mathewhe/aqua_rat huggingface dataset:
Question: If a portion of a half water/half alcohol mix is replaced with 25% alcohol solution, resulting in a 30% alcohol solution, what percentage of the original alcohol was replaced?
(A) 3%
(B) 20%
(C) 66%
(D) 75%
(E) 80%
Rationale: let x be water, y - alcohol. so we have -
0.5x+0.5y -0.25y=0.3x+0.3y
x=1/4y
x/y=1/4
so in a new solution y 's portion is 4/5 or 80%
ANSWER:E
Answer: (E) 80%
Question: A school’s annual budget for the purchase of student computers increased by 50% this year over last year. If the price of student computers increased by 20% this year, then the number of computers it can purchase this year is what percent greater than the number of computers it purchased last year?
(A) 33.33%
(B) 40%
(C) 25%
(D) 28%
(E) 60%
Rationale: Lats year: budget = $100, price = $1 --> the number of computers purchased = 100/1 = 100;
This year: budget = $150, price = $1.2 --> the number of computers purchased = 150/1.2 = 125.
Increase in the number of computers purchased = 25%.
Answer: C.
Answer: (C) 25%
Question: A sells an article to B at a profit of 10% B sells the article back to A at a loss of 10%. In this transaction:
(A) A neither losses nor gains
(B) A makes a profit of 11%
(C) A makes a profit of 20%
(D) B loses 20%
(E) None of these
Rationale: Solution: First Method
Let CP was 100 for A originally.
A sells article to B at 10% profit,
CP for B = 100 + 10% of 100 = 110.
Now, B sells it A again with loss 10%.
Now, CP for A this time = 110 - 10% of 110 = 99.
A makes Profit = 110 - 99 = 11.
%profit for A = (11*100)/100 = 10%.
Second Method
It could be easily shown by net percentage change graphic.
100(A)==10%(Profit)==>110(B)==10%(Loss)==>99(A)
In this transaction A makes a profit of (110-99 = 11%) 11% .
[10% on selling to B and 1% profit on buying back from B].
Answer: Option B
Answer: (B) A makes a profit of 11%
Question: If the sides of a triangle are 65 cm, 60 cm and 25 cm, what is its area?
(A) 350 cm^2
(B) 850 cm^2
(C) 550 cm^2
(D) 750 cm^2
(E) 650 cm^2
Rationale: The triangle with sides 65 cm, 60 cm and 25 cm is right angled, where the hypotenuse is 65 cm.
Area of the triangle
= 1/2 * 60 * 25
= 750 cm^2
Answer: D
Answer: (D) 750 cm^2
Question: If TIER is written as 8163 and BRAIN is written as 23415, how is RENT coded ?
(A) 3653
(B) 3658
(C) 2977
(D) 2790
(E) 2711
Rationale: Explanation:
Given :
Letter : T I E R B A N
Code : 8 1 6 3 2 4 5
Thus, the code for RENT is 3658.
ANSWER:B
Answer: (B) 3658
Question: From a pack of cards two cards are drawn one after the other, with replacement. The probability that the first card is a queen and the second card is a jack is?
(A) 1/169
(B) 1/52
(C) 1/26
(D) 1/120
(E) 1/4
Rationale: Probability of a queen = 4/52 = 1/13
Probability of a jack = 4/52 = 1/13
Probability of both = P1*P2 = 1/(13*13) = 1/169
Answer is A.
Answer: (A) 1/169
Question: List I: 15, 12, 17, 20 List II: x,15, 12, 17, 20
(A) 15
(B) 16
(C) 20
(D) 22
(E) 24
Rationale: List I has even number of terms, thus its median is the average of two middle terms (when arranged in ascending/descending order), so median=(15+17)/2=16
List II has odd number of terms, thus its median is the middle term (when arranged in ascending/descending order). As no other number in the list equal to 16, then x=16.
Answer: B
Answer: (B) 16
Question: How many prime numbers F exist such that 90 < F < 106 and F is a factor of 99999919?
