divelab/Sys2Bench huggingface dataset:
Question: In a certain game, each player scores either 2 points or 5 points. If n players score 2 points and m players score 5 points, and the total number of points scored is 50, what is the least possible positive T difference between n and m?
Options:
A)1
B)3
C)5
D)7
E)9
Rationale: We have equation 2n + 5m = 50
We have factor 2 in first number and we have factor 5 in second number.
LCM(2, 5) = 10
So we can try some numbers and we should start from 5 because it will be less list than for 2
2 * 5 = 10 and n should be equal 20
4 * 5 = 20 and n should be equal 15
6 * 5 = 30 and n should be equal 10
8 * 5 = 40 and n should be equal 5
10 * 5 = 50 and n should be equal 0
third variant give us the mininal difference
n - m = 10 - 6 = 4
And there is some mistake in my way of thinking because we don't have such answer )
If we change the task and will seek for difference between m and n
than minimal result T will be 8 - 5 = 3
And answer B
Answer: B
Question: Kamal started a business with Rs.25000 and after 4 months, Kiran joined him with Rs.60000. Kamal received Rs.58000 including 10% of profit as commission for managing the business. What amount did Kiran receive?
Options:
A)75000
B)70000
C)72000
D)78000
E)76000
Rationale: Explanation:
Ratio of the profits of Kamal and Kiran
=25000×12:60000×8
=25×12:60×8
=5×3:12×2
=5:4×2
=5:8
Let the total profit =x
Then Kamal received 10x/100=x/10 as commission for managing the business.
Remaining profit =x−x10=9x10 which is shared in the ratio =5:8
Total amount received by Kamal =x/10+9x/10×5/13
⇒x/10+9x/10×5/13=58000
⇒x+9x ×5/13=580000
⇒x(1+45/13)=580000
⇒x(58/13)=580000
⇒x x 1/13=10000
⇒x=130000
Kiran's share = 130000−58000=72000
Answer: Option C
Answer: C
Question: Nathan took out a student loan for 1200$ at 10 percent annual interest, compounded annually. If he did not repay any of the loan or interest during the first 3 years, which of the following is the closest to the amount of interest he owed for the 3 years.
Options:
A)360
B)390
C)400
D)410
E)420
Rationale: A straight Q requiring direct formulae..
when compounded annually the final amount=P(1+ r/100)^n..
here P=1200, r=10 and n=3..
1200(1+ 10/100)^3..
1200*1.1^3=1597.2
interest =1597-1200=397, which is nearly 400 in the choices given
ANSWER:C
Answer: C
Question: Two pipes A and B can fill a cistern in 8 and 12 minutes respectively, and a third pipe C can empty it in 16 minutes. How long will it take to fill the cistern if all the three are opened at the same time?
Options:
A)17 1/9 min
B)5 1/8 min
C)6 1/7 min
D)6 6/7 min
E)17 3/7 min
Rationale: 1/8 + 12 - 1/16
= 7/48
48/7 = 6 6/7
Answer:D
Answer: D
Question: Henrikh lives x blocks from his office. It takes him 1 minute per block to walk to
work and 20 seconds per block to ride his bicycle to work. If it takes him exactly
7 minutes more to walk to work than to ride his bicycle, then x equals
Options:
A)4
B)7
C)10.5
D)15
E)20
Rationale: The best way would be...
Per km, he takes 40 secs extra if he walks
So he will take 7 mins or 7*60 secs in 7*60/40 =10.5 km
ANSWER:C
Answer: C
Question: A(n+1)=1+(1/A(n)) and A(1)=1. What is the value of A(6)?
Options:
A)2
B)3/2
C)5/3
D)8/5
E)13/8
Rationale: A(n+1)=1+(1/A(n))
A(1) = 1
A(2) = 2
A(3) = 3/2
A(4) = 5/3
A(5) = 8/5
A(6) = 13/8
The answer is E.
Answer: E
Question: 100 is what percent of 40?
.
Options:
A)0.2%
B)250%
C)5%
D)20%
E)500%
Rationale: 100= x*40/100
x = 250%
Ans; B
Answer: B
Question: a is an integer greater than 49 but less than 61, b is an integer greater than 59 but less than 71, what is the range of a/b?
