divelab/Sys2Bench huggingface dataset:
Question: A 360 meter long train crosses a man standing on the platform in 6 sec. What is the speed of the train?
Options:
A)229
B)108
C)278
D)216
E)112
Rationale: S = 360/6 * 18/5 = 216 kmph
Answer: D
Answer: D
Question: 7 points are marked on a straight line and another 5 points are marked on a second straight line with no points in common. How many triangles can be constructed with vertices from among the above points?
Options:
A)91
B)105
C)175
D)21
E)14
Rationale: getting the answer 175 which is not in the choices, what is the source of the problem?
7C2* 5C1 + 5C2* 7C1 = 175
C
Answer: C
Question: It takes 30 days to fill a laboratory dish with bacteria. If the size of the bacteria doubles each day, how long did it take for the bacteria to fill 1/32 of the dish?
Options:
A)25
B)26
C)27
D)28
E)29
Rationale: The bacteria doubles each day, so after 29 days, the dish was half full.
After 28 days, the dish was one quarter full.
After 27 days, the dish was one eighth full.
After 26 days, the dish was one sixteenth full.
After 25 days, the dish was 1/32 full.
The answer is A.
Answer: A
Question: Mr. Evans will states that each of his children will receive an equal share of his estate and that his grandchildren will split a portion of the estate that is equal to the share received by each of his children. If Mr. Evans has 3 children and 5 grandchildren, then approximately what percentage of Mr. Evans estate will each grandchild receive?
Options:
A)20%
B)17%
C)5.0%
D)3.3%
E)2.8%
Rationale: 25/5=5
Answer : C
Answer: C
Question: X and Y started a business with capitals Rs. 20000 and Rs. 25000. After few months Z joined them with a capital of Rs. 30000. If the share of Z in the annual profit of Rs. 50000 is Rs. 14000, then after how many months from the beginning did Z join?
Options:
A)6
B)7
C)8
D)9
E)5
Rationale: Investments of X, Y and Z respectively are Rs. 20000, Rs. 25000 and Rs. 30000
Let investment period of Z be x months.
Ratio of annual investments of X, Y and Z is (20000 * 12) : (25000 * 12) : (30000 * x)
= 240 : 300 : 30x = 8 : 10 : x
The share of Z in the annual profit of Rs. 50000 is Rs. 14000.
=> [x/ (18 + x)] 50000 = 14000 => [x/ (18 + x)] 25 = 7
=> 25x = 7x + (18 * 7) => x = 7 months.
Z joined the business after (12 - 7) months. i.e., 5 months.
Answer:E
Answer: E
Question: Farmer Charlie has a chicken farm. On a certain day, Charlie calculates in how many days he will run out of chicken-food. He notices that if he would sell 75 of his chickens, he could feed the remaining chickens twenty days longer with the chicken-food he has, and that if he would buy 100 extra chickens, he would run out of chicken-food fifteen days earlier.
How many chickens does farmer Charlie have?
Options:
A)100
B)500
C)300
D)400
E)600
Rationale: C
300
Let n be the number of chickens and let d be the number of days in which Charlie will run out of chicken-food with this number of chickens. The total amount of chicken-food always equals the number of chickens multiplied by the number of days the food lasts. Therefore, the total amount of chicken-food equals n × d.
If Charlie would sell 75 of his chickens, he could feed the remaining chickens twenty days longer, so the total amount of chicken-food would then equal
( n - 75 ) × ( d + 20 ).
But the total amount of chicken-food does not change, so
( n - 75 ) × ( d + 20 ) = n × d
which can be rewritten to equation 1:
d = 4/15 × n - 20.
If Charlie would buy 100 extra chickens, he would run out of chicken-food fifteen days earlier, so the total amount of chicken-food would then equal
( n + 100 ) × ( d - 15 ).
But the total amount of chicken-food does not change, so
( n + 100 ) × ( d - 15 ) = n × d
which can be rewritten to equation 2:
d = 3/20 × n + 15.
