divelab/Sys2Bench huggingface dataset:
Question: If x dollars is invested at 10 percent for one year and y dollars is invested at 8 percent for one year, the annual income from the 10 percent investment will exceed the annual income from the 8 percent investment by $83. If $2,000 is the total amount invested, how much is invested at 8 percent?
Options:
A)$550
B)$650
C)$750
D)$850
E)$950
Rationale: 0.1x = 0.08(2000-x)+83
0.18x = 243
x = 1350
Then the amount invested at 8% is $2000 - $1350 = $650
The answer is B.
Answer: B
Question: An equilateral triangle is inscribed in a circle, as shown above. What is the area of the shaded region, if the area of the circle is 2?
Options:
A)2 - 3√3
B)2 - 3√3/∏
C)2 - 3√3/4
D)2 - 3√3/(2∏)
E)2∏ - 3√3/(2∏)
Rationale: 1) since we are subtracting from overall so first term should be 2... E out
2) the area of triangle that is to be subtracted should be in terms of π...A and C are out.. also A gives you answer in negative
3) in B, ans would be around 0.3 and in D, ans will be around 1.2...
Clearly the shaded and unshaded are close to 1/2 each..
D is the answer
Answer: D
Question: Let X be the smallest positive integer such that 10 and 14 are factors of 250 + X, so the value of X is:
Options:
A)0
B)10
C)20
D)30
E)40
Rationale: You can calculate the LCM (10,14) = 70.
After that you should check which of the possible X values will result in a number divisible by 70.
The only possibility for this is 30 ( because 250 + 30 = 280 = 70*4)
Answer D
Answer: D
Question: Two friends P & Q started a business investing amounts in the ratio of 5 : 6. R joined them after six months investing an amount equal to that of Q’s amount. At the end of the year 20% profit was earned which was equal to 98,000. What was the amount invested by R?
Options:
A)2,10,000
B)1,05,000
C)1,75,000
D)Data inadequate
E)None of these
Rationale: Ratio for amount invested by P, Q & R
= 5x × 12 : 6x × 12 : 6x × 6
= 60x : 72x : 36x
= 5x : 6x : 3x
Profit = 98000 = 20% of T
where, T = Total amount
T = 490000
Amount received by
R = 3x /3x+6x+5x(490000)
= 105000
Answer B
Answer: B
Question: In how many H ways can a four-letter password be chosen, using the letters A, B, C, D, E, and/or F, such that at least one letter is repeated within the password?
Options:
A)720
B)864
C)900
D)936
E)1,296
Rationale: Total number of four letter passwords = 6*6*6*6= 1296 ------(1)
Total number of passwords in which no letter repeats = 6C4*4!= 15*24=360------(2)
therefore required value H= (1)-(2)= 1296-360=936.D
Answer: D
Question: How many of the positive factors of 16 are not factors of 20
Options:
A)2
B)3
C)4
D)1
E)5
Rationale: factors of 16 - 1, 2, 4, 8, 16
factors of 20 -1, 2, 4, 5, 10, 20.
Comparing both, we have 2 factors of 16 which are not factors of 20- 8,16
Answer: A
Answer: A
Question: Line m lies in the xy-plane. The y-intercept of line m is -2, and line m passes through the midpoint of the line segment whose endpoints are (2, 8) and (14,4). What is the slope of line m?
Options:
A)-2
B)-1
C)0
D)1
E)2
Rationale: The midpoint of (2,8) and (14,4) is (8,6).
The slope of a line through (0,-2) and (8,6) is (6-(-2))/(8-0) = 8/8 = 1
The answer is D.
Answer: D
Question: A student took five papers in an examination, where the full marks were the same for each paper. His marks in these papers were in the proportion of 6:7:8:9:10. In all papers together, the candidate obtained 60% of the total marks then, the number of papers in which he got more than 50% marks is
Options:
A)1
B)3
C)4
D)5
E)7
Rationale: Solution: Let the marks obtained in five subjects be 6x, 7x, 8x, 9x and 10x.
