divelab/Sys2Bench huggingface dataset:
Question: Tom purchased 8kg of apples at the rate of 70 per kg and 9 kg of mangoes at the rate of 45 per kg. How much amount did he pay to the shopkeeper?
Options:
A)A)1040
B)B)1045
C)C)965
D)D)1060
E)E)1075
Rationale: Cost of 8 kg apples= 70 × 8 = 560.
Cost of 9 kg of mangoes = 45 × 9 = 405.
Total cost he has to pay = 560 + 405 = 965.
C)
Answer: C
Question: Which one of the following numbers is exactly divisible by 11?
Options:
A)415618
B)415620
C)415621
D)415623
E)415624
Rationale: (4 + 5 + 2) - (1 + 6 + 3) = 1, not divisible by 11.
(2 + 6 + 4) - (4 + 5 + 2) = 1, not divisible by 11.
(4 + 6 + 1) - (2 + 5 + 3) = 1, not divisible by 11.
(4 + 6 + 1) - (2 + 5 + 4) = 0, So, 415624 is divisible by 11.
E)
Answer: E
Question: A single letter is selected at random from the word 'PROBABILITY'. The probability that it is a vowel is..??
Options:
A)2/11
B)3/11
C)4/11
D)0
E)1
Rationale: total vowels = 4, total number of letters = 11
so probability = 4/11
ANSWER:C
Answer: C
Question: The average number of shirts with Salman, Ambani and Dalmiya is 60, if all of them reached a shopping mall in Delhi and purchased 4 shirts each of them then average number of shirt each of them now has
Options:
A)66
B)63
C)62
D)64
E)61
Rationale: Required average
= Old average + New average
= 60 + 4 = 64
answer :D
Answer: D
Question: Ifaequals the sum of the even integers from 2 to 20, inclusive, andbequals the sum of the odd integers from 1 to 19, inclusive, what is the value of a * b ?
Options:
A)10000
B)11000
C)19000
D)20000
E)21000
Rationale: Yes! there is really a faster way to solve it.
Sum of consecutive odd or even integers = (no. of odd or even ints) * (first int + last int) / 2
Here A = sum of even ints from 2 to 20, inclusive
number of even ints = 10,
first int + last int = 2+20 = 22
A = 10*22 / 2 = 110
B = sum of odd ints from 1 to 19, inclusive
number of odd ints = 10,
first int + last int = 1+19 = 20
A = 10*20 / 2 = 100
A*B = 110 * 100 = 11000
Ans : B
Answer: B
Question: If two numbers are in the ratio 2:5. If 10 is added to both of the numbers then the ratio becomes 3:7 then find the smallest number?
Options:
A)40
B)80
C)60
D)20
E)100
Rationale: Given ratio - 2:5
2x + 10 : 5x + 10 = 3 : 7
7[2x + 10] = 3[5x + 10]
14x + 70 = 15x + 30
15x - 14x = 70 - 30
x = 40
Then smallest number is = 2
2x = 80
ANS - B
Answer: B
Question: An Olympic diver received the following scores: 5, 6, 3, 2. The standard deviation of her scores is in which of the following ranges?
Options:
A)5.01 to 5.99
B)3.01 to 3.99
C)4.01 to 4.99
D)2.01 to 2.99
E)1.01 to 1.99
Rationale: 5+6+3+2/4=4
∣5-4∣^2 =1^2 = 1
∣6-4∣^2 =2^2 = 4
∣3-4∣^2 =1^2 = 1
∣2-4∣^2 =2^2 = 4
sqrt 10/4 =1.58
Answer : E
Answer: E
Question: Claire has 3 books. She averages the amount of pages of each book to have 305 pages. If her mom buys her a new book which has 400 pages, what will the new average be?
Options:
A)342.5
B)328.75
C)330.87
D)342.75
E)335
Rationale: (sum of the pages of the 3 books)/3 = 305
sum of the pages of the 3 books = 915
new sum = 915+400 = 1315
new average = 1315/4 = 328.75
ans: B
Answer: B
Question: When the oil from a circular cylinder leaked, the formula for the speed of the leak is V = kh^2, where h was the height of the remaining oil and k was constant. If the height of the cylinder is 4, the speed of the leak is Vâ€™, When the height of the oil remaining is 16, what was the speed of the leak, in terms of Vâ€™?
