mathewhe/aqua_rat huggingface dataset:
Question: The banker's discount on a sum of money for 3/2 years is Rs. 120. The true discount on the same sum for 2 years is Rs.150. What is the rate per cent?
(A) 3(1/3)%
(B) 4(1/3)%
(C) 3(2/3)%
(D) 4(2/3)%
(E) None of these
Rationale: Explanation :
BD for 1(1/2) years = Rs. 120
=> BD for 2 years = 120 × (2/3) × 2 = Rs.160
TD for 2 years = Rs. 150
F = (BD ×TD)/(BD – TD) = (160 × 150)/(160 – 150) = (160 × 150)/10 = Rs. 2400
=> Rs.160 is the simple interest on Rs. 2400 for 2 years
⇒ 160 = (2400 × 2 × R)/100
⇒ R = (160 × 100)/(2400×2) = 160/48 = 10/3 = 3(1/3)% Answer A
Answer: (A) 3(1/3)%
Question: The average of 7 consecutive numbers is 20. The largest of these numbers is :
(A) 21
(B) 22
(C) 23
(D) 24
(E) 25
Rationale: Explanation:
Let the numbers be x, x + 1, x + 2, x + 3, x + 4, x + 5 and x + 6,
Then (x + (x + 1) + (x + 2) + (x + 3) + (x + 4) + (x + 5) + (x + 6)) / 7 = 20.
or 7x + 21 = 140 or 7x = 119 or x =17.
Latest number = x + 6 = 23. Answer: C
Answer: (C) 23
Question: X can do a piece of work in 40days. He works at it for 8days and then Y finished it in 20 days. How long will Y take to complete the work?
(A) 10
(B) 12
(C) 25
(D) 18
(E) 20
Rationale: Work done by X in 8days = 8*1/40 = 1/5
Remaining work = 1 - 1/5 = 4/5
4/5 work is done by Y in 20 days
Whole work will be done by Y in 20*5/4 = 25days
Answer is C
Answer: (C) 25
Question: Which of the following are divisible by both 2 and 3?
I. 234,124,422
II. 88,865,544,264
III. 5,555,554,674
(A) I​ only
(B) I, II​ & III
(C) II and III
(D) II Only
(E) I​ and III
Rationale: I. is divisible by 3 since sum of the digits is 24 , which is divisible by 3
II. is divisible by 3 since sum of the digits is 60 , which is divisible by 3
III. is divisible by 3 since sum of the digits is divisible by 3
Thus among the given options only (B) holds true.
Answer: (B) I, II​ & III
Question: How many of the positive factors of 75 are not factors of 95?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
Rationale: factors of 75- 1, 3, 5, 15, 25, 75,
Factors of 95 - 1, 5, 19, 95,
Comparing both, we have three factors of 75 which are not factors of 95- 3, 15, 25, 75,
The answer is E
Answer: (E) 4
Question: In a room filled with 7 people, 4 people have exactly 1 sibling in the room and 3 people have exactly 1 siblings in the room. If two individuals are selected from the room at random, what is the probability that those two individuals are NOT siblings?
(A) 5/21
(B) 3/7
(C) 4/7
(D) 5/7
(E) 2/7
Rationale: There are suppose A B C D E F G members in the room 4 people who have exactly one sibling....A B C D....(A is Bs∘SSsibl∈g∘SSand∘SSviceversa)∘SS(C∘SSis∘SSDs∘SSsibl∈g∘SSand∘SSviceversa)∘SS(C∘SSis∘SSDssibl∈gandviceversa)(CisDs sibling and viceversa) (C is Ds sibling and viceversa)...now remaning EFG are 3 people who have exactly 1 siblings....(E has F and G as his/her sibling and so on..)
there are now 3 different set of siblings (A and B)
(C and D);(EFG)
Now first selecting 1 people out of 7 is 7C1=7
first sibling pair----(A and B)--selecting 1 people --1C1=1
second sibling pair (C and D)--selecting 1 people--1C1=1
third sibling pair (E F G)--selecting 1 out of 3 --3C1=3
total= 1+1+3=5
but,a/c to formula P(success)-1-p(fail)
here,p(failure)is selecting 1 people who are siblings
=5/7(7 is 7C1)
=1-5/7
=2/7
ANS E
Answer: (E) 2/7
Question: Which value of x does statisfy the inequality 2x2 + x – 3 < 0?