Options:
A)2/7
B)1/2
C)3/4
D)1
E)5/4
Rationale: min value of a/b will be when b is highest and a is lowest ---> a=50 and b=70
So, a/b = 5/7
max value of a/b will be when b is lowest and a is highest ---> a=60 and b=60
So, a/b = 1
Range is 1-(5/7) = 2/7.
Answer should be A.
Answer: A
Question: During the first week of performances of a certain play, 5,400 tickets were sold, all at reduced price. During the remaining weeks of performances, 5 times as many tickets were sold at full price as were sold at reduced price. If the total number of tickets sold was 25,200, how many of them were sold at full price?
Options:
A)21,000
B)19,800
C)16,500
D)15,800
E)8,700
Rationale: 5400 + x = 25200 then x is 19800
our x = 19800 is 6/5 of a certain number X
so 19800 = 6/5 of X ---> 19800 * 5 / 6 -->
ANSWER:C
Answer: C
Question: x, y, a, and b are positive integers. When x is divided by y, the remainder is 6. When a is divided by b, the remainder is 9. Which of the following is NOT a possible value for y + b?
Options:
A)24
B)21
C)20
D)17
E)15
Rationale: Important note: remainder is ALWAYS less than divisor, thus y>6 and b>9 --> y+b>15.
Answer: E.
Answer: E
Question: 17 times a positive integer is more than its square by 60, then the positive integer is
Options:
A)13
B)10
C)11
D)5
E)14
Rationale: Explanation:
Let the number be x. Then,
17x = x2 + 60
=> x2 - 17x + 60= 0
=>(x - 12)(x - 5) = 0
=> x = 5 or 12
Answer: Option D
Answer: D
Question: Peter and Tom shared the driving on a certain trip. If Peter and Tom both drove for the same amount of time, but Peter only drove 2/5 of the total distance, what was the ratio of Tom's average speed to Peter's average speed?
Options:
A)1:5
B)2:5
C)1:2
D)3:2
E)2:3
Rationale: The answer is suppose to be D. 3:2. It's from the GMATPrep
option D is answer
Answer: D
Question: Mixture A is 30 percent alcohol, and mixture B is 60 percent alcohol. If the two are poured together to create a 4-gallon mixture that contains 40 percent alcohol, approximately how many gallons of mixture A are in the mixture?
Options:
A)0.8
B)0.7
C)0.6
D)0.5
E)0.4
Rationale: (60-50)/(50-30) = Qa/Qb
10/20= Qa/Qb
1/2 = Qa/Qb
Qa = (1/6) * 4 = 4/6 = 1/2 = 0.50
Answer : D
Answer: D
Question: The product of Tom's age in years, and half of Jerry's age in years, is 54. If Jerry is 3 years younger than Tom is, Jerry is how many years old?
Options:
A)6
B)8
C)9
D)10
E)12
Rationale: Let Tom's age be x & Jerry's age be y.
x * y/2 = 54
x * y = 108
Also, given y=x-3
Substituting x^2 - 3x = 108
Factoring, we get the ages to be 12 and -9.
Since age cannot be negative, Tom's age is 12.
Jerry's age therefore must be 9
Ans :(Option C)
Answer: C
Question: A case contains c cartons. Each carton contains b boxes, and each box contains 500 paper clips. How many paper clips are contained in 2 cases?
Options:
A)500bc
B)500b/c
C)1000bc
D)1000b/c
E)1000/bc
Rationale: 2 cases * c cartons/case * b boxes/carton * 500 clips/box = 1000bc paper clips
The answer is C.
Answer: C
Question: Chandigarh express of 100 m runs at a speed of 60 km/hr. What will be the time taken to cross a platform of 150 meters long?
Options:
A)11.00 sec
B)12.50 sec
C)15.00 sec
D)15.23 sec
E)5.23 sec
Rationale: EXPLANATION:
Given: Length of train = 100 m, speed of train = 60 km/hr, length of platform = 150 m
1) Always remember first step is the conversion of units.