Options:
A)2Vâ€™
B)4Vâ€™
C)Vâ€™/2
D)Vâ€™/4
E)16Vâ€™
Rationale: When h=4 v=V'
So V' = k.16
Hence k = V'/16
Now when h=16
v=(V'/16).16^2
v=V'.16
v=16V'
Ans : E
Answer: E
Question: Visitors to show were charged Rs.15 each on the first day. Rs.7.50 on the second day, Rs.2.50 on the third day and total attendance on the three days were in ratio 2:5:13 respectively. The average charge per person for the whole show is?
Options:
A)6
B)9
C)5
D)3
E)4
Rationale: 2: 5: 13
2x 5x 13x
15 7.5 2.5
30x + 37.5x + 32.5x = 100x/20x
Average = 5
Answer: C
Answer: C
Question: Suppose we have six marbles: 3 blue marbles, 2 red marbles, and one green marble. Suppose we are going to put them into three cups: a black cup, a white cup, and a purple cup. The only restriction is that the two red marbles can’t be in the same cup. We could put as many as five (all except one of the reds) in any cup. We could leave one cup empty, or put some in each of the three cups. All combinations are allowed that don’t involve the two red marbles in the same cup. How many combinations are possible?
Options:
A)90
B)180
C)360
D)540
E)720
Rationale: 3 Blue Marble:
Different distribution : (1) All 3 in the same cup (2) Split 2-1 in two cups (3) Split 1-1-1
Case (1) 3 possibilities
Case (2) 6 possibilities ,
Case (3) 1 possibility
tot. 10 possibilities.
One Green Marble :
3 possibilities (one for each cup at the time)
First Red marble:
3 possibilities (one for each cup at the time)
Second Red marble:
2 possibilities ( because can't go in the same cup with the other Red marble)
TOTAL:
10*3*3*2 = 180 , answer, B .
Answer: B
Question: If c is an integer greater than 6, which of the following must be divisible by 3?
Options:
A)c (c+4) (c-2)
B)c (c+2) (c-1)
C)c (c+3) (c-5)
D)c (c+1) (c-4)
E)c (c+5) (c-6)
Rationale: anything in the form of (c-1) (c) (c+1) is divisible by 3. in other word, a product of any 3 consecutive intevers is divisible by 3.
c (c+1) (c-4) = c (c+1) ((c-1)-3) is equivalant to (c-1) (c) (c+1)
c (c+2) (c-1) is equivalant to (c+1) missing.
c (c+3) (c-5) is equivalant to (c-1) missing and c repeating.
c (c+4) (c-2) is equivalant to odd/even consqcutive integers
c (c+5) (c-6) is equivalant to (c+1) missing and c repeating.
Answer : D
Answer: D
Question: The Kiljaro Highway is marked with Milestones denoting the distance to the town of Kiljaro. Tommy left kiljaro and drove the highway, passing the 40 km milestone at 8:30. Some time afterwards, Tommy got a phone call asking him to return home, and he made a U-turn at the 160 km milestone. At 09:A0 Tommy passed the milestone marking 70 km to Kiljaro. The variable A represents the tens digit of the minutes in 09:A0. Assuming Tommy maintained the same constant speed during the entire drive, how many kilometers did Tommy travel in one minute?
Options:
A)210/(30+10A)
B)210/(30+60A)
C)210/35A
D)210/(30+10A)
E)220/40A
Rationale: Since we are dealing with the variables in the answer choices,the best possible method according to me would be substitution.
Substitute A with 3.meaning tommy would have travelled a distance of ((160-40) + (160-70)) in 60 minutes.
210 Kms in 60 minutes ==> 3.5km/hr.
Substitute A with 3 in the answer options.