Combining equations 1 and 2 gives:
4/15 × n - 20 = 3/20 × n + 15.
Solving this equations gives n = 300, so farmer Charlie has 300 chickens.
Answer: C
Question: If the perimeter of a rectangular garden is 800 m, its length when its breadth is 100 m is?
Options:
A)300 m
B)777 m
C)200 m
D)167 m
E)128 m
Rationale: 2(l + 100) = 800 => l
= 300 m
Answer:A
Answer: A
Question: At an election 2 candidates are participated a candidate got 30% of votes and defeated by 5000 votes. 100 votes are invalid. Find the total polled votes?
Options:
A)11520
B)12600
C)15000
D)13560
E)12560
Rationale: winners votes = 100-30 = 70%
invalid votes = 100
polled votes = [(100*5000)/(2*70-100)]+100 = 12600
Answer is B
Answer: B
Question: The sum of how many terms of the series 6 + 12 + 18 + 24 + ... is 1800 ?
Options:
A)19
B)23
C)13
D)26
E)24
Rationale: This is an A.P. in which a = 6, d = 6 and Sn = 1800
Then,	n/2*	[2a + (n - 1)d] = 1800
n/2*	[2 x 6 + (n - 1) x 6] = 1800
2
3n (n + 1) = 1800
n(n + 1) = 600
n^2 + n - 600 = 0
n^2 + 25n - 24n - 600 = 0
n(n + 25) - 24(n + 25) = 0
(n + 25)(n - 24) = 0
n = 24
Number of terms = 24
Answer is E.
Answer: E
Question: In the number 11,0AB, A and B represent the tens and units digits, respectively. If 11,0AB is divisible by 55, what is the greatest possible value of B × A?
Options:
A)0
B)5
C)10
D)15
E)25
Rationale: You should notice that 55*2=110 so 11,000 is divisible by 55: 55*200=11,000 (or you can notice that 11,000 is obviously divisible by both 5 and 11 so by 55) --> B*A=0*0=0.
Next number divisible by 55 is 11,000+55=11,055: B*A=5*5=25 (next number won't have 110 as the first 3 digits so we have only two options 0 and 25).
Answer: E
Answer: E
Question: If the average (arithmetic mean) of 5 positive temperatures is y degrees Fahrenheit, then the sum of the 3 greatest of these temperatures, in degrees Fahrenheit, could be:
Options:
A)6y
B)4y
C)5y/3
D)3y/2
E)3y/5
Rationale: The sum of three greatest should be more than sum of two lowest.
The total sum is; 5y
A. 6y; 6y is more than 5y. Not possible.
B. 4y; 5y-4y=y(Possible)
C. 5y/3; 10y/3; 10y/3 > 5y/3. Not possible
D. 3y/2; 7y/2; 7y/2 > 3y/2. Not possible
E. 3y/5; 22y/5; 22y/5 > 3y/5. Not possible.
Ans:B
Answer: B
Question: A trade analyst announced 10% reduction in the unit price of bike. As a result, the sales volume went up by 5%. What was the net effect on the sales revenue?
Options:
A)no change
B)decreases by 5.5%
C)increases by 5.5%
D)increases by 5%
E)None of these
Rationale: Explanation :
Reduction of price = (100 -10)% = 90% = 0.9
Increase of sale = (100+5)% = 105% = 1.05
Total effect = 0.9 X 1.05 =94.5%, Decreases by 5.5%
Answer : B
Answer: B
Question: E is the sister of F and G. H is F's daughter. I is F's son. Which of the following statements is definitely false?
Options:
A)E is F's sister
B)G is E's uncle
C)F is G's brother
D)G is I's uncle
E)I is G's nephew
Rationale: Explanation:
E,F and G are children of same parents. So. G cannot be E's uncle.