Total marks obtained= 40x
Max. Marks of the five subjects = 40x/0.6 [40x is 60% of total marks]
Max. Marks in each subject = 40x/0.6*5 = 13.33x
Hence, % of each subject = 6x*100/13.33 = 45.01%
Or, 7x*100/13.33 = 52.51
In same way other percentage are 60.01%, 67.52%, 75.01%.
Hence, number of subjects in which he gets more than 50% marks = 4.
Answer: Option C
Answer: C
Question: How many integers are between 4 and 87/8, inclusive?
Options:
A)4
B)5
C)7
D)9
E)10
Rationale: 87/8 = 10.xx
We are not concerned about the exact value of 87/8 as we just need the integers.
Since the values are small, we can write down the integers.
The different integers between 4 and 87/8 would be 4, 5, 6, 7, 8, 9, 10
Total number of integers = 7
Option C
Answer: C
Question: The average age of a group of 5 members is 20 years. Two years later, a new member joins the group. The average age of the group becomes 21 years. What is the age of the new member ?
Options:
A)20 years
B)21 years
C)16 years
D)23 years
E)24 years
Rationale: The average age of a group of 5 members is 20 years --> the sum of the ages is 5*20=100;
Two years later the sum of the ages of these 5 members would be 100+5*2=110;
Now, say the age of the new member is x years, so the sum of the ages of a new 6 member group is 110+x. Since given that the average age of this group of 6 members is 21 years then: 21*6=110+x --> x=16.
Answer: C.
Answer: C
Question: A certain family has 3 sons: Richard is 6 years older than David, and David is 8 years older than Scott. If in 8 years, Richard will be twice as old as Scott, then how old was David 3 years ago?
Options:
A) 8
B) 11
C) 12
D) 14
E) 16
Rationale: Let's say
Age of Richard isR
Age of David isD
Age of Scott isS
Now
Richard is 6 years older than David,
i.e. R = D +6
David is 8 years older than Scott
i.e. D = S +8
If in 8 years, Richard will be twice as old as Scott
i.e. R+8 = 2x(S+8)
i.e. R+8 = 2S + 16
i.e. R = 2S+8
But R = D+6 = (S+8)+6 = S+14
therefore, 2S + 8 = S +14
i.e. S = 6
i.e. R = 20
i.e. D = 14
Now,
how old was David 3 years ago?
i.e. D-3 = 14-3 = 11 years
Answer: Option
B
Answer: B
Question: Margaret is 7 years more than twice the age of his son. The age of son is 12. Find the age of mother and find the difference between their ages
Options:
A)19yrs
B)20yrs
C)30yrs
D)40yrs
E)50yrs
Rationale: Let, age of son x=12
Margaret is 7 years more than twice the age of his son, y = 7+2(x)
=7+2(12)
=7+24
=31yrs
Difference = 31 - 12
=19yrs
ANSWER:A
Answer: A
Question: Barbata invests $2800 in the National Bank at 5%. How much additional money must she invest at 8% so that the total annual income will be equal to 6% of her entire investment?
Options:
A)1200
B)3000
C)1000
D)1400
E)2400
Rationale: Let the additional invested amount for 8% interest be x;
Equation will be;
2800+0.05*2800+x+0.08x = 2800+x+0.06(2800+x)
0.05*2800+0.08x = 0.06x+0.06*2800
0.02x = 2800(0.06-0.05)
x = 2800*0.01/0.02 = 1400
Ans: "D"
Answer: D
Question: If December 3rd, 1999 is a Friday, what day is January 5th, 2000?
Options:
A)Wednesday
B)Thursday
C)Friday
D)Saturday
E)Sunday
Rationale: There is difference of 33 days from Dec. 3rd 1999 to Jan. 5th 2000.
33/7 has a remainder of 5.
Jan. 5th is: Friday + 5 days = Wednesday
The answer is A.
Answer: A
Question: In a class of 40 students, 2 students did not borrow any books from the library, 12 students each borrowed 1 book, 11 students each borrowed 2 books, and the rest borrowed at least 3 books. If the average number of books per student was 2, what is the maximum number of books any single student could have borrowed?
Options:
A)3
B)4
C)5
D)6
E)7
Rationale: The class borrowed a total of 40*2 = 80 books.