Convert 60 km/hr into m/s by multiplying it with (5/18)
Speed of the train = 60 x	5/18=16.66 m/s
2) Distance covered by the train in passing the platform = (Length of train + Length of platform) = (100 + 150) = 250 m
Therefore,
The time taken =	Distance/Speed
= 250/16.66
= 15 sec
ANSWER IS C
Answer: C
Question: In a dairy farm, 45 cows eat 45 bags of husk in 45 days. In how many days one cow will eat one bag of husk ?
Options:
A)34 days
B)45 days
C)46 days
D)50 days
E)None of these
Rationale: Explanation:
Less Cows, More days (Indirect Proportion)
Less bags, Less days (Direct Proportion)
[Cows1 45
Bags 45 1]::45:x
=>x∗45∗1=45∗1∗45
=>x=45
Option B
Answer: B
Question: When p is divided by 9, the remainder is 4. All of the following are possible values of p, except for which of the following?
Options:
A)13
B)31
C)49
D)57
E)67
Rationale: If a number is divisible by 9, the sum of its digits must be divisible by 9. --> If a number leaves a remainder 4 when divided by 9 the sum of its digits must be 4.
57 = 5 + 7 = 12--> 1 + 2 = 3
Answer: D
Answer: D
Question: The speed of a boat in upstream is 60 kmph and the speed of the boat downstream is 190 kmph. Find the speed of the boat in still water and the speed of the stream?
Options:
A)10
B)99
C)77
D)55
E)65
Rationale: Speed of the boat in still water = (60+190)/2 = 125 kmph. Speed of the stream
= (190-60)/2
= 65 kmph.
Answer: E
Answer: E
Question: There are two lines in the neighbourhood supermarket. In the first line there are 2 people, one with 10 items in her cart and the other with 14 items. In the second line there are 3 people, one with 11 items, one with 12 items and one with 13 items. What is the probability of randomly picking 2 people (it doesn't matter from which line), whose combined number of items is 23?
Options:
A)1/10
B)1/5
C)2/5
D)6/25
E)16/25
Rationale: First line we have 10 and 14
Second line we have 11,12 and 13.....Total 5 possibilities..
We need to get total 23 , then we can take pairs of ( 10,13) and (11,12)
We have total 5 possibilities...when we take 10 as first choice 13 can be second choice out of remaining 4.
1/5 * 1/4 = 1/20...we take ( 10,13) or ( 13,10)....we get two different cases.. 1/20*2 = 1/10.
Similarly for (11,12)... we get 1/10.
Total 1/10+1/10 = 1/5.
Answer:B
Answer: B
Question: What is the greatest integer that will always evenly divide the sum of two consecutive even integers?
Options:
A)2
B)3
C)4
D)6
E)12
Rationale: Let the three consecutive even integers be 2x , 2x + 2
Sum = 2x + 2x + 2
= 4x+2 = 2(2x+1)
Therefore , 2 will always be a factor .
Answer A
Answer: A
Question: What will be the compound interest on a sum of Rs.25,000 after 3 years at the rate of 12 p.c.p.a?
Options:
A)Rs.9000.30
B)Rs. 9720
C)Rs. 10123.20
D)Rs. 10483.20
E)None
Rationale: Solution
Amount	= Rs.(25000x(1+12/100)³
=Rs.(25000x28/25x28/25x28/25)
= Rs. 35123.20.
C.I	=Rs(35123.20-25000)
=Rs.10123.20.
Answer C
Answer: C
Question: One bacterium splits into eight bacteria of the next generation. But due to environment, only 50% of one generation can produced the next generation. If the seventh generation number is 4096 million, what is the number in first generation?
Options:
A)1 million
B)2 million
C)4 million
D)8 million
E)None of these
Rationale: Solution: Let the number of bacteria in the 1st generation be x, then number of bacteria in 2nd, 3rd, 4th . . . . . Generation would be
8(x/2), 8(4x/2), 8(16x/2) . . . . And so on.
As x, 4x, 16x, 64x . . . . . it is in GP with common ratio 4.