(A) -3⁄2 < x < 1
(B) -1 < x < 3⁄2
(C) x > 1
(D) x < -2⁄5
(E) None of these
Rationale: 2x2 + x – 3 < 0
⇒ (x – 1)(2x + 3) < 0 or, -3⁄2 < x < 1
Answer A
Answer: (A) -3⁄2 < x < 1
Question: One half of a two digit number exceeds its one third by 4. What is the sum of the digits of the number?
(A) A)3
(B) B)6
(C) C)7
(D) D)9
(E) E)11
Rationale: x/2 – x/3 = 4 => x =24
2 + 4 = 6
ANSWER:B
Answer: (B) B)6
Question: What is the 4 digit number in which the 1st digit is 1/3 of the second, the 3rd is the sum of the 1st and 2nd, and the last is three times the second?
(A) 1244
(B) 1532
(C) 1349
(D) 1423
(E) 1543
Rationale: First digit is 1/3 second digit => The numbers can be 1 & 3, 2& 6, 3 & 9.
First + second = third => we can eliminate 3 & 9 since 3 + 9 = 12.
Last is 3 times the second => we can eliminate option 2 & 6 since 3 * 6 = 18.
Hence the number is 1349
C
Answer: (C) 1349
Question: If the sum of the 4th term and the 12th term of an arithmetic progression is 16, what is the sum of the first 15 terms of the progression?
(A) 80
(B) 100
(C) 105
(D) 120
(E) 110
Rationale: 4th term + 12th term = 16
i.e., (a+3d)+(a+11d) = 16
Now, Sum of first 15 terms = (15/2) * [2a + (15-1)d]
= (15/2) * [2a + 14d]
= (15/2) * 16 --------------- From (1)
=120
Answer : D
Answer: (D) 120
Question: A can complete a project in 20 days and B can complete the same project in 30 days. If A and B start working on the project together and B quits 5 days before the project is completed, in how many days total will the project be completed?
(A) 10
(B) 12
(C) 14
(D) 16
(E) 18
Rationale: A's rate is 1/20 of the project per day.
B's rate is 1/30 of the project per day.
The combined rate is 1/12 of the project per day.
In the last 5 days, A can do 1/4 of the project.
Thus A and B must complete 3/4 of the project, which takes 9 days.
The total number of days is 9 + 5 = 14.
The answer is C.
Answer: (C) 14
Question: Compound interest earned on a sum for the second and the third years are Rs.12000 and Rs.13800 respectively. Find the rate of interest?
(A) 15% p.a.
(B) 22% p.a.
(C) 20% p.a.
(D) 24% p.a.
(E) None of these.
Rationale: Rs.13800 - 12000 = Rs.1800 is the interest on Rs.12000 for one year.
Rate of interest = (1800/12000) * 100 = 15% p.a
ANSWER:A
Answer: (A) 15% p.a.
Question: If a population of women in a town is 70% of men . What is the population of men as a % of population of women ?
(A) A)200%
(B) B)144%
(C) C)50%
(D) D)65%
(E) E)110%
Rationale: We're told that the number of Women in a town is equal to 50% of the number of Men in that town.
IF....
Men = 10
Women = 7
We're asked for the number of Men, as a percentage of the number of Women.
M/W = 10/7 = 144%
Answer is B
Answer: (B) B)144%
Question: S is the set of all fractions defined by the formula n/(n + 1), where n is a positive integer less than 20. What is the product Z of all the fractions that are in S?
(A) 1) 1/20
(B) 2) 1/21
(C) 3) 1/2
(D) 4) 19/40
(E) 5) 19/20
Rationale: 1/2 * 2/3 * 3/4 * ... 19/20
= 1/20
Answer - A
Answer: (A) 1) 1/20
Question: Median T of price of the car is 52,000. which could be the median of the other two.
35000, 44000, x, y, 57000.
(A) 38000
(B) 47000
(C) 48000
(D) 51,000
(E) 56,000
Rationale: Median of the car is 52,000 therefore 52,000 is the middle number. Assuming Y >= X, X will have to be the median value i.e. 52,000. Therefore the remaining value would have to be between 52,000 and 57,000 inclusive. The only answer choice that fits T is 56,000.E
Answer: (E) 56,000
Question: The area of the party hall of the kitchen is 50 m2 that of a longer wall 10 m2 and of the shorter wall 5 m2, find the edge of the new cube?
(A) 460 m3
(B) 150 m2
(C) 90 m3
(D) 40 m3
(E) 50 m3
Rationale: lb = 50 ; lh = 10 ; fh = 5
(lbh)2 = 50 * 10 * 5 => lbh = 50 m3
ANSWER:E
Answer: (E) 50 m3
Question: If x is an integer and 6.1 × 10^x is less than 620 what is the greatest possible value for x?