The 25 students who borrowed 0, 1, or 2 books borrowed a total of 12 + 11*2 = 34.
To maximize the number of books borrowed by 1 student, let's assume that 14 students borrowed 3 books and 1 student borrowed the rest.
80 - 34 - 3*14 = 4
The maximum number of books borrowed by any student is 4.
The answer is B.
Answer: B
Question: If the price of petrol increases by 25% and Benson intends to spend only an additional 15% on petrol, by how much % will he reduce the quantity of petrol purchased?
Options:
A)A)8%
B)B)7%
C)C)10%
D)D)6%
E)E)9%
Rationale: Explanation:
Assume that the initia price of 1 Litre petrol = Rs.100 ,Benson spends Rs.100 for petrol,
such that Benson buys 1 litre of petrol
After the increase by 25%, price of 1 Litre petrol = 100 × (100+25)/100 = Rs.125
Since Benson spends additional 15% on petrol,
amount spent by Benson = 100× (100+15)/100 = Rs.115
Hence Quantity of petrol that he can purchase = 115/125 Litre
Quantity of petrol reduced = (1−115/125) Litre
Percentage Quantity of reduction = (1−115125)/1 × 100 = 10/125 × 100 = 105 × 4 = 2 × 4 = 8%
Answer: Option A
Answer: A
Question: If 50 apprentices can finish a job in 4 hours, and 30 journeymen can finish the same job in 6 hours, how much of the job should be completed by 10 apprentices and 15 journeymen in one hour?
Options:
A)1/9
B)29/180
C)26/143
D)2/15
E)39/121
Rationale: 50 apprentices can finish the job in 4 hours,thus:
10 apprentices can finish the job in 4*5 = 20 hours;
In 1 hour 10 apprentices can finish 1/20 of the job.
30 journeymen can finish the same job in 4,5 hours,thus:
15 journeymen can finish the job in 6*2 = 12 hours;
In 1 hour 15 journeymen can finish 1/12 of the job.
Therefore, in 1 hour 10 apprentices and 15 journeymen can finish 1/20+1/12=2/15 of the job.
Answer: D.
Answer: D
Question: A taxi leaves Point A 3 hours after a bus left the same spot. The bus is traveling 30 mph slower than the taxi. Find the speed of the taxi, if it overtakes the bus in three hours.
Options:
A)60
B)72
C)48
D)36
E)64
Rationale: Let the speed of bus be v - 30, speed of taxi be v
The bus travelled a total of 6 hrs and taxi a total of 3 hrs.
Hence 6 * (v-30) = 3v
6v - 180 = 3v
3v = 180
v = 60 mph
A
Answer: A
Question: What is the 8th digit to the right of the decimal point in the decimal equivalent of 73/11?
Options:
A)1
B)3
C)4
D)5
E)2
Rationale: 73/11 = 6.6363....
63 is non-terminating repeating decimal.
The 8th digit to the right of decimal point will be 3.
Answer B
Answer: B
Question: In a certain deck of cards, each card has a positive integer written on it. In a multiplication game, a child draws a card and multiples the integer on the card by the next larger integer. If each possible product is between 28 and 200, then the least and greatest integers on the card could be
Options:
A)3 and 15
B)3 and 20
C)5 and 13
D)4 and 14
E)5 and 14
Rationale: There child draws one number then multiplies that number by the number above it. The number must be more than 28 and less than 200.
x * (x+1)
Answer gives us choices of 3,4 and 5 (JUST ABOVE 28)
3*(3+1) =12 <- WRONG
4*(4+1) =20 <- WRONG
5*(5+1) =30 <- CORRECT AS IT IS ABOVE 28
Answer gives us choices 13,14,15 and 20 (BELOW 200)
Immediately by knowing squares you should be able to rule out 15 (225) and 20 (400). And common sense dictates that as 14^2 is 196 that 14*(14+1) is above 200.
13*(13+1)=182 <- CORRECT
Answer is C) 5 and 13
Answer: C
Question: Marcus deposited $8,000 to open a new savings account that earned five percent annual interest, compounded semi-annually. If there were no other transactions in the account, what the amount of money in Marcuss account one year after the account was opened?