Answer: B
Answer: B
Question: Three partner’s A,B,C start a business. Twice A’s capital is equal to thrice B’s capital and B’s capital is four times C’s capital. Out of a total profit of Rs.16500 at the end of the year, B’s share is:
Options:
A)Rs.4000
B)Rs.6000
C)Rs 7500
D)Rs 7500
E)Rs.6600
Rationale: Let C = x. Then B = 4x and 2A = 3 * 4x = 12x. or A = 6x.
Therefore, A : B : C = 6x : 4x : x = 6 : 4 : 1.
Therefore, B’s capital = Rs. 16500 * 4/11
= Rs.6000.
ANSWER:B
Answer: B
Question: If 3<x<6<y<7, then what is the greatest possible positive integer difference of x and y?
Options:
A)3
B)4
C)5
D)6
E)7
Rationale: 3 < x < 6 < y < 7;
3 < x
y < 7
3 + y < x + 7
y - x < 4.
Positive integer difference is 3(for example y = 6.5 and x = 3.5)
Answer:A.
Answer: A
Question: N, which is a set of natural numbers is partitioned into subsets S1 = {1}, S2 = {2,3}, S3 = {4,5,6}, S4 = {7,8,9,10} and so on. The sum of the elements of the subset S50 is
Options:
A)(a) 61250
B)(b) 65525
C)(c) 42455
D)(d) 62525
E)(e) 55425
Rationale: The question is based heavily on pattern-matching skills, and is far more 'layered' than what you would likely see on the Official GMAT on this subject. You'll likely find it easiest to define the patterns one-at-a-time, so that you can see how they impact the question.
To start, we're given information on the sub-sets of numbers:
-The 1st set has 1 number
-The 2nd set has 2 numbers
-The 3rd set has 3 numbers
Etc.
So the 50th set will have 50 numbers in it.
Since the numbers in the subsets are consecutive, we can figure out ALL of the numbers that show up BEFORE we get to the 50th set by usingbunching...
The 1st set has 1 number and the 49th set has 49 numbers....1 + 49 = 50 numbers
The 2nd set has 2 numbers and the 48th set has 48 numbers...2 + 48 = 50 numbers
Etc.
This pattern will continue all the way down to...
The 24th set has 24 numbers and the 26th set has 26 numbers...24 + 26 = 50 numbers
Thus, we have 24 'pairs' of 50 numbers and one set (the 25th set with 25 numbers) that doesn't have a 'pair-match'...
So 24(50) + 25 = 1225 consecutive numbers exist in the 49 sets BEFORE the 50th set - that's the numbers 1 to 1225, inclusive...
Thus, the 50th set starts with 1226 and ends with 1275. We can use 'bunching' again to figure out the sum of this group (although there's no 'middle term' this time)...
25(1226+1275) =
25(2501) =
62525
D
Answer: D
Question: 19! is equal to which of the following?
Options:
A)121,645,100,408,832,916
B)121,645,100,408,832,225
C)121,645,100,408,832,424
D)121,645,100,408,832,378
E)121,645,100,408,832,000
Rationale: After 4!, the units digit of every factorial is 0.
5!=120
6!=720
etc...
The answer is E.
Answer: E
Question: A train overtakes 2 girls who are walking inthe opposite direction in which the train is going at the rate of 3 km/hour & 6km/hour and passes them completely in 36sec & 30 sec respectively. Find the length of the train is?
Options:
A)90 m
B)100 m
C)150 m
D)180 m
E)190 m
Rationale: Let the length of the train e x meter, and let the speed of train be y km/h, then
\inline x=\left ( y+3 \right )\frac{5}{18}\times 36 ........(1)
and \inline x=\left ( y+6\right )\frac{5}{18}\times 30 ........(2)
From eq (1) and (2), we get
\inline (y+3)\times 36 = ( y+6)\times 30
y = 12 km/h
\inline \therefore \inline x=(y+3)\times \frac{5}{18}\times 36
x= 150 m
C
Answer: C
Question: Ram and Shakil run a race of 2000m. First Ram gives Shakil a start of 200m and beats him by 1 minute.Next Ram gives shakil a start of 6 min and is beaten by 1000 meters . Find the time in minutes in which Ram and Shakil can run the race seperately.