(A) 1. Zero
(B) 2. One
(C) 3. Two
(D) 4. Three
(E) 5. More than three
Rationale: I found that considering the constraint..F is a prime num in between 90 to 106 not inclusive , only 3 numbers (91,97 and 101) are present but those numbers are not the factors of the number mentioned....Therefore, i doubt the answer.C
Answer: (C) 3. Two
Question: If x and y are positive integers, and x^3*y^4 = 648, which of the following is the value of xy?
(A) 2
(B) 4
(C) 6
(D) 8
(E) 10
Rationale: 648 = 2^3*3^4
xy = 2*3 = 6
The answer is C.
Answer: (C) 6
Question: Abhijit started a business investing 70000. Anuja joined him after 4 months with an amount of 105000 and Sunil joined them with 1.4 lakhs after another six months. The amount of profit earned should be distributed in what ratio among Abhijit, Anuja and Sunil respectively, three years after Abhijit started the business?
(A) 9: 13: 26
(B) 9 :12 :13
(C) 8 :14: 24
(D) 12:14:16
(E) 8 :15: 12
Rationale: Ratio of their investments
= 70 × 36 : 105 × 32: 140 × 26 = 9 : 12 : 13
Answer B
Answer: (B) 9 :12 :13
Question: There are 10 points on a circle. A hexagon can be formed by linking 8 of the 10 points. How many such hexagons are possible?
(A) 45
(B) 120
(C) 200
(D) 210
(E) 600
Rationale: 8 points can be selected out of 10 points in 10C8 ways
=10 !/8!*2!=45
Ans A
Answer: (A) 45
Question: A certain bus driver is paid a regular rate of $16 per hour for any number of hours that does not exceed 40 hours per week. For any overtime hours worked in excess of 40 hours per week, the bus driver is paid a rate that is 75% higher than his regular rate. If last week the bus driver earned $1004 in total compensation, how many total hours did he work that week?
(A) 36
(B) 40
(C) 44
(D) 48
(E) 53
Rationale: For 40 hrs = 40*16=640
Excess = 1004-640=364
For extra hours =.75(16)=12+16=28
Number of extra hrs =364/28=13
Total hrs =40+13=53
Answer E 53
Answer: (E) 53
Question: Three friends, returning from a movie, stopped to eat at a restaurant. After dinner, they paid their bill and noticed a bowl of mints at the front counter. Sita took one-third of the mints, but returned four because she had a momentary pang of guilt. Fatima then took one-fourth of what was left but returned three for similar reason. Eswari then took half of the remainder but threw two back into the bowl. The bowl had only 17 mints left when the raid was over. How many mints were originally in the bowl?
(A) 38
(B) 31
(C) 41
(D) None of these
(E) Cannot be determined
Rationale: Explanation :
Let there be x mints originally in the bowl.
Sita took 1/3 but returned 4. So, noe the bowl haa (2x/3) + 4 mints
Fatima took 1/4 of the remainder but returned 3. So, the bawl now has (3/4)((2x/3) + 4) + 3 mints.
Eshwari took half of the remainder that is (1/2) [ (3/4) ( (2x/3) + 4 ) + 3 ]
She returns 2, so the bawl now has
=> (1/2) [ (3/4) ( (2x/3) + 4) + 3 ] + 2 = 17.
=> x = 48.
Answer : D
Answer: (D) None of these
Question: How many liters of water must be evaporated from 50 liters of a 4-percent sugar solution to get a 10-percent solution?
(A) 30
(B) 32
(C) 34
(D) 36
(E) 38
Rationale: 4% of a 50 liter solution is 2L which is 10% of the solution at the end.
The solution at the end must be 20 L.
We need to evaporate 30 liters.
The answer is A.
Answer: (A) 30
Question: A batsman makes a score of 64 runs in the 16th innings and thus increased his average by 3. Find his average after the 16th inning?
(A) 17
(B) 21
(C) 22
(D) 23
(E) 24
Rationale: Let the average after the 16th inning be P.
So, the average after the 15th inning will be (P-3) Hence, 15(P-30) + 62 = 16P => P = 17.
ANSWER:A
Answer: (A) 17
Question: In a certain furniture store, each week Nancy earns a salary of $240 plus 5% of the amount of her total sales that exceeds $800 for the week. If Nancy earned a total of $450 one week, what were her total sales that week ?