Option A
Answer: A
Question: A, B and C started a business A's investment is 2 times of B's investment is 5 times of C's investment. Find the profit of B in the total profit of Rs. 1600.
Options:
A)Rs. 25600
B)Rs. 8500
C)Rs. 7200
D)Rs. 500
E)None of these
Rationale: Explanation:
A = 2B and B = 5C
=> A : B = 2:1 and B : C = 5 : 1
=> A : B : C = 10 : 5 : 1
Ratio of capitals of A, B and C = 10 : 5 : 1
B's share = Rs.[(5/16) × 1600] = Rs. 500
Answer: Option D
Answer: D
Question: A certain number when divided by 39 leaves a remainder 20, what is the remainder when the same number is divided by 13?
Options:
A)11
B)5
C)8
D)7
E)9
Rationale: 39 + 20 = 59/13 = 7 (Remainder)
ANSWER D
Answer: D
Question: The average of eight numbers is 14. The average of six of these numbers is 16.The average of the remaining two numbers is
Options:
A)14×8 – 16×6)/9
B)14×8 – 16×6)/1
C)14×8 – 16×6)/2
D)14×8 – 16×6)/5
E)14×8 – 16×6)/6
Rationale: Average of eight numbers = 14
Average of six numbers = 16
Average will be = (14×8 – 16×6)/2
\Answer:	C
Answer: C
Question: In what time will a train 100 m long cross an electric pole, it its speed be 144 km/hr?
Options:
A)2.5 sec
B)2.8 sec
C)7.5 sec
D)2.3 sec
E)1.5 sec
Rationale: Speed = 144 * 5/18
= 40 m/sec
Time taken = 100/40
= 2.5 sec.
Answer:A
Answer: A
Question: A man is trying 2 different pairs of pants &6 different shirts. How many combinations of 1 pair of pants &1 shirt are possible?
Options:
A)10
B)12
C)16
D)19
E)21
Rationale: Use a tree diagram to illustrate the possible selections. In the diagram, use P1 and P2 to represent the pants and S1, S2, S3, S4, S5, and S6 to represent the shirts.
Using the Fundamental Counting Principle, 2 × 6 = 12 outfits are possible.
B
Answer: B
Question: What is the sum of the greatest common factor and the lowest common multiple of 12 and 36?
Options:
A)48
B)22
C)32
D)36
E)38
Rationale: Prime factorization of 12 = 2 x 2 x 3
Prime factorization of 36 = 2 x 2 x 3 x 3
GCF = 12
LCM = 36
Sum = 48.
Answer A.
Answer: A
Question: On a certain day, Jared's farm harvested 2526 oranges. If Jared distributes his oranges evenly across 7 different retail shops, how many oranges would remain with him?
Options:
A)4 oranges
B)7 oranges
C)1 orange
D)2 oranges
E)14 oranges
Rationale: This is equivalent to finding the first number that is divisible by 7 that occurs before 2135.
In order to divide the sum in 9 parts, the amount must be divisible by 7
Divisibility rule of 7: The sum of the digits must be divisible by 7
Sum of digits of 2526 = 15 and 7 is divisible by 7.
Hence, we need to remove 1 to this number for it to be divisible by 7
Correct Option: C
Answer: C
Question: A father was as old as his son's present at the time of your birth. If the father's age is 38 years now, the son's age six years back was?
Options:
A)10 years
B)12 years
C)13 years
D)16 years
E)18 years
Rationale: Let the son's present age be x years. Then, (38 - x) = x
2x = 38.
x = 19.
Son's age 6 years back (19 - 6) = 13 years.
C
Answer: C
Question: The compound interest on $ 30,000 at 7% per annum is $4347. The period (in years) is:
Options:
A)2
B)2 1/2
C)3
D)4
E)5
Rationale: Amount = $(30000 + 4347) = $. 34347.
Let the time be n years.
Then, 30000 1 +	7 n	= 34347
100
107 n	=	34347	=	11449	= 107 2
100 30000 10000 100
n = 2 years.
ANSWER A - 2
Answer: A
Question: If the cost price is 82% of the selling price, then what is the profit percent?