Options:
A)$8,200
B)$8,205
C)$8,400
D)$8,405
E)$8,500
Rationale: Approach #1:
5 percent annual interest compounded semi-annually --> 2.5% in 6 moths.
For the first 6 moths interest was 2.5% of $8,000, so $200;
For the next 6 moths interest was 2.5% of $8,000, plus 2.5% earned on previous interest of $200, so $200+$5=$205;
Total interest for one year was $200+$205=$405, hence balance after one year was $8,000+ $405=$8,405.
Answer: D.
Answer: D
Question: If a is the interest on y and y is the interest on z, the rate and time is the same on both the cases. What is the relation between a, y and z?
Options:
A)Y^2 = aZ
B)Y^3 = aZ
C)Y^3 = aY
D)Y^1 = aZ
E)Z^3 = aZ
Rationale: a = (Y*NR)/100 Y = (Z*NR)/100
a/Y = NR/100 Y/Z = NR/100
a/Y = Y/Z
Y^2 = aZ
ANSWER:B
Answer: B
Question: The table shows the number of calls received by each of five operators during each of 4 one-hour periods. For which operator was the standard deviation of the numbers of calls received during these 4 periods the least
Options:
A)Operator A: 3, 7, 7, 3
B)Operator B: 4, 5, 5, 6
C)Operator C: 8, 2, 5, 5
D)Operator D: 6, 4, 4, 6
E)Operator E: 3, 4, 5, 8
Rationale: E
it has 2 numbers right at the average, E has none.
Answer: E
Question: On Sunday, Bill ran 4 more miles than he ran on Saturday. Julia did not run on Saturday, but she ran twice the number of miles on Sunday that Bill ran on Sunday. If Bill and Julia ran a total of 32 miles on Saturday and Sunday, how many miles did Bill run on Sunday?
Options:
A)5
B)6
C)7
D)8
E)9
Rationale: Let Bill run x on saturday, so he will run x+4 on sunday..
Julia will run 2*(x+4) on sunday..
totai= x+x+4+2x+8=32..
4x+12=32..
x=5..
ans =x+4=5+4=9
Answer E
Answer: E
Question: If a > 1 and b = 2^(a −1), then 4^a =
Options:
A)16b^2
B)4b^2
C)b^2
D)b^2/4
E)b^2/16
Rationale: If a > 1 and b = 2^(a −1), then 4^a
Given a>1, so let's assume a=2
b=2^(a-1) = 2^(2-1) = 2, so b=2
hence, 4^a = 4^2 = 16
only 1 ans. choice can satisfy this:
A) 16b^2 --> clearly > 16
B) 4b^2 --> 4*2^2 = 16(we can stop after this as there can be only 1 right answer)
C) b^2 --> clearly < 16
D) b^2/4 --> clearly < 16
E) b^2/16 --> clearly < 16
Ans. B) 4b^2
Answer: B
Question: A man can row a boat at 20 kmph in still water. If the speed of the stream is 8 kmph, what is the time taken to row a distance of 60 km downstream?
Options:
A)30/18
B)30/29
C)30/14
D)30/13
E)30/82
Rationale: Speed downstream = 20 + 8 = 28 kmph.
Time required to cover 60 km downstream = d/s = 60/28
= 30/14 hours.
Answer:C
Answer: C
Question: A person spends 1/3rd of the money with him on clothes, 1/5th of the remaining on food and 1/4th of the remaining on travel. Now, he is left with Rs 500. How much did he have with him in the beginning?
Options:
A)s 200
B)s 1250
C)s 300
D)s 450
E)s 550
Rationale: Suppose the amount in the beginning was Rs ’x’
Money spent on clothes = Rs 1x/3 Balance = Rs 2x/3
Money spent on food = 1/5 of 2x/3 = Rs 2x/15
Balance = 2x/3 - 2x/15 = Rs 8x/15
Money spent on travel = 1/4 of 8x/15 = Rs 2x/15 = 8x/15 - 2x/15 = 6x/15 = Rs2x/5
Therefore 2x/5 = 500 = 1250
ANSWER:B
Answer: B
Question: If a store owner increases a product’s price by 20 percent and then increases this price by another 15 percent, what percent of the original price is the total price increase?