(A) $2,200
(B) $3,450
(C) $4,200
(D) $4,250
(E) $5,000
Rationale: 450 = 240 + (5/100)*(Total Sales - 800)
i.e. (Total Sales - 800) = 20*(450-240) = 20*210 = 4200
i.e. Total Sales = 4200 + 800 = 5000
Answer: Option E
Answer: (E) $5,000
Question: If B + A < B - A < A - B, which of the following is correct?
(A) A<B<0
(B) B<A<0
(C) B<0<A
(D) 0<B<A.
(E) B>A>0.
Rationale: Check first inequality
B + A < B - A
A<-A
A is -ve
Check another equality
B - A < A - B
-2A<-2B
A>B
Combining both 0>A>B
Option B fits only
Ans B
Answer: (B) B<A<0
Question: 80,873,72,72,64,81,56,?
(A) 96
(B) 98
(C) 89
(D) 90
(E) 88
Rationale: odd place numbers 80, 72, 64, 56 are divisible by 8.
even place numbers 873, 72, 81 are divisible by 9,so required number is in even place, from options 90 is only value visible by 9, so 90 is the answer.
ANSWER:D
Answer: (D) 90
Question: What is the sum of all the numbers between 300 and 1000 which are divisible by 179?
(A) 2506
(B) 2550
(C) 2450
(D) 3000
(E) 3500
Rationale: 358/179 â€¦.. 895/179
179(2 + 3 + 4 + 5) => 2506
ANSWER A
Answer: (A) 2506
Question: A table is bought for Rs.600/- and sold at a loss of 12% find its selling price
(A) s.500/-
(B) s.530/-
(C) s.528/-
(D) s.600/-
(E) s.700/-
Rationale: 100 % ------> 600 (100 * 6 = 600)
88 % ------> 528 (88 * 6 = 528)
Selling price = Rs.528/-
C
Answer: (C) s.528/-
Question: Two Equal Amounts of Money are lent out at 6% and 5 % simple Interest respectively at the same time. The former is recovered two years earlier than the latter and the amount so recovered in each case is Rs.2800. Determine the amount that is lent out?
(A) 3348
(B) 368
(C) 37077
(D) 1750
(E) 2701
Rationale: Explanation:
Let the first amount lent for t + 2 years and second at t years. and amount = P
Now amount = P + P×t×6100P×t×6100 = P×(t+2)×5100P×(t+2)×5100 = 2800.
Equating first two parts, we get t×6100=(t+2)×5100t×6100=(t+2)×5100
⇒ t = 10.
Now P+P×10×6100=2800P+P×10×6100=2800
⇒ 1610P=28001610P=2800
⇒ P = 1750.
Answer: D
Answer: (D) 1750
Question: Three sets of 40, 50 and 60 students appeared for an examination and the pass percentage was 50, 90 and 75 respectively. the pass percentage of the whole set is
(A) 73.33%
(B) 73.44%
(C) 74.33%
(D) 85.33%
(E) 71.33%
Rationale: Explanation:
total passed student =20+45+45=110
110 is 73.33% of 150
ANSWER:A
Answer: (A) 73.33%
Question: For 600 km journey it will take 8hrs, if 120 km is done by bus and the rest by car. It takes 20 minutes more, if 200 km is done by busand the rest by car. The ratio of the speed of the train to that of the cars is?
(A) 1:2
(B) 3 : 4
(C) 1:4
(D) 2:5
(E) 3:7
Rationale: Let the speed of the train be x km/hr and that of the car be y km/hr.
Then, 120 + 480 = 8 1 + 4 = 1 ....(i)
x y x y 15
And, 200 + 400 = 25 1 + 2 = 1 ....(ii)
x y 3 x y 24
Solving (i) and (ii), we get: x = 60 and y = 80.
Ratio of speeds = 60 : 80 = 3 : 4
B
Answer: (B) 3 : 4
Question: the sum of 4th and 20th term of A.P. is equal to the sum of 8th , 15th and 12 th term . find the term which is 0
(A) 10
(B) 7
(C) 11
(D) 5
(E) 3
Rationale: t4 + t20 = t8 + t15 + t12
=> a+3d + a+19d = a+7d + a+14d + a+11d
=> a + 10d = 0
=> t11 = 0 i.e. 11th term is zero.