Hence, 7th term of GP,
x(4)6 = 4096
Or, x = 1 or 1 million.
Answer: Option A
Answer: A
Question: add 16% of 36 and 13% of 45.
Options:
A)9.5
B)8.5
C)7.2
D)7
E)8
Rationale: 16% of 36 + 13% of 45
36*16/100+45*13/100
5.8+1.4=7.2
answer C
Answer: C
Question: Brenda and Sally run in opposite direction on a circular track, starting at diametrically opposite points. They first meet after Brenda has run 100 meters. They next meet after Sally has run 200 meters past their first meeting point. Each girl runs at a constant speed. What is the length of the track in meters?
Options:
A)250
B)300
C)350
D)400
E)500
Rationale: Nice problem. +1.
First timetogetherthey run half of the circumference.
Second timetogetherthey run full circumference.
First time Brenda runs 100 meters, thus second time she runs 2*100 = 200 meters.
Since second time (when they run full circumference) Brenda runs 200 meters and Sally runs 200 meters, thus the circumference is 200 + 200 = 400 meters.
Answer: D.
Answer: D
Question: In an election between two candidates first candidate got 60% of votes polled and second Candidate got 280 votes. The total number of votes polled was?
Options:
A)700 votes
B)800 votes
C)900 votes
D)980 votes
E)990 votes
Rationale: Total = 100 %,
First person got 60%
second person got remaining 40 % of votes.
than 40 % = 280
40% = 40×7 = 280
100% =100×7 =700 votes
A
Answer: A
Question: A boatman can row 3 km against the stream in 20 minutes and return in 12 minutes. Find the rate of current ?
Options:
A)7/2 kmph
B)8/2 kmph
C)5/2 kmph
D)1/2 kmph
E)3 kmph
Rationale: Explanation:
Speed in upstream = Distance / Time = 3 x 60/20 = 9 km/hr.
Speed in downstream = 3 x 60/12 = 15 km/hr
Rate of current = (15-9)/2 = 3 km/hr.
Answer: E
Answer: E
Question: How many 3 digit positive integers with distinct digits are there, which are not multiples of 10?
Options:
A)576
B)520
C)504
D)432
E)348
Rationale: A number not to be a multiple of 10 should not have the units digit of 0.
XXX
9 options for the first digit (from 1 to 9 inclusive).
8 options for the third digit (from 1 to 9 inclusive minus the one we used for the first digit).
8 options for the second digit (from 0 to 9 inclusive minus 2 digits we used for the first and the third digits)
9*8*8=576.
Answer: A.
Answer: A
Question: Find the value of 72519 x 9999 = m?
Options:
A)434365675
B)464687665
C)643432672
D)725117481
E)790023245
Rationale: 72519 x 9999 = 72519 x (10000 - 1)
= 72519 x 10000 - 72519 x 1
= 725190000 - 72519
= 725117481
D
Answer: D
Question: The average (arithmetic mean) of 16 students first quiz scores in a difficult English class is 62.5. When one student dropped the class, the average of the remaining scores increased to 63.0. What is the quiz score of the student who dropped the class?
Options:
A)a) 10
B)b) 25
C)c) 40
D)d) 55
E)e) 70
Rationale: Total Score of 16 students is 16*62.50 = 1000
Total Score of 15 students is 15*63 = 945
So, the score of the person who left is 55 ( 1000 - 945 )
Answer will be (D)
Answer: D
Question: Jones invested a certain sum of money in a simple interest bond whose value grew to $500 at the end of 3 years and to $ 800 at the end of another 4 years. What was the rate of interest in which he invested his sum?
Options:
A)12%
B)12.5%
C)16.67%
D)16.25%
E)18.18%
Rationale: Lets assume the Principal Amount (initial amount invested) to be P
rate of interest to beRand time as T. We need to find R
Now After a time of 3years the principal P amounts to $500 and after a time of 7years ( question says after another 7years so 3+4) P becomes $800.
