibility, the question writers have to add a restriction that removes the option that a 0 could occur in the denominator.
Here, we're told that B CANNOT = 1, which is a bit strange because that restriction doesn't seem to impact the original equation much. In fact, it impacts JUST ONE of the answer choices - so you have to ask WHY that restriction is even there. It's actually because that one answer is the correct one.
Final Answer:
B
Answer: B
Question: P can complete a work in 12 days working 8 hours a day.Q can complete the same work in 8 days working 10 hours a day. If both p and Q work together,working 8 hours a day,in how many days can they complete the work?
Options:
A)60/11
B)61/11
C)71/11
D)72/11
E)70/11
Rationale: Explanation:
P can complete the work in (12 * 8) hrs = 96 hrs
Q can complete the work in (8 * 10) hrs=80 hrs
P's 1 hour work=1/96 and Q's 1 hour work= 1/80
(P+Q)'s 1 hour's work =(1/96 + 1/80)=11/480
so both P and Q will finish the work in 480/11hrs
Number of days of 8 hours each =(480/11 * 1/8)=60/11
ANSWER IS A
Answer: A
Question: Find the number of different 4-letter words with or without meaning that can be formed from the letters of the word " NUMBER"
Options:
A)340
B)360
C)320
D)420
E)440
Rationale: There are 6 letters in the word "NUMBER". So the number of 4-letter words 6P4 =360 Answer : B
Answer: B
Question: How many 3 digit numbers can be formed from the digits 2, 3, 5, 6, 7 and 9 which are divisible by 5 and none of the digits is repeated?
Options:
A)20
B)16
C)8
D)24
E)29
Rationale: Explanation :
A number is divisible by 5 if the its last digit is a 0 or 5
We need to find out how many 3 digit numbers can be formed from the 6 digits (2,3,5,6,7,9)
which are divisible by 5.
Since the 3 digit number should be divisible by 5, we should take the digit 5
from the 6 digits(2,3,5,6,7,9) and fix it at the unit place.
There is only 1 way of doing this
1
Since the number 5 is placed at unit place, we have now five digits(2,3,6,7,9) remaining.
Any of these 5 digits can be placed at tens place
5 1
Since the digits 5 is placed at unit place and another one digits is placed at tens place,
we have now four digits remaining. Any of these 4 digits can be placed at hundreds place.
4 5 1
Required Number of three digit numbers = 4 x 5 x 1 = 20.. Answer : Option A
Answer: A
Question: In a certain animal shelter, the ratio of the number of dogs to the number of cats is 15 to 7. If 8 additional cats were to be taken in by the shelter, the ratio of the number of dogs to the number of cats would be 15 to 11. How many dogs are in the shelter?
Options:
A)15
B)25
C)30
D)45
E)60
Rationale: This ratio question can be solved in a couple of different ways. Here's an Algebraic approach...
We're told that the ratio of the number of dogs to the number of cats is 15:7. We're then told that 8 more cats are added to this group and the ratio becomes 15:11. We're asked for the number of dogs.
Algebraically, since the number of dogs is a multiple of 15 and the number of cats is a multiple of 7, we can write this initial relationship as...
15X/7X
When we add the 18 cats and factor in the 'ending ratio', we have an equation....
15X/(7X+8) = 15/11
Here we have 1 variable and 1 equation, so we can solve for X....
(15X)(11) = (7X+8)(15)
(X)(11) = (7X+8)(1)
11X = 7X + 8
4X = 8
X = 2
With this X, we can figure out the initial number of dogs and cats...
Initial dogs = 15X = 15(2) = 30
Final Answer: C
Answer: C
Question: Before being simplified, the instructions for computing income tax in country R were to add 7 percent of one's annual income to the average(arithmetic mean) of 100 units of Country R's currency and 1 percent of one's annual income. Which of the following represents the simplified formula for computing the income tax, in country R's currency, for a person in that country whose annual income is I?
Options:
A)50 + I/200
B)50 + 15I/100
C)50+ I/40
D)100+ I/50
E)100+ 3I/100
Rationale: Income of a person is I
7 percent of ones annual income = 7I/100
100 units of Country R's currency = 100
1 percent of one's annual income = I/100
Average of 100 units and 1 percent annual income = 50 + I/200
Sum of average and 7 percent = 7I/100 + 50 + I/200
= 50 + 15I/200
So answer is B.
Answer: B
Question: 10men and 10 women are there, they dance with each other, is there possibility that 2 men are dancing with same women and vice versa?
Options:
A)22
B)20
C)13
D)5
E)none
Rationale: in question they gave "they dance with each other" , so there is no possibility that 2 men are dancing with same women...
ANSWER:E
Answer: E