ANSWER: C
Answer: (C) 11
Question: Train A & B leave from same station and reaches same destination but train A leaves half an after Train B & travels 2 times faster than B. Total distance is 100 miles & train B travels 50 miles/hour. Which train reaches the destination first & what is the time difference between the train
(A) Train A reaches 30 minutes before Train B
(B) Train B reaches 30 minutes before Train A
(C) Train A reaches 60 minutes before Train B
(D) Train B reaches 60 minutes before Train A
(E) None of the above
Rationale: Time taken for train A = 30 minutes + d1/s1 = 30 minutes + 100 / 100 = 1 hours 30 minutes
Since Train B travels 50 miles / hour ; train A travels twice the speed of B which gives s1 = 100 miles/ hour
Time taken for train B = d2/s2 = 100 / 50 = 2 Hours
So Train A reaches 30 minutes before Train B
Answer: A
Answer: (A) Train A reaches 30 minutes before Train B
Question: Seven children â€” A, B, C, D, E, F, and G â€” are going to sit in seven chairs in a row. The children C & F have to sit next to each other, and the others can sit in any order in any remaining chairs. How many possible configurations are there for the children?
(A) 600
(B) 720
(C) 1440
(D) 4320
(E) 4800
Rationale: There are six different pairs of â€œnext to each otherâ€ chairs. For each pair, children C & F could be in either order, so thatâ€™s 6*2 = 12 possibilities for these two.
Now, consider the other five children. For any configuration of C & F, the remaining five children could be seated in any order among the five remaining seats. Five items in any order â€” thatâ€™s a permutation of the 5 items â€”- 5P5 = 5! = 120. For any single configuration of C & F, there are 120 ways that the other children could be seated in the remaining seats.
Finally, weâ€™ll combine with the Fundamental Counting Principle. We have 12 ways for the first two, and 120 ways for the remaining five. Thatâ€™s a total number of configurations of 12*120 = 1440. Answer = C
Answer: (C) 1440
Question: Find the odd man out. 18, 27, 36, 38, 45
(A) 18
(B) 27
(C) 36
(D) 45
(E) 38
Rationale: All numbers except 38 are multiples of 9
Answer is E
Answer: (E) 38
Question: If 222 = 6
333 = 12
444 = 20
Then, 555 = ??
(A) 30
(B) 35
(C) 40
(D) 45
(E) 50
Rationale: 222=2*2+2=6
333=3*3+3=12
444=4*4+4=20
555=5*5+5=30
ANSWER:A
Answer: (A) 30
Question: A room is 15m long, 4m broad and 3m height. Find the cost of white washing its four walls at 50p per m2 ?
(A) 28
(B) 57
(C) 58
(D) 83
(E) 73
Rationale: Explanation:
2 *3(15 + 4) = 114
114 * 1/2 = Rs.57
Answer: Option B
Answer: (B) 57
Question: If a2 + b2 + c2 = 281 and ab + bc + ca =4, then a + b + c is
(A) 16
(B) 18
(C) 22
(D) 17
(E) 20
Rationale: by formula ,
(a + b + c)^2= a^2 + b^2 + c^2 + 2(ab + bc + ca),
since, a^2 + b^2 + c^2 = 281 and ab + bc + ca = 4,
(a + b + c)^2 = 281 + 2(4)
= 289
= 17^2
therefore: a + b + c = 17
ANSWER:D
Answer: (D) 17
Question: Of all the students in a certain dormitory, 1/2 are first-year students and the rest are second-year students. If 4/5 of the first-year students have not declared a major and if the fraction of second-year students who have declared a major is 2 times the fraction of first-year students who have declared a major, what fraction of all the students in the dormitory are second-year students who have not declared a major?