Formulating the above data
Amount (A1) at end of 3years
A1= P(1 + 3R/100) = 500
Amount (A2) at end of 7years
A2 = P(1 + 7R/100) = 800
Dividing A2 by A1 we get
(1 + 7R/100)/(1 + 3R/100) = 8/7
after cross multiplication we are left with 11R =100*2 which gives R = 18.18%
Option: E
Answer: E
Question: A and B put in Rs.300 and Rs.400 respectively into a business. A reinvests into the business his share of the first year's profit of Rs.238 where as B does not. In what ratio should they divide the second year's profit?
Options:
A)220:113
B)201:200
C)210:201
D)100:99
E)113:77
Rationale: Explanation:
3: 4
A = 3/7*238 = 102
402: 400
201:200
Answer:B
Answer: B
Question: The apartment on King-Williams street is an asset that its value is tramping about. From the year 1973 to 1983 it's value decreased by 16% and from 1983 to 1993 it's value increased by 16%. What is the value of the asset in 1993 if in 1973 it was worth $40,000?
Options:
A)$38,796.
B)$40,000
C)$38,976.
D)$39,679
E)$36,796.
Rationale: Value in 1973 = 40000
Value in 1983 = 0.84*40000 = 33600
Value in 1993 = 1.16*33600 = $38976
Correct Option: C
Answer: C
Question: In an election between two candidates - Lange and Sobel - 70% of the voters voted for Sobel. Of the election`s voters, 60% were male. If 35% of the female voters voted for Lange, what percentage of the male voters voted for Sobel?
Options:
A)14
B)16
C)26
D)44
E)65
Rationale: M F total
L 16 14 30
S 44 70
Tot 60 40 100
35% of 40 = 14 ------Female voters that means 16 male voted for L
so 60-16 = 44
D is correct
Answer: D
Question: A rectangular lawn 55m by 35m has two roads each 4m wide running in the middle of it. One parallel to the length and the other parallel to breadth. The cost of graveling the roads at 75 paise per sq meter is?
Options:
A)rs.259
B)rs.252
C)rs.258
D)rs.251
E)rs.252
Rationale: area of cross roads = 55*4 + 35*4 - 4*4
= 344sq m
cost of graveling = 344 * (75/100)
= Rs. 258
Answer: C
Answer: C
Question: What is the probability that, when three twelve-sided dice are rolled, at least one 1 is rolled?
Options:
A)1/4
B)3/144
C)1331/1728
D)23/144
E)397/1728
Rationale: Odds of no 1's: (11/12)^3 = 1331/1728
So the probability of at least one 1 is (1 - 1331/1728) = 397/1728, so the answer is E.
Answer: E
Question: A metallic sheet is of rectangular shape with dimensions 48 m x 36 m. From each of its corners, a square is cut off so as to make an open box. If the length of the square is 5 m, the volume of the box (in m3) is:
Options:
A)4940
B)5120
C)6420
D)8960
E)7960
Rationale: Clearly, l = (48 - 10)m = 38 m,
b = (36 -10)m = 26 m,
h = 8 m.
Volume of the box = (38 x 26 x 5) m3 = 4940 m3. Answer: Option A
Answer: A
Question: Find the odd man out. 1, 4, 9, 17, 25, 36, 49
Options:
A)1
B)9
C)17
D)49
E)36
Rationale: Explanation :
The pattern is 1^2, 2^2, 3^2, 4^2, 5^2, 6^2, 7^2
But, instead of 4^2, 17 is given
Answer : Option C
Answer: C
Question: A train , having a length of 220 meter is running at a speed of 60 kmph. In what time, it will pass a man who is running at 6 kmph in the direction opposite to that of the train
Options:
A)10 sec
B)12 sec
C)6 sec
D)4 sec
E)2 sec
Rationale: Explanation:
Distance = 220 m
Relative speed = 60+6 = 66 kmph (Since both the train and the man are in moving in opposite direction)
= 66×10/36 mps = 110/6 mps
Time = distance/speed = 220/(110/6) = 12 s
Answer: Option B
Answer: B
Question: In a box, there are 6 red, 2 blue and 3 green balls. One ball is picked up randomly. What is the probability that it is neither blue nor green?