(A) 2
(B) 6
(C) 5
(D) 4
(E) 3
Rationale: If x=2
6.1 × 10^2 = 610 < 620
So, x = 2
Answer : A
Answer: (A) 2
Question: The game of blackjack is played with a deck consisting of 13 cards (one of each of the numbers 2-10, one jack, one queen, one king, and one of ace) in each of four suits: clubs, diamonds, hearts, and spades.
In a game of blackjack, if your first card is a spade, what are the E odds that it is an ace?
(A) 1/52
(B) 1/26
(C) 1/13
(D) 1/4
(E) 5/13
Rationale: The question should ask about the probability not the odds.
There are 13 spades, the probability E that the spade we already have is an ace is therefore 1/13.
Answer: C.
Answer: (C) 1/13
Question: A bag contains 5 red, 4 blue and M green
balls if the probability of getting both the balls
green, when two balls are selected at
random is 1/7, find M
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: mC2/m+9C2=1/7
on solving
(m! / (m-2! * 2!) ) / (m+9! / (m+7! * 2!) ) =1/7 From nCr=n! / r!*(n-r)!
on solving
(m! / (m-2)! ) * ( (n-7)! / (n+7)!) =1/7
after solving and cross multiplication
m^2+4m-12=0
on solving
m=2,-6
so m will be 2.
ANSWER:B
Answer: (B) 2
Question: At a conference table, 7 employees gather around a table. One of the employees is the manager and he sits at the head of the table. Two of the employees sit on either side of the table. How many different seating arrangements can be made with these 7 employees?
(A) 740
(B) 750
(C) 720
(D) 760
(E) 790
Rationale: Head's sit is fixed. Now 6 people is left with 6 seats.
6 people can sit on 6 seats in 6! ways or 720 ways.
Ans is C
Answer: (C) 720
Question: How much interest can a person get on Rs. 8200 at 17.5% p.a. simple interest for a period of two years and six months?
(A) 3587.51
(B) 3587.98
(C) 3587.5
(D) 3587.29
(E) 3572.5
Rationale: I = (8200 * 2.5 * 17.5)/100
= (8200 * 5 * 35)/(100 * 2 * 2)
= Rs.3587.50
Answer: C
Answer: (C) 3587.5
Question: In a barrel of juice there is 50 liters; in a barrel of beer there are 80 liters. If the price ratio between barrels of juice to a barrel of beer is 3:4, what is the price ratio between one liter of juice and one liter of beer?
(A) 3:2.
(B) 2:1.
(C) 3:1.
(D) 4:3.
(E) 6:5
Rationale: Juice barrel : beer Barrel = 50:80 i.e. 3:8
price of Juice : Price of Beer = 3 : 4
so for 5/8 costs 3/4, ie 5J / 8B = 3/4.
Solving for J/B, we get 6:5
Answer E.
Answer: (E) 6:5
Question: A single discount equivalent to the discount series of 20%, 10% and 25% is?
(A) 31.9
(B) 31.7
(C) 31.6
(D) 31.5
(E) 46
Rationale: 100*(80/100)*(90/100)*(75/100) = 54
100 - 54 = 46
Answer:E
Answer: (E) 46
Question: If a copier makes 2 copies every 4 seconds, then continues at this rate, how many minutes will it take to make 8,000 copies?
(A) 266.67
(B) 130
(C) 140
(D) 135
(E) 141
Rationale: 2 copies 4 seconds
8000 copies = (8000*4)/2 seconds
= 16000/60 minutes
= 266.67 minutes
Answer : A
Answer: (A) 266.67
Question: There are 32 students in a certain geometry class. If two thirds of the students are boys and three fourths of the boys are under six feet tall, how many boys in the class are under six feet tall?
(A) 6
(B) 12
(C) 16
(D) 24
(E) 27
Rationale: 32*2/3 *3/4= 16
Answer: C
Answer: (C) 16
Question: Given the equation e=-g^4, which of the following must be true?
I. If g is negative then e is negative.
II. e is negative.
III. g is non-negative.
(A) II only
(B) I only
(C) II and III only
(D) III only
(E) I and II only
Rationale: If e=-g^4, which of the following must be true?
First of all notice g^2 is always non-negative, so -g^2 is non-positive (zero or negative), which means that e is zero when g=0 and e is negative for ANY other value of g.
I. e is negative --> not necessarily true, if g=0 then e=-m^2=0;
II. g is non-negative. g can take ANY value: positive, negative, zero. We don't have any restrictions on its value;
III. If g is negative then e is negative. m is negative means that m is not zero.
Answer: B (I only).