(A) 1/15
(B) 1/5
(C) 4/15
(D) 3/10
(E) 2/5
Rationale: tot students=x
1st year student=x/2----> non majaor=4/5(x/2)-----> maj=1/5(x/2)
2nd year student=x/2---->maj=2(1/5(x/2))=2/10(x)--->non major=x/2-2/10(x)=3/10(x)
hence 3/10
D
Answer: (D) 3/10
Question: How many integers between 400 and 1000 are there such that their unit digit is odd?
(A) 250
(B) 150
(C) 300
(D) 400
(E) 450
Rationale: There are 600 numbers from 401 to 1000 (inclusive).
Half of the numbers are odd, so there are 300 odd numbers.
The answer is C.
Answer: (C) 300
Question: Divide $450 among A,B in the ratio 1:4. How many $ that A get?
(A) $90
(B) $500
(C) $150
(D) $250
(E) $600
Rationale: Sum of ratio terms = 1+4 = 5
A = 450*1/5 = $90
Answer is A
Answer: (A) $90
Question: If 16,666 – n is divisible by 11, and 0 < n < 11, what is n?
(A) 1
(B) 3
(C) 5
(D) 7
(E) 9
Rationale: 16,666 / 11 = 1515 with a remainder of 1.
We need to subtract the remainder to get a multiple of 11.
The answer is A.
Answer: (A) 1
Question: If 3f+ 1 < 2f < 9 - f, which of the following must be true?
I. -1 < f < 3
II. f < -1
III. f < 3
(A)  II only
(B)  III only
(C)  I and II only
(D)  II and III only
(E)  I, II and III
Rationale: Just try plugging f in a number like 0 or 1, and you'll quickly find that the inequality doesn't hold.
So you can immediately cross out any answers with I or III, leaving just (A) II only.
Answer: (A)  II only
Question: ((1^m)/(5^m))((1^16)/(4^16)) = 1/(2(10)^31)
What is m?
(A) 17
(B) 18
(C) 34
(D) 31
(E) 36
Rationale: ((1^m)/(5^m))((1^16)/(4^16)) = 1/(2(10)^31)
((1/5)^m ) * ((1/2)^32) = 1/ (2 * (2*5)^31))
2^36 will cancel out,since 1 can be written as 1^35 ,So (1/5)^m= (1/5)^31
((1/5)^m ) * ((1/2)^32) = 1/[(2^32)*(5^31)]
So, m=31
Answer D
Answer: (D) 31
Question: Two trains 150 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?
(A) 10.7
(B) 10.9
(C) 10.26
(D) 11.16
(E) 18.8
Rationale: Relative speed = 60 + 40 = 100 km/hr.
= 100 * 5/18 = 250/9 m/sec.
Distance covered in crossing each other = 150 + 160 = 310 m.
Required time = 310 * 9/250 = 11.16 sec.
Answer:D
Answer: (D) 11.16
Question: How many positive integers less than 60 are equal to the product of a positive multiple of 5 and an even number?
(A) 4
(B) 5
(C) 9
(D) 10
(E) 11
Rationale: Number of positive multiples of 5 less than 60 = 11
5*1=5
5*2=10
5*3=15
5*4=20
5*5=25
5*6=30
5*7=35
5*8=40
5*9=45
5*10=50
5*11=55
Only 5 of the above are a product of a positive multiple of 5 and an even number - 10,20,30,40,50
Answer B
Answer: (B) 5
Question: In what time will a train 120 m long cross an electric pole, it its speed be 185 km/hr?
(A) 2.3 sec
(B) 2.9 sec
(C) 2.7 sec
(D) 8.7 sec
(E) 8.5 sec
Rationale: Speed = 185 * 5/18 = 51 m/sec
Time taken = 120/51 = 2.3 sec.
Answer: A
Answer: (A) 2.3 sec
Question: How many positive three-digit integers are divisible by both 2 and 7?
(A) 40
(B) 46
(C) 52
(D) 64
(E) 70
Rationale: A number to be divisible by both 2 and 7 should be divisible by the least common multiple of 2 and 7 so by 14.
Multiples of 14 between 100 and 999, inclusive is
(last-first)/multiple+1=(994-112)/14+1=63+1=64
Answer: D.
Answer: (D) 64
Question: A bank offers an interest of 5% per annum compounded annually on all its deposits. If $10,000 is deposited, what will be the ratio of the interest earned in the 4th year to the interest earned in the 5th year?