Options:
A)5%
B)22%
C)13%
D)21%
E)19%
Rationale: Let S.P. = $100
C.P. = $82
Profit = $18
Profit% = 18/82 * 100 = 25/6 = 22% approximately
Answer is B
Answer: B
Question: Can you find the last number in the number sequence given below?
10 : 10 : 20 : 45 : 110 : 300 : ?
Options:
A)880
B)756
C)390
D)610
E)930
Rationale: E
930
Explanation:
New number = Last number * multiplication factor (increased by 0.5 every time) + sum factor (increased by 5 every time)
10
10 * 0.5 + 5 => 10
10 * 1.0 + 10 => 20
20 * 1.5 + 15 => 45
45 * 2.0 + 20 => 110
110 * 2.5 + 25 => 300
300 * 3.0 + 30 => 930 , desired answer
Answer: E
Question: Calculate the largest 6 digit number which is exactly divisible by 99?
Options:
A)999991
B)999965
C)999912
D)999936
E)999930
Rationale: Largest 4 digit number is 999999
After doing 999999 ÷ 96 we get remainder 55
Hence largest 4 digit number exactly divisible by 88 = 9999 - 55 = 9944
ANSWER : D
Answer: D
Question: A, B and C play a cricket match. The ratio of the runs scored by them in the match is A:B = 2:3 and B:C = 2:5. If the total runs scored by all of them are 75, the runs scored by B are?
Options:
A)11
B)18
C)13
D)17
E)12
Rationale: A:B = 2:3
B:C = 2:5
A:B:C = 4:6:15
6/25 * 75 = 18
Answer:B
Answer: B
Question: The average of five consecutive odd numbers is 61. What is the difference between the highest and lowest numbers :
Options:
A)4
B)8
C)12
D)16
E)18
Rationale: Explanation:
Let the numbers be x, x + 2, x + 4, x + 6 and x + 8.
Then [x + (x + 2) + (x + 4) + (x + 6) + (x + 8) ] / 5 = 61.
or 5x + 20 = 305 or x = 57.
So, required difference = (57 + 8) - 57 = 8 Answer: B
Answer: B
Question: If $120 invested at a certain rate of simple interest amounts to $160 at the end of 3 years,How much will $150 amount to at the same rate of interest in 6 years?
Options:
A)$190
B)$180
C)$200
D)$240
E)$250
Rationale: 120 amounts to 160 in 3 years.
i.e (principal + interest ) on 120 in 3 years = 160
120 + 120*(r/100)*(3) = 160 => r = 100/9
150 in 6 years = principal + interest
= 150 + 150*(r/100)*(6)
250
Answer is E.
Answer: E
Question: A certain industrial machine requires 15 quarts (480 ounces) of oil every day, and it is given a mixture of oil A and oil B. Oil A consists of 5% special additives while oil B consists of 9% special additives. If the machine needs exactly 30 ounces of the special additives to ensure smooth operation, then how much of oil A, in ounces, should be in the mixture?
Options:
A)a.	A – 260
B)b.	B – 280
C)c. C – 290
D)d.	D – 330
E)e.	E – 380
Rationale: 5%*x + 9% *(480-x)=30
13.2 = 4 %*x
x=330
D
Answer: D
Question: The sum of two numbers is 50 and their product is 1050. What will be the sum of their reciprocals?
Options:
A)(11/140)
B)(1/21)
C)(35/4)
D)(75/8)
E)None
Rationale: Solution
x+y=50 xy=1050 1/x+1/y=x+y/xy 50/1050 = (1/21).
Answer B
Answer: B
Question: To fill a tank, 25 buckets of water is required. How many buckets of water will be required to fill the same tank if the capacity of the bucket is reduced to two-fifth of its present ?