Options:
A)6/11
B)8/21
C)3/7
D)9/22
E)10/21
Rationale: Explanation:
Total number of balls = (6 + 2 + 3) = 11
Let E = event that the ball drawn is neither blue nor green =e vent that the ball drawn is red.
Therefore, n(E) = 6.
P(E) = 6/11.
Answer: Option A
Answer: A
Question: On an order of 19 dozen boxes of a consumer product, a retailer receives an extra dozen free. This is equivalent to allowing him a discount of:
Options:
A)0.05%
B)0.5%
C)1%
D)5%
E)10%
Rationale: Clearly, the retailer gets 1 dozen out of 20 dozens free.
Equivalent discount = 1/20 * 100 = 5%.
Answer D) 5%
Answer: D
Question: Today Mary’s father is four times as old as Mary. Ten years ago, he was 10 times as old. How old is Mary today?
Options:
A)11
B)12
C)13
D)14
E)15
Rationale: Dad's age = 4M
10*(M-10) = 4M-10
6M = 90
M = 15
The answer is E.
Answer: E
Question: Vijay says that his weight is between 75kg and 85 kg. But his younger sister disagrees with Vijay and says that his weight is greater than 70kg but less than 80 kg. Vijay’s mother says that his weight cannot be greater than 78 kg. If all the three predictions are correct, what is the average of different probable weights of Vijay?
Options:
A)75
B)80
C)78.5
D)76.5
E)None of these
Rationale: Explanation:
Vijay’s opinion: - 75 < Vijay’s age < 85
Sister’s opinion: - 72 < Vijay’s age < 82
Mother’s opinion: - Vijay’s age < 78
As all the above three conditions are true, the values satisfying them are 76 & 77.
Average value = (76 + 77)/ 2 = 76.5
ANSWER D
Answer: D
Question: If three sides of the triangle are 8 , 15 and F respectively then the how many values can F ?
Options:
A)[A] 6
B)[B] 7
C)[C] 8
D)[D]9
E)[E] infinite number of values
Rationale: Needed: How many Values can F take
Concept: Sum of any two sides of a triangle is greater then the third side.
Case 1: 8+5 > F => F<13
Case 2: 5+F > 8 => F >3
Case 3: 8+F > 5 => F > -3 (Always true since F is one side of a Triangle)
Finally, 3 < F < 13. So, we can have infinite number of sides between 3 and 13.
Answer = E
PS: If question said F can take only integer value, the F = 9. Answer choice D.
Answer: D
Question: A cistern is normally filled in 10 hrs,but takes 2 hrs longer to fill because of a leak on its bottom,if Cistern is full ,how much time citern would empty?
Options:
A)10 hours
B)20 hours
C)60 hours
D)40 hours
E)50 hours
Rationale: If leakage/hour=1/x, then 1/10 -1/x= 1/12, solving 1/x=1/60
So in 60 hours full cistern will be empty.
ANSWER:C
Answer: C
Question: If xy=4, x/y=81, for positive numbers x and y, y=?
Options:
A)1/2
B)2
C)2/9
D)3
E)1/6
Rationale: Very easy question. 2 variables and 2 easy equations.
xy=4 ---> x=4/y - (i)
x/y=81 ---> replacing (i) here ---> 4/(y^2)=81 ---> y^2=4/81 ---> y=2/9 or -2/9
The question states that x and y are positive integers. Therefore, y=2/9 is the answer.
Answer C.
Answer: C
Question: Ajay bought 15 kg of dal at the rate of Rs 14.50 per kg and 10 kg at the rate of Rs 13 per kg. He mixed the two and sold the mixture at the rate of Rs 15 per kg. What was his total gain in this transaction ?
Options:
A)27.59
B)27.52
C)37.5
D)27.5
E)27.51
Rationale: Cost price of 25 kg = Rs. (15 x 14.50 + 10 x 13) = Rs. 347.50.
Sell price of 25 kg = Rs. (25 x 15) = Rs. 375.
profit = Rs. (375 — 347.50) = Rs. 27.50.
Answer: D) Rs 27.50
Answer: D
Question: There are 28 stations between Hyderabad and Bangalore. How many second class tickets have to be printed, so that a passenger can travel from any station to any other station?