Options:
A)20%
B)35%
C)38%
D)65%
E)135%
Rationale: let the initial price be 100
1st increase =20 % the price now is 120
2nd increase of 15% on 120 =18
final price =138, total increase =38%
ANSWER:C
Answer: C
Question: Today is Peter's birthday. One year, from today he will be twice as old as he was 9 years ago. How old is Peter today ?
Options:
A)25 years
B)19 years
C)17 years
D)23 years
E)21 years
Rationale: let Peter's age=xx+1=2(x-9)x=19ANSWER:B
Answer: B
Question: In a certain game, you perform three tasks. You flip a coin, and success would be tail. You roll a single die, and success would be a six. You pick a card from a full playing-card deck, and success would be picking a spades card. If exactly one of these three tasks is successful, then you win the game. What is the probability of winning?
Options:
A)11/16
B)23/48
C)15/32
D)14/36
E)17/56
Rationale: The answer is B
Probability of just one enent will be happining
So, Probability heads=1/2
Probability number 6 =1/6
Probability picking a spades card =1/4
so, Probability win by getting tails= 1/2*5/6*3/4 = 15/48
Probability win by getting number 6 = 1/2*1/6*3/4 = 3/48
Probability win by picking a spades card =1/2*5/6*1/4=5/48
Probability wining= 15/48+3/48+5/48 =23/48
Answer: B
Question: Kathleen can paint a room in 3 hours, and Anthony can paint an identical room in 4 hours. How many hours would it take Kathleen and Anthony to paint both rooms if they work together at their respective rates?
Options:
A)8/15
B)4/3
C)15/8
D)24/7
E)15/4
Rationale: (1/3 + 1/4)t=2
t=24/7
Answer: D
Answer: D
Question: The marks obtained by Vijay and Amith are in the ratio 4:4 and those obtained by Amith and Abhishek in the ratio of 3:2. The marks obtained by Vijay and Abhishek are in the ratio of?
Options:
A)3:2
B)6:1
C)6:5
D)6:2
E)6:3
Rationale: 4:4
3:2
-------
12:12:8
12:8
3:2
Answer: A
Answer: A
Question: A work as fast as B. If B can complete a work in 24days independently,the number of days in which A and B can together finish the work in?
Options:
A)2days
B)3days
C)8days
D)5days
E)6days
Rationale: Ratio of rates of working of A and B = 2:1
ratio of times taken = 1:2
A's 1day work = 1/12
B's 1day work = 1/24
A+B 1day work = 1/12 + 1/24 = 3/24 = 1/8
A and B can finish the work in 8days
Answer is C
Answer: C
Question: one person Tharak speed with the current is 15 km/hr and the speed of the current is 6 km/hr. Tharak's speed against the current is:
Options:
A)0 km/hr
B)1 km/hr
C)2 km/hr
D)3 km/hr
E)4 km/hr
Rationale: Man's speed with the current = 15 km/hr
=> speed of the man + speed of the current = 15 km/hr
speed of the current is 6 km/hr
Hence, speed of the man = 15-6 = 9 km/hr
man's speed against the current = speed of the man - speed of the current
= 9-6 = 3 km/hr
ANSWER:D
Answer: D
Question: An investor bought 200 shares of stock in ABCD company in 1990. By 1992, the investment was worth only 2/3 of its original value. By 1995, the 200 shares were worth only 1/5 of their value in 1990. By what percent did the value of the investment drop from 1992 to 1995?
Options:
A)16 2/3%
B)70%
C)33 1/3%
D)50%
E)66 2/3%
Rationale: Let price of each share in 1990 = X.
Total cost in 1990 = 200X
Now Price in 1992 = 2/3 * 200X = 400/3 * X
Now price in 1995 = 1/5 *200X= 40X
%Change in 1995 from 1992 = [(400/3* X -40X) / (400/3 *X) ] *100 = 70%
Answer B
Answer: B
Question: Pat wants to invest at the local bank that offers a rate of 10% per annum per year. If the interest is compounded half-yearly, how much will Pat have to invest to get Rs. 20000 at the end of a year?