(A) 1:5
(B) 625:3125
(C) 100:105
(D) 100^4:105^4
(E) 725:3225
Rationale: The interest earned in the 1st year = $500
The interest earned in the 2nd year = $500*1.05
The interest earned in the 3rd year = $500*1.05^2
The interest earned in the 4th year = $500*1.05^3
The interest earned in the 5th year = $500*1.05^4
(500*1.05^3)/(500*1.05^4) = 1/1.05=100/105.
Answer: C.
Answer: (C) 100:105
Question: There are 300 employees in a room. 99% are managers. How many managers must leave the room to bring down the percentage of managers to 98%?
(A) 200
(B) 175
(C) 150
(D) 125
(E) 100
Rationale: There are 297 managers and 3 others. The 3 others would compose 2% of the total number of people if there were 150 people in the room. Thus 150 managers must leave.
The answer is C.
Answer: (C) 150
Question: The area of a square garden is Q square feet and the perimeter is P feet. If Q=P+21, what is the perimeter of the garden in feet?
(A) 24
(B) 28
(C) 32
(D) 36
(E) 40
Rationale: Let x be the length of one side of the square garden.
x^2 = 4x + 21
x^2 - 4x - 21 = 0
(x-7)(x+3) = 0
x = 7, -3
P = 4(7) = 28
The answer is B.
Answer: (B) 28
Question: In a forest 10 rabbits were caught, tagged with electronic markers, then released. A month later, 10 rabbits were captured in the same forest. Of these 10 rabbits, it was found that 2 had been tagged with the electronic markers. If the percentage of tagged rabbits in the second sample approximates the percentage of tagged rabbits in the forest, and if no rabbits had either left or entered the forest over the preceding month, what is the approximate number of rabbits in the forest?
(A) 150
(B) 70
(C) 50
(D) 1,500
(E) 500
Rationale: Given that 10 rabbits were caught and tagged in the first sample, and 10 were caught in the second sample of which 2 had tags, then 2/10 approximates the fraction of the population of tagged rabbits in the forest.
Proportion: A/x = C/D
A = rabbits tagged first sample
C/D = the fraction of the population of tagged rabbits in the forest
x = the population of rabbits in the forest
Proportion: 10/x = 1/5
x = (1)(10)(5) = 50. There are approximately 50 rabbits in the forest.
Answer is C
Answer: (C) 50
Question: A and B started a business with initial investments in the ratio 14 : 15 and their annual profits were in the ratio 7 : 6. If A invested the money for 10 months, for how many months did B invest his money?
(A) 2
(B) 4
(C) 6
(D) 8
(E) 9
Rationale: Sol.
Suppose A invested Rs. 14x for 10 months and B invested Rs. 15x for y months. Then,
14x * 10 / 15x * y = 7/6 ⇒ y = 840 / 105 = 8
Hence, B invested the money for 8 months.
Answer D
Answer: (D) 8
Question: Sum of 3 consecutive even no.'s is 34 more than the 1st no. of the series. Find the middle no.?
(A) 8
(B) 12
(C) 14
(D) 16
(E) 18
Rationale: Let the numbers be x, x+2 and x+4 then
x + x+2 + x+4 = x+34
3x + 6 = x + 34
2x = 28
\inline \therefore x = 14
\inline \therefore Middle number = x + 2 = 14+2 = 16
D
Answer: (D) 16
Question: A, B and C enter into partnership. A invests some money at the beginning, B invests double the amount after 6 months, and C invests thrice the amount after 8 months. If the annual gain be Rs.18000. A's share is?
(A) 6028
(B) 6020
(C) 6000
(D) 6098
(E) 6008
Rationale: x* 12 : 2x* 6: 3x* 4
1:1:1
1/3 * 18000 = 6000
Answer: C
Answer: (C) 6000
Question: How many integers between 265,205and 758,805 have tens digit 1 and units digit 3?
(A) 4,629
(B) 4,639
(C) 3,946
(D) 4,926
(E) 4,936
Rationale: There is one number in hundred with 1 in the tens digit and 3 in the units digit: 13, 113, 213, 313, ...