Options:
A)12,18
B)10,18
C)10,12
D)8,10
E)8,9
Rationale: let speed of ram and shakil be x and y resp.
case1: ram gives a start of 200m and beats shakil by 1 minute.
2000/x - 1800/y= -60
2000/x= 1800/y -60---------------------(1)
case2: ram gives shakil a start of 6 min and is beaten by 1000 meters
distance travelled by shakil in 6 minutes= (6*60*y) meters = 360y meters
1000/x = (2000- 360y)/y------------------(2)
solve for x, y..
answer is x=8minutes, y= 10minutes
ANSWER:D
Answer: D
Question: A company plans to award prizes to its top 3 salespeople, with the largest prize going to the top salesperson, the next-largest prize to the next salesperson, and a smaller prize to the third-ranking salesperson. If the company has 6 salespeople on staff, how many different arrangements of winners are possible?
Options:
A)120
B)1,440
C)1,320
D)220
E)6
Rationale: [quote=Bunuel]A company plans to award prizes to its top 3 salespeople, with the largest prize going to the top salesperson, the next-largest prize to the next salesperson, and a smaller prize to the third-ranking salesperson. If the company has 6 salespeople on staff, how many different arrangements of winners are possible?
6*5*4
=120
Answer : A
Answer: A
Question: If you roll one fair six-sided die, what is the probability that the number is even or greater than 3?
Options:
A)1/2
B)1/3
C)2/3
D)3/4
E)5/6
Rationale: The numbers which satisfy the conditions are 2, 4, 5, and 6.
The probability is 4/6=2/3
The answer is C.
Answer: C
Question: There are 30 doors marked with numbers 1 to 30. There are 30 individuals marked 1 to 30.
An operation on a door is defined as changing the status of the door from open to closed or vice versa. All the doors are closed to start with. One at a time, one randomly chosen individual goes and operates the doors. The individual however operates only those doors which are a multiple of the number he/she is carrying. For example, the individual marked with number 5 operates the doors marked with 5, 10, 15, 20, 25, and 30. If every individual in the group gets one turn, then how many doors are open at the end?
Options:
A)0
B)1
C)2
D)4
E)5
Rationale: If a door is closed at the start, it requires an odd number of people to operate to be open at the end. Only the perfect squares have an odd number of factors.
The doors which are open at the end are: 1, 4, 9, 16, 25 for a total of 5 doors.
The answer is E.
Answer: E
Question: If x/4 years ago Roger was 14 years old and x/4 years from now he will be 4x years old, how old will he be 4x years from now?
Options:
A)31
B)35
C)30
D)40
E)28
Rationale: Assume the current age = a
a - x/4 = 14 (i)
a + x/4 = 4x
Or a = 15x/4 (ii)
Putting the value of a from (ii) in (i)
15x/4 - x/4 = 14
Or 14x/4 = 14 Therefore x = 4 and a = 15
4x years from now, age will be 15 + 4*4 = 31
Option A
Answer: A
Question: In a forest 110 deer were caught, tagged with electronic markers, then released. A week later, 50 deer were captured in the same forest. Of these 50 deer, it was found that 5 had been tagged with the electronic markers. If the percentage of tagged deer in the second sample approximates the percentage of tagged deer in the forest, and if no deer had either left or entered the forest over the preceding week, what is the approximate number of deer in the forest?
Options:
A)150
B)750
C)1,250
D)1,500
E)2,500
Rationale: The percentage of tagged deer in the second sample = 5/50*100=10%.
So, 150 tagged deers comprise 10% of total # of deers --> total # of deers = 110*10 = 1,100.
Answer: D.
Answer: D
Question: Each of the 47 members in a high school class is required to sign up for a minimum of one and a maximum of three academic clubs. The three clubs to choose from are the poetry club, the history club, and the writing club. A total of 14 students sign up for the poetry club, 22 students for the history club, and 20 students for the writing club. If 3 students sign up for exactly two clubs, how many students sign up for all three clubs?