Options:
A)18,140.59
B)18,410.95
C)18,590.41
D)18,950.14
E)18,150.49
Rationale: Amount = 20000; R = 10% p.a. = 5% per half-year; T = 1 year = 2 half-year
20000 = [P * (1 + 5/100)2]
P = 20000 / (1.05)2 = 18140.59
Answer: A
Answer: A
Question: The parameter of a square is equal to the perimeter of a rectangle of length 16 cm and breadth 14 cm. Find the circumference of a semicircle whose diameter is equal to the side of the square. (Round off your answer to two decimal places)
Options:
A)23.58 cm
B)23.17 cm
C)28.17 cm
D)23.77 cm
E)23.57 cm
Rationale: Let the side of the square be a cm.
Parameter of the rectangle = 2(16 + 14) = 60 cm Parameter of the square = 60 cm
i.e. 4a = 60
A = 15
Diameter of the semicircle = 15 cm
Circimference of the semicircle
= 1/2(∏)(15)
= 1/2(22/7)(15) = 330/14 = 23.57 cm to two decimal places
Answer:E
Answer: E
Question: A train when moves at an average speed of 40 kmph, reaches its destination on time. When its average speed becomes 35 kmph, then it reaches its destination 15 minutes late. Find the length of the journey
Options:
A)40km
B)50km
C)60km
D)70km
E)80km
Rationale: Difference between timings = 15 min =0.25hr.
Let the length of journey be x km.
Then,
x/35-x/40=0.25
8x - 7x = 70
x = 70km.
ANSWER:D
Answer: D
Question: In a rectangular coordinate system, what is the area of a triangle whose vertices have the coordinates (2, 0), (7, 4), and (7, -4)?
Options:
A)18
B)19
C)20
D)21
E)22
Rationale: The triangle is symmetric about the x-axis.
The part above the x-axis forms a triangle with a base of 5 and a height of 4.
The area of this part is (1/2)(5)(4).
We can double this to find the area of the whole triangle.
The total area is (2)(1/2)(5)(4) = 20.
The answer is C.
Answer: C
Question: The area of square ABCD above is 22. The shaded region is the intersection of the square and a circular region centered at C. What is the area of the shaded region?
Options:
A)18−9/4∗π
B)22−11/2∗π
C)9+9/4∗π
D)9+9/2∗π
E)9/2−9/4∗π
Rationale: =Square - Quarter circle
=22- pi*22/4
=22- pi*11/2
ANSWER:B
Answer: B
Question: If 9 is added to twice a number and this sum is multiplied by 3, the result is the same as if the number is multiplied by 4 and 13 is added to the product. What is the number?
Options:
A)-7
B)-8
C)-9
D)-10
E)-11
Rationale: let the number be x;
3(9+2x)=4x+13;
x=-7
ANSWER:A
Answer: A
Question: A man can row with a speed of 14 kmph in still water. If the stream flows at 8 kmph, then the speed in downstream is?
Options:
A)22
B)28
C)20
D)82
E)34
Rationale: M = 14
S = 8
DS = 14 + 8 = 22. Answer:A
Answer: A
Question: A shopkeeper sold an article offering a discount of 4% and earned a profit of 32%. What would have been the percentage of profit earned if no discount was offered?
Options:
A)24.5
B)28.5
C)30.5
D)32.5
E)37.5
Rationale: Let C.P. be Rs. 100.
Then, S.P. = Rs. 132
Let marked price be Rs. x. Then, 96/100 x = 132
x = 13200/96 = Rs. 137.5
Now, S.P. = Rs. 137.5, C.P. = Rs. 100
Profit % = 37.5%.
ANSWER:E
Answer: E
Question: The denominator of a fraction is 1 less than twice the numerator. If the numerator and denominator are both increased by 1, the fraction becomes 3/5. Find the fraction?