Options:
A)35
B)43
C)62.5
D)71
E)72.5
Rationale: Let the capacity of bucket be 10 Litres
They said that it requires 25 buckets to fill the tank
Therefore capacity of tank=25*10=250
If the capacity of the bucket is reduced to to 2/5th of original capacity then New capacity of bucket=(2/5)10=4litres
No. of buckets required to fill the tank=250/4 = 62.5
answer:C
Answer: C
Question: In 10 years, A will be twice as old5as B was 10 years ago. If A is now 8 years older than B, the present age of B is
Options:
A)35
B)37
C)38
D)41
E)42
Rationale: Explanation:
Let B's age = x years.
Then, As age = (x+ 8) years.
(x+8+10)=2(x—10)
hence x=38.
Present age of B = 38 years
Answer: Option C
Answer: C
Question: Ice-ColdIce-cream factory produces only tricolor ice-cream products, where each ice-cream has three stripes of different colors. The factory uses the colors pink, purple, orange, silver, blue and GRAY. How many different ice-cream products have at least one stripe out of the following colors: pink, purple or orange (assume that the order of the stripes in a single ice-cream does not matter)?
Options:
A)12
B)14
C)18
D)19
E)20
Rationale: IMO: D - 19
There are 6C3 = 20 ways to create different colored ice cream products. Out of these 20, only 1 (Silver, Blue, GRAY) will not contain at least one of the colors pink, purple, or orange. 20 - 1 = 19.
The other way would be to calculate the number of ice cream products that contain at least one of the colors pink, purple, or orange (PPO).
#1: Pick one out of PPO and two out of SBP: 3C1 * 3C2 = 3 * 3 = 9
#2: Pick two out of PPO and one out of SBP: 3C2 * 3C1 = 3 * 3 = 9
#3: Pick three out of PPO: 3C3 = 1
9 + 9 + 1 = 19
answer is D
Answer: D
Question: If X and Y are sets of integers, X # Y denotes the set of integers that belong to set X or set Y, but not both. If X consists of 8 integers, Y consists of 10 integers, and 6 of the integers are in both X and Y, then X # Y consists of how many integers?
Options:
A)6
B)16
C)22
D)30
E)174
Rationale: The number of integers that belong to set X ONLY is 8-6=2;
The number of integers that belong to set Y ONLY is 10-6=4;
The number of integers that belong to set X or set Y, but not both is 2+4=6.
Answer: A.
Answer: A
Question: A bulldog received 1,600 votes in a bulldog competition, giving him 20 percent of the votes. What percent of the remaining votes would he have needed to receive in order to win 28 percent of the total votes?
Options:
A)10%
B)12.5%
C)15%
D)17.5%
E)20%
Rationale: There were 80% of the votes remaining and he needed 8%/80% = 1/10 = 10%
The answer is A.
Answer: A
Question: What is the smallest integer that is the sum of 2 distinct prime integers, each greater than 80 ?
Options:
A)170
B)172
C)173
D)199
E)186
Rationale: First of all, discard 173 and 199 since they are odd. Sum of two primes greater than 2 will always be even because both primes will be odd.
Both numbers need to be greater than 80 i.e. their sum needs to be greater than 160. Since two of the given sums, 170 and 172, are quite close to 160, it should be fair to assume that if they can be written as sum of two primes, we will find the primes between 80 to 90.
Between 80 and 90, there are only 2 primes: 83 and 89 (if you don't remember this, you just need to check for 81, 83, 87 and 89)
83+89 = 172 so answer is (B)
Answer: B
Question: A motor pool has 300 vehicles of which 30 percent are trucks. 20 percent of all the vehicles in the motor pool are diesel, including 15 trucks. What percent of the motor pool is composed of vehicles that are neither trucks nor diesel?
Options:
A)165%
B)90%
C)65%
D)55%
E)10%
Rationale: Solution
Percentage of vehicles neither trucks nor diesel = Total Number of trucks - (Diesel Trucks +Non Diesel Trucks +Other Diesel Vehicles)/Total Number of trucks = 300-(75+15+45)/300= 165/300= 55%
Ans D
Answer: D
Question: In a group of buffaloes and ducks, the number of legs are 24 more than twice the number of heads. What is the number of buffaloes in the group?