Options:
A)1
B)2
C)3
D)4
E)5
Rationale: The total number in the three clubs is 14+22+20=56.
All 47 students signed up for at least one club.
3 of those students signed up for exactly one more club.
56 - 50 = 6 so 3 students must have signed up for exactly three clubs.
The answer is C.
Answer: C
Question: The product of x and y is a constant. If the value of x is increased by 30%, by what percentage must the value of y be decreased?
Options:
A)16%
B)23.07%
C)25%
D)30%
E)35%
Rationale: x*y = constt.
Let x = y = 100 in beginning
i.e. x*y = 100*100 = 10000
x (100) ---becomes---> 1.3x (130)
i.e. 130*New 'y' = 10000
i.e. New 'y' = 10000/130 = 76.92
i.e. y decreases from 100 to 76.92 i.e. Decrease of 23.07%
B
Answer: B
Question: Mike's age is 60 years. If he is 3 more than three times the age of his son, find the age of his son.
Options:
A)25years
B)22 years
C)20 years
D)18 years
E)19 years
Rationale: Let Mike's son age be x.
3 + 3x = 60
x = 19
Hence Mike's son age is 19 years
Answer : E
Answer: E
Question: In how many ways can you seat 9 people on a bench if one of them, Rohit, does not want to sit on the middle seat or at either end?
Options:
A)720
B)1720
C)2880
D)5040
E)241920
Rationale: Since Rohit does not want to sit on the middle seat or at either end (3 chairs), then he can choose 6 chairs to sit. The remaining 8 people can sit in 8! ways. Thus the # of arrangements is 6*8! = 241,920.
Answer: E.
Answer: E
Question: On multiplying a number by 3, the product is a number each of whose digits is 7. What is the smallest such number?
Options:
A)259129
B)259219
C)259279
D)259259
E)None of the above
Rationale: Explanation:
Let's use hit and trial method here.
Smallest number from the given choices = 259129
259129 × 3 = 777387
Next highest number from the given choices = 259219
259219 × 3 = 777657
Next highest number from the given choices = 259259
259259 × 3 = 777777
Hence 259259 is the answer.
Answer: D
Answer: D
Question: A teacher will pick a group of 9 students from a group of 14 students that includes Bart and Lisa. If one of all the possible 9-student groups is picked at random, what is the probability of picking a group that includes both Bart and Lisa?
Options:
A)11/70
B)36/91
C)21/47
D)121/390
E)3/71
Rationale: Probability = Favorable Outcomes / Total Outcomes
Total Outcomes= Total No. of ways of Picking Group of 9 out of 14 = 14C9 = 14! / (9! * 5!) = 2002
Favorable Outcomes= Total No. of ways of Picking Group of 9 out of 14 such that B and L are always in the group (i.e. we only have to pick remaining two out of remaining 12 as B and L must be there is group) = 12C7 = 792
Hence,Probability=792/2002=36/91
Answer: Option B
Answer: B
Question: The radius of a semi circle is 6.3 cm then its perimeter is?
Options:
A)12.9
B)32.4
C)32.1
D)32.2
E)32.7
Rationale: 36/7 r = 6.3
= 32.4
Answer: B
Answer: B
Question: Find the odd man out
10,20,40,80,90,160
Options:
A)10
B)90
C)20
D)80
E)160
Rationale: 10*2 = 20
20*2 =40
40*2=80
80*2=160
160*2=320
ANSWER:B
Answer: B
Question: Rs. 6000 is lent out in two parts. One part is lent at 5% p.a simple interest and the other is lent at 10% p.a simple interest. The total interest at the end of one year was Rs. 450. Find the ratio of the amounts lent at the lower rate and higher rate of interest?