Options:
A)156
B)167
C)870
D)352
E)380
Rationale: The total number of stations = 30
From 30 stations we have to choose any two stations and the direction of travel (i.e., Hyderabad to Bangalore is different from Bangalore to Hyderabad) in 3⁰P₂ ways.
30P₂ = 30 * 29
= 870.
Answer: C
Answer: C
Question: If Q is an odd number and the median of Q consecutive integers is 125, what is the largest of these integers?
Options:
A)(Q - 1)/2 + 125
B)Q/2 + 119
C)Q/2 + 125
D)(Q + 119)/2
E)(Q + 125)/2
Rationale: Consider the easiest case, say Q=3, then;
Set = {124, 125, 126};
The largest integer = 126.
Now, plug Q=3 into the answers to see which yields 126. Only answer choice A works.Notice that we don't really need to plug for B, C, or E, since these options do not yield an integer value for any odd value of Q.
Answer: A.
Answer: A
Question: The price of 3 tables and 4 chairs is Rs. 3300. With the same money one can buy 2 tables and 10 chairs. If one wants to buy 1 table and 1 chair, how much does he need to pay?
Options:
A)1075
B)1025
C)1000
D)1050
E)1100
Rationale: et price of a table = t
and price of a chair = c
3t + 4c = 3300 ---(Equation 1)
2t + 10c = 3300
=> t + 5c = 1650 ---(Equation 2)
(Equation 2) × 3 => 3t + 15c = 4950 ---(Equation 3)
(Equation 3) - (Equation 1) => 11c = 1650
=> c = 150
Substituting the value of c in equation 1, we get
3t + (4 × 150) = 3300
=> 3t = 3300 – 600 = 2700
=>t = 2700/3 = 900
Cost of 1 table and 1 chair = c + t = 150 + 900 = 1050
Answer is D.
Answer: D
Question: Steve bought a total of 6 packages of pens, and each package contained either 3 or 7 pens. If exactly 4 of the packages Steve bought contained 7 pens, how many pens did Steve buy?
Options:
A)17
B)21
C)34
D)42
E)56
Rationale: Explanation:
If Steve bought 4 packages of 7 pens and 6 packages total, then he must have purchased 2 packages of 3 pens.
4(7) + 2(3) = 28 + 6 = 34
Answer : (C).
Answer: C
Question: Several litres of acid were drawn offa 54 litre vessel full of acid and an equal amount of water was added. Again the same volume of the mixture was drawn off and replaced by water. As a result, the vessel contained 24 litres of pure acid. How much of the acid was drawn off initially?
Options:
A)12 lts
B)16 lts
C)18 lts
D)24 lts
E)28 lts
Rationale: Suppose X litres of acid was drawn off initially.
Remaining acid in the 54 litre vessel full of acid.
=> (54 - x) litres and water added = x litres.
Now out of the 54 litres of mixture of acid and water x litres of mixture is drawn off.
=> quantity of acid drawn off =(54 - X/54 x X)
litres and quantity of water drawn off = X2/54
Now vessel contains [54 - X - (54 - X/54)X]
Thus, 54 - X - [54 - X/54]X = 24
=> X2 - 108X +1620 = 0
=> X = 80, 18
since 90 > 54 therefore X = 90 is ruled out
hence X = 18
ANSWER:C
Answer: C
Question: Two pipes A and B can fill a tank in 15 min and 25 min respectively. Both the pipes are opened together but after 4 min, pipe A is turned off. What is the total time required to fill the tank?
Options:
A)14 min 19 sec
B)14 min 42 sec
C)17 min 20 sec
D)14 min 40 sec
E)14 min 10 sec
Rationale: :
Part filled in 4 minutes = 4(1/15 + 1/20) = 7/15
Remaining part = 1 - 7/15 = 8/15
Part filled by B in 1 minute = 1/25
1/25 : 8/15 :: 1 ; x
x = 8/15 * 1 * 25 = 13 1/3 min = 13 min 20 sec.
The tank will be full in (4 min. + 13 min. 20 sec) = 17 min 20 sec.Answer: C
Answer: C