Options:
A)1/3
B)2/3
C)5/9
D)5/7
E)7/11
Rationale: Explanation:
Let the numerator and denominator of the fraction be 'n' and 'd' respectively.
d = 2n - 1
(n + 1)/(d + 1) = 3/5
5n + 5 = 3d + 3
5n + 5 = 3(2n - 1) + 3 => n = 5
d = 2n - 1 => d = 9
Hence the fraction is : 5/9
C
Answer: C
Question: How many different subsets of the set {0, 1, 2} do not contain 0?
Options:
A)A.6
B)B.7
C)C.1
D)D.4
E)E.2
Rationale: Number of subset
Since we have 2 digits other than 0, we can take any numbers from the set of 2 to make a subset. Also it is a matter of selection and not arrangement.So we will consider combinations.
2c1+2c2=3
And one set is the NULL set having no elements in it so
3+1=4.
ANSWER D.
Answer: D
Question: A, B and C completed a piece of work costing Rs.1800. A worked for 6 days, B for 4 days and C for 9 days. If their daily wages are in the ratio 5 : 6 : 4, how much amount will be received by A?
Options:
A)Rs.800
B)Rs. 600
C)Rs.900
D)Rs.750
E)Rs.850
Rationale: Explanation:
The new ratio = wages ratio × No. of days
A = 5 × 6 = 30
B = 6 × 4 = 24
C = 4 × 9 = 36
Therefore, the ratio of the amount received = 30 : 24 : 36 = 5 : 4 :6
Total ratio = 15
1 unit of ratio = 1800/15 = Rs. 120
Therefore, amount received by A = 5 units = 5 × 120 = Rs.600.
Answer: Option B
Answer: B
Question: The number of defects in the first five cars to come through a new production line are 9, 7, 11, 4, and 6, respectively. If the sixth car through the production line has either 3, 7, or 12 defects, for which of theses values does the mean number of defects per car for the first six cars equal the median?
I. 3
II. 7
III. 12
Options:
A)I only
B)II only
C)III only
D)I and III only
E)I, II, and III
Rationale: C
for 7 we will have mean as 7.16(approx) and median as 7 but for 3 we will have mean and median = 6.5 and for 12 we will have median and mean =8
Answer: C
Question: If x and y are numbers such that (x+6)(y-6)=0, what is the smallest possible value of x^2 + y^2
Options:
A)0
B)16
C)25
D)36
E)49
Rationale: From (x+6)(y-6)=0 it follows that either x=-6 or y=6. Thus either x^2=36 or y^2=36.
Now, if x^2=36, then the least value of y^2 is 0, so the least value of x^2 + y^2 = 36 + 0 = 36.
Similarly if y^2=36, then the least value of x^2 is 0, so the least value of x^2 + y^2 = 0 + 36 = 36.
Answer: D.
Answer: D
Question: The ratio between the sale price and the cost price of an article is 8:5. What is the ratio between the profit and the cost price of that article?
Options:
A)23
B)1:2
C)2:5
D)3:5
E)25
Rationale: C.P. = Rs. 5x and S.P. = Rs. 8x.
Then, Gain = Rs. 3x
Required ratio = 3x : 5x = 3:5
D
Answer: D
Question: Which answer is closest to the √17?
Options:
A)a 4.1
B)b 4.2
C)c 4.4
D)d 4.5
E)e 4.6
Rationale: Try filling the numbers into the y's. y x y =
4.1 x 4.1= 16.81
4.2 x 4.2 = 17.64
Answer: A
Answer: A
Question: Find the value of 72518 x 9999 = m?
Options:
A)456578972
B)436567874
C)653658791
D)725117481
E)725107482
Rationale: 72518 x 9999 = 72518 x (10000 - 1)
= 72518 x 10000 - 72518 x 1
= 725180000 - 72518
= 725107482
E
Answer: E
Question: A train running at the speed of 60 km/hr crosses a pole in 9 sec. What is the length of the train?
Options:
A)118
B)150
C)277
D)258
E)191
Rationale: Speed = 60 * 5/18 = 50/3 m/sec
Length of the train = speed * time = 50/3 * 9 = 150 m
Answer: B
Answer: B