Options:
A)1:1
B)5:6
C)5:2
D)5:8
E)5:2
Rationale: Let the amount lent at 5% be Rs. x
Amount lent at 10% is Rs. (6000 - x)
Total interest for one year on the two sums lent
= 5/100 x + 10/100 (6000 - x) = 600 - 3x/100
=> 600 - 3/100 x = 450 => x = 3000
Amount lent at 10% = 3000
Required ratio = 1:1
Answer:A
Answer: A
Question: If m and n are positive integers of K such that m is a factor of n, how many positive multiples of m are less than or equal to 2n ?
Options:
A)2m/n + 1
B)2n/m + 1
C)2n/(m+1)
D)2m/n
E)2n/m
Rationale: Lets say N=10, M=5
2N=20. so the answer should be 4 (20/5)
lets try to plug in the answers:
A-not an integer
B-not an integer
C-not an integer
D-1 (not the answer)
E-4 - the answer. (the only one).
I would choose E.
Method 2
N=M*A (A is an integer)
So - A=N/M
therefore in 2N A will be 2N/M
Again - Answer is E.
Answer: E
Question: On the shelf, there are four books of poetry, four novels, and three reference works. Suppose we picked two books at random. What is the probability that we pick one novel and one reference work?
Options:
A)7/15
B)8/25
C)9/35
D)11/45
E)12/55
Rationale: We could pick one novel and then one reference work, or, we could choose one reference work and then one novel.
P(one novel and one reference work) = 4/11*3/10 + 3/11*4/10 = 12/55
The answer is E.
Answer: E
Question: The average weight of 8 person's increases by 2.5 kg when a new person comes in place of one of them weighing 45 kg. What might be the weight of the new person?
Options:
A)65 kg
B)90 kg
C)85 kg
D)Data inadequate
E)None of these
Rationale: A
65 kg
Total weight increased = (8 x 2.5) kg = 20 kg.
Weight of new person = (64 + 20) kg = 65 kg.
Answer: A
Question: Ms. Popez deposits $ 130 in an account that pays 20% interest, compounded semiannually. How much money will there be in the account at the end of one year?
Options:
A)$118.00
B)$120.00
C)$157.30
D)$122.00
E)$140.00
Rationale: Using Formula - A = P(1+r/n)^nt
Given
P=130
n=2
t=1
r=0.2
Substituting value in formula
A = 130(1+0.2/2)^2
A= 157.30$=C
Answer: C
Question: Salaries of A, B and C were in the ratio of 3 : 5 : 7 respectively. If their salaries were increased by 50%, 60% and 50% respectively, what will be the new ratio of their respective salaries?
Options:
A)3 : 6 : 7
B)4 : 5 : 7
C)4 : 5 : 8
D)Data inadequate
E)None of these
Rationale: Suppose the salaries of A, B and C were 300k, 500k and 700k respectively.
After increment salary of
A = 300k + 50% of 300k = 450k
B = 500k + 60% of 500k = 800k
C = 700k + 50% of 700k = 1050k
Hence, new ratio of the respective salaries of A, B and C = 450k : 800k : 1050k = 9 : 16 : 21
Answer E
Answer: E
Question: Reena took a loan of Rs. 1200 with simple interest for as many years as the rate of interest. If she paid Rs. 192 as interest at the end of the loan period, what was the rate of interest?
Options:
A)4
B)6
C)18
D)Cannot be determined
E)None of these
Rationale: let rate = R% and time = R years
Then ( 1200 x R x R /100) = 192
=> 12R2= 192
=> R2= 16
=> R= 4
Answer A
Answer: A
Question: If v=(10^10)-47, what is the sum of all the digit of v?
Options:
A)40
B)45
C)50
D)55
E)80
Rationale: Start small and check for any pattern:
10^2 - 47 = 53 -> number of digits = power of 10; number of 9s = (power of 10) - 2; 53 is the last 2 digits
10^3 - 47 = 953 -> number of digits = power of 10; number of 9s = (power of 10) - 2; 53 is the last 2 digits
...extrapolate
10^10 - 47 -> number of digits = 10; number of 9s = 8; 53 will be the last 2 digits
v = 9*8 + 5 + 3 = 80.