Options:
A)12
B)3
C)5
D)8
E)10
Rationale: Let the number of buffaloes be x and the number of ducks be y.
Then 4x+2y=2(x+y)+24
=>x=12
ANSWER A 12
Answer: A
Question: An employee’s annual salary was increased $5,000. If her new annual salary now equals $25000 what was the percent increase?
Options:
A)15%
B)80%
C)20%
D)22%
E)24%
Rationale: New annual salary = $25000
Salary increase = $5000.
Original salary = $25000 - $5,000.
= $20,000
%Increase = ($15,000/ $75,000 )*100
=80%
Hence B.
Answer: B
Question: If x ¤ y = (x + y)^2 - (x - y)^2. Then √7 ¤ √7 =
Options:
A)0
B)5
C)10
D)15
E)28
Rationale: X = √7 and Y also =√7
Applying the function (√7+√7)^2 - (√7-√7)^2 = (2√7)^2 - 0 = 4 x 7 = 28.
Note: Alternative Approach is the entire function is represented as X^2 - Y^2 = (X+Y)(X-Y) which can be simplified as (x+y+x-y)(x+y-(x-y)) = (2x)(2y)=4xy. Substituting x=√7 and y = √7 you get the answer 28.
Answer E
Answer: E
Question: A wire in the form of a circle of radius 3.5 m is bent in the form of a rectangule, whose length and breadth are in the ratio of 6 : 5. What is the area of the rectangle?
Options:
A)76 cm2
B)30 cm2
C)56 cm2
D)45 cm2
E)19 cm2
Rationale: The circumference of the circle is equal to the permeter of the rectangle.
Let l = 6x and b = 5x 2(6x + 5x) = 2 * 22/7 * 3.5
=> x = 1
Therefore l = 6 cm and b = 5 cm Area of the rectangle = 6 * 5
= 30 cm2
Answer:B
Answer: B
Question: Divide Rs. 1500 among A, B and C so that A receives 1/3 as much as B and C together and B receives 2/3 as A and C together. A's share is?
Options:
A)387
B)320
C)375
D)372
E)322
Rationale: A+B+C = 1500
A = 1/3(B+C); B = 2/3(A+C)
A/(B+C) = 1/3
A = 1/4 * 1500 =>
375
Answer: C
Answer: C
Question: At Deluxe paint store, Fuchsia paint is made by mixing 4 parts of red paint with 2 parts of blue paint. Mauve paint is made by mixing 3 parts of red paint with 6 parts blue paint. How many liters of blue paint must be added to 24 liters of Fuchsia to change it to Mauve paint?
Options:
A)9
B)12
C)15
D)16
E)24
Rationale: in 24 liters, Red = 4/6 * 24 = 16 and Blue = 8
so, 16/(8+x) = 3/6
or, x = 24 (Answer E)
Answer: E
Question: The average age of an adult class is 40 years. 12 new students with an avg age of 34years join the class. Therefore decreasing the average by 4 years. Find what was the original average age of the class?
Options:
A)6
B)12
C)16
D)20
E)22
Rationale: Let original strength = y
Then , 40y + 12 x 34 = ( y + 12) x 36
â‡’ 40y + 408 = 36y + 432
â‡’ 4y = 48
âˆ´ y = 6
A
Answer: A
Question: A box contains seven light out of which 3 are defective. If three light are chosen at random, find the probability that all the three light are defective?
Options:
A)2/35
B)3/35
C)1/35
D)3/37
E)None of these
Rationale: Out of nine light , five are good and four are defective.
Required probability = 3C3/7C3 = 1/35
C
Answer: C
Question: In the office supply store, Brittany bought 17 pens of three kinds: ball pens, gel pens, and ink pens, which cost $0.05, $0.10 and $0.25 each. The total that Brittany paid was $2.05. If Brittany bought twice as many gel pens as ink pens, how many ball pens did she buy?