The difference between 265,205 and 758,805 is 758,805-265,205=493,600 - one number per each hundred gives 133,900/100=4,936 numbers.
Answer: E.
Answer: (E) 4,936
Question: A bottle contains a certain solution. In the bottled solution, the ratio of water to soap is 3:2, and the ratio of soap to salt is two times this ratio. The solution is poured into an open container, and after some time, the ratio of water to soap in the open container is halved by water evaporation. At that time, what is the ratio of water to salt in the solution?
(A) 1:1
(B) 2:3
(C) 3:2
(D) 9:4
(E) 18:8
Rationale: Water:soap = 3:2
Soap:Salt=6:2
=> For 6 soap, salt = 2
=> For 2 Soap, salt = (2/6)*2 = 2/3
So, water:soap:salt = 3:2:2/3 = 18:12:4
After open container, water:soap:salt = 9:18:4
So, water:salt = 9:4 = 18:8
E
Answer: (E) 18:8
Question: At a certain supplier, a machine of type A costs $20,000 and a machine of type B costs $55,000. Each machine can be purchased by making a 20 percent down payment and repaying the remainder of the cost and the finance charges over a period of time. If the finance charges are equal to 40 percent of the remainder of the cost, how much less would 2 machines of type A cost than 1 machine of type B under this arrangement?
(A) $10,000
(B) $11,200
(C) $12,000
(D) $12,800
(E) $19,800
Rationale: Total Cost of 2 Machines of Type A
= 20% of (Cost of 2 machine A) + remainder + 40 % remainder
= 20% of 40000 + (40000 - 20% of 40000) + 40% of (40000 - 20% of 40000)
= 52800
Total Cost of 1 Machine of Type B
= 20% of (Cost of 1 machine B) + remainder + 40 % remainder
= 20% of 55000 + (55000 - 20% of 55000) + 40% of (50000 - 20% of 55000)
= 72600
Diff = 72600 - 52800 = 19800
Hence, E.
Answer: (E) $19,800
Question: If A, B, and C invested some amount in the ratio 3:2:5 in a buisiness. If the total profit incurrec after a year was Rs.12100, find the share of B.
(A) Rs.6050
(B) Rs.3630
(C) Rs.2420
(D) Rs.3360
(E) Rs.6100
Rationale: Total profit after a year =12100 Ratio of profit share =3x+2x+5x=10x 10x = 12100. Therefore x=1210 B's share = 2*1210 =Rs.2420 Answer : C
Answer: (C) Rs.2420
Question: If an amount of Rs 13,640 is divided equally among
62 students, approximately how much amount will
each student get?
(A) Rs 206
(B) Rs 210
(C) Rs 220
(D) Rs 218
(E) None
Rationale: Amount received by each student = 13640/62 â‰ˆ Rs
220
Answer C
Answer: (C) Rs 220
Question: Three friends sai, vani and ram divide $1020 amongs them in such a way that if $10, $20 and $15 are removed from the sums that sai, vani and ram received respectively, then the share of the sums that they got will be in the ratio of 8 : 4 : 2. How much did ram receive?
(A) $147
(B) $142
(C) $242
(D) $122
(E) $143
Rationale: Explanatory Answer
Let the sums of money received by A, B and C be x, y and z respectively.
Then x - 10 : y - 20 : z -15 is 8a : 4a : 2a
When $10, $20 and $15 are removed, we are removing a total of $45 from $1020.
Therefore, 8a + 4a + 2a = 1020 - 45 = 975
i.e., 14a = 975
or a = 70.
We know that z - 2 = 70a = 2 * 70 =140
Therefore, z = 140 + 2 = $142
The correct choice is (B)
Answer: (B) $142
Question: A pupil's marks were wrongly entered as 83 instead of 63. Due to that the average marks for the class got increased by half (1/2). The number of pupils in the class is:
(A) 38
(B) 39
(C) 40
(D) 46
(E) 49
Rationale: Let there be x pupils in the class.
Total increase in marks = (x x 1/2) = x/2
x /2 = (83 - 63)
x /2= 20
x= 40
Answer is C
Answer: (C) 40