Answer (E).
Answer: E
Question: The difference of the squares of two consecutive even integers is divisible by which of the following numbers?
Options:
A)4
B)3
C)7
D)6
E)9
Rationale: Let the consecutive even integers are n and (n + 2)
difference of the squares = (n + 2)^2 - n^2 = (n^2 + 4n + 4) - n^2 = 4n + 4 = 4(n + 1)
which is divisible by 4
Answer is A
Answer: A
Question: Two trains 170 m and 160 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions on parallel tracks. The time which they take to cross each other is?
Options:
A)10.9
B)10.7
C)10.3
D)11.88
E)12.2
Rationale: Relative speed = 60 + 40 = 100 km/hr.
= 100 * 5/18 = 250/9 m/sec.
Distance covered in crossing each other = 170 + 160 = 330 m.
Required time = 330 * 9/250 = 297/25 = 11.88 sec.
'Answer: D
Answer: D
Question: How many different combinations of outcomes can you make by rolling three standard (6-sided) dice if the order of the dice does not matter?
Options:
A)24
B)30
C)56
D)120
E)216
Rationale: 1) All dice have the same number:
you have 6 possibilities.
2) 2 dice have the same number, but the 3rd is different:
you have 6*5
3) 3 dice are all different:
you have 6*5*4/3! = 20.
Because the question says the order does not matter, u have to divide it by 3!.
so totally you have 56.
ANS:C. 56.
Answer: C
Question: The sale price sarees listed for Rs.600 after successive discount is 10% and 5% is?
Options:
A)227
B)513
C)342
D)787
E)191
Rationale: 600*(90/100)*(95/100)
= 513
Answer: B
Answer: B
Question: The cost of 8 sharpeners and 12 pens is Rs.76/-. What is the cost of 20 sharpeners and 30 pens?
Options:
A)Rs.172
B)Rs.186
C)Rs.190
D)Rs.195
E)Rs.250
Rationale: Explanation:
From the above statement we have,
The cost of 4 sharpeners + 6 pens = Rs.38/-
Multiplying each term by 5, we get
20 sharpeners + 30 pens = Rs.38x5 =Rs.190
Answer: Option C
Answer: C
Question: By mixing two brands of tea and selling the mixture at the rate of Rs. 177 per kg. a shopkeeper makes a profit of 18%. If to every 2 kg of one brand costing Rs. 200 per kg, 3 kg of the other brand is added, then how much per kg does the other brand cost?
Options:
A)Rs. 110
B)Rs. 120
C)Rs. 140
D)Rs. 160
E)None of these
Rationale: Let the cost of the brand be Rs. X per kg.
C.P. of 5 kg = (2 * 200 + 3 * x) = Rs. (400 + 3x)
S.P of 5 kg = Rs. (5 * 177) = Rs. 885
[885 - (400 + 3x)]/(400 + 3x) * 100 = 18
24250 - 150x = 3600 + 27x
177x = 20650 => x = 116 2/3
So, cost of the other brand = Rs. 116.66.
ANSWER:E
Answer: E
Question: If r is the square of a positive integer, which of the following must be equal to the square of the next positive integer?
Options:
A)√n + 1
B)n + 1
C)n^2 + 1
D)r + 2√r + 1
E)n^2 + 2n + 1
Rationale: If r is the square of a positive integer, which of the following must be equal to the square of the next positive integer?
r = (x)^2 where x is a positive integer
To calculate -
(x+1)^2 = x^2 + 2x + 1
root(r) = x
Ans - r + 2 root(r) + 1
This should be D
Answer: D
Question: Robert spent $104 in buying raw materials, $175 in buying machinery and 10% of the total amount he had as cash with him. What was the total amount?
Options:
A)A)$150
B)B)$210
C)C)$250
D)D)$310
E)E)$200
Rationale: Let the total amount be x
then, (100-10)% of x = 104+175
90% of x = 279
90x/100 = 279
x = $310
Answer is D
Answer: D