Options:
A)4
B)5
C)7
D)8
E)10
Rationale: Denote each pen with the first letter of its kind and build a system of equations:
5B+10G+25I=205
B+G+I=17
G=2I
B+9I=41
B+3I=17
6I=24
I=4
B=5
Answer: B
_____________
Answer: B
Question: The average amount with a group of seven numbers is Rs. 20. If the newly joined member has Rs. 50 with him, what was the average amount with the group before his joining the group?
Options:
A)15
B)25
C)18
D)22
E)30
Rationale: Total members in the group = 7
Average amount = Rs. 20
Total amount with them = 7 * 20 = Rs. 140
One number has Rs. 50. So, the amount with remaining 6 people = 140 - 50 = Rs. 90
The average amount with them = 90/6 = Rs. 15.
ANSWER A
Answer: A
Question: A worker makes a toy in every 2h. If he works for 100h, then how many toys will he make ?
Options:
A)40
B)54
C)50
D)39
E)None
Rationale: No. of toys = 100/2 = 50
Answer : C
Answer: C
Question: The average of five number is 27. if one number is excluded, the average becomes 25. The excluded number is :
Options:
A)25
B)27
C)30
D)35
E)None of these
Rationale: Solution
Excluded number = (27 × 5) - (25 × 4) = 135 - 100 = 35. Answer D
Answer: D
Question: The area of an isosceles trapezoid with sides of length 5 and bases of length 10 and 16 is?
Options:
A)48
B)40
C)52
D)54
E)58
Rationale: Isosceles trapezoid indicates that if we draw perpendicular from two vertex of the smaller side, the longer side with side 16 will be divided into 3 parts= 10, 3 and 3 (Making one square and two right triangles)
For the right triangle, height will be= (5^2-3^2)^1/2= 4
And the area of trapezoid = 1/2 (B1+B2)H= 1/2*26*4= 52
C is the answer
Answer: C
Question: The difference between compound interest and simple interest on a certain amount of money at 5% per annum for 2 years is 17. Find the sum :
Options:
A)4500
B)7500
C)5000
D)6800
E)None of these
Rationale: Sol.(d) Let the sum be 100.
Therefore, SI = 100×5×2100=10100×5×2100=10
and CI = 100(1+5100)2−100100(1+5100)2−100
∴ =100×21×2120×20−100=414=100×21×2120×20−100=414
Difference of CI and SI = 41⁄4 - 10 = 1⁄4
If the difference is 1⁄4 , the sum = 100
=> If the difference is 17, the sum
= 400 × 17 = 6800 Answer D
Answer: D
Question: Jackie has two solutions that are 4 percent sulfuric acid and 12 percent sulfuric acid by volume, respectively. If these solutions are mixed in appropriate quantities to produce 60 liters of a solution that is 5 percent sulfuric acid, approximately how many liters of the 4 percent solution will be required?
Options:
A)18
B)20
C)24
D)36
E)26.25
Rationale: let a=amount of 4% acid and b= amount of 12% acid.
Now, The equation translates to,
0.04a + .12b = .05(a+b)
but a+b= 60
therefore .04a + .12b = .05(60)
=> 4a + 12b = 300
but b=60-a
therefore
4a+ 12(60-a) = 300
=> 16a = 420
hence a = 26.25.
Answer : E
Answer: E
Question: A chemist mixes one liter of pure water with x liters of a 50% salt solution, and the resulting mixture is a 10% salt solution. What is the value of x?
Options:
A)1/4
B)1/3
C)1/2
D)1
E)3
Rationale: Concentration of salt in pure solution = 0
Concentration of salt in salt solution = 50%
Concentration of salt in the mixed solution = 10%
The pure solution and the salt solution is mixed in the ratio of --> (50 - 10)/(10 - 0) = 4/1
1/x = 4/1
x = 1/4
Answer: A
Answer: A
Question: P and Q started a business investing Rs. 85,000 and Rs. 15,000 respectively. In what ratio the profit earned after 2 years be divided between P and Q respectively?
Options:
A)3:4
B)3:5
C)15:23
D)17:23
E)None of these
Rationale: Explanation:
P:Q = 85000 : 15000 = 17:3.
ANSWER IS E
Answer: E