Answer: (B) I only
Question: A group of 10 representatives is to be selected out of 12 seniors and 10 juniors. In how many different ways can the group be selected, if it should have 5 seniors and 5 juniors?
(A) ¹²C₅ * 10
(B) ¹²C₇ * 10
(C) ¹²C₇ * ¹⁰C₅
(D) 12 * ¹⁰C₅
(E) None of these
Rationale: Here, five seniors out of 12 seniors can be selected in ¹²C₅ ways. Also, five juniors out of ten juniors can be selected ¹⁰C₅ ways. Hence the total number of different ways of selection = ¹²C₅ * ¹⁰C₅ = ¹²C₇ * ¹⁰C₅
= ¹²C₅ = ¹²C₇
ANSWER:C
Answer: (C) ¹²C₇ * ¹⁰C₅
Question: The difference between compound interest and simple interest on a certain amount of money at 5% per annum for 2 years is 16. Find the sum :
(A) 4500
(B) 7500
(C) 5000
(D) 6400
(E) None of these
Rationale: Sol.(d) Let the sum be 100.
Therefore, SI = 100×5×2/100=10
and CI = 100(1+5/100)2−100
∴ =100×21×21/20×20−100=41/4
Difference of CI and SI = 41⁄4 - 10 = 1⁄4
If the difference is 1⁄4 , the sum = 100
=> If the difference is 16, the sum
= 400 × 16 = 6400 Answer D
Answer: (D) 6400
Question: Stacy has a 12 page history paper due in 12 days. How many pages per day would she have to write to finish on time?
(A) 9
(B) 8
(C) 10
(D) 1
(E) 6
Rationale: 12/12=1
Answer : D
Answer: (D) 1
Question: Look at this series: VI, 10, V, 11, __, 12, III, ... What number should fill the blank?
(A) II
(B) IV
(C) IX
(D) 14
(E) None
Rationale: Explanation: This is an alternating addition and subtraction series. Roman numbers alternate with Arabic numbers. In the Roman numeral pattern, each number decreases by 1. In the Arabic numeral pattern, each number increases by 1.
Answer: Option B
Answer: (B) IV
Question: Two pipes A and B can separately fill a tank in 2 minutes and 15 minutes respectively. Both the pipes are opened together but 4 minutes after the start the pipe A is turned off. How much time will it take to fill the tank?
(A) 2
(B) 7
(C) 8
(D) 6
(E) 10
Rationale: 4/12 + x/15 = 1
x = 10
Answer: E
Answer: (E) 10
Question: The sum of two numbers is 50. Their difference is 10. The bigger number is
(A) 20
(B) 25
(C) 30
(D) 35
(E) 45
Rationale: X + Y = 50
X - Y = 10
Adding 2X = 60 ==> X = 30 and Y = 50 - 30 = 20
Bigger number is X = 30
Answer C.
Answer: (C) 30
Question: A bowl was filled with 10 ounces of water, and 0.08 ounce of the water evaporated each day during a 50-day period. What percent of the original amount of water evaporated during this period?
(A) 0.004%
(B) 0.04%
(C) 40%
(D) 4%
(E) 40%
Rationale: Total amount of water evaporated each day during a 50-day period = .08 * 50
=.08 * 100/2
= 8/2
= 4
percent of the original amount of water evaporated during this period = (4/10) * 100%
= 40 %
Answer C
Answer: (C) 40%
Question: There are 3 department available in XYZ company,namely Finance, Marketing, HR.The total expenditure of the company $69700.the ratio of department expenditure are 11:14:16.Then find out the total expenditure of marketing department?
(A) $27560
(B) $28900
(C) $27250
(D) $15600
(E) $23800
Rationale: Finance:Marketing:HR ratio of expenditure = 11+14+16=41;
Expenditure of marketing department = 14/41 * $69700 = $23800.
Answer =E
Answer: (E) $23800
Question: Barbata invests $2400 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?
(A) 1200
(B) 3000
(C) 1000
(D) 3600
(E) 2400
Rationale: Let the additional invested amount for 8% interest be x;
Equation will be;
2400+0.05*2400+x+0.08x = 2400+x+0.06(2400+x)
0.05*2400+0.08x = 0.06x+0.06*2400
0.02x = 2400(0.06-0.05)
x = 2400*0.01/0.02 = 1200
Ans: "A"
Answer: (A) 1200
Question: Ramu bought an old car for Rs. 45000. He spent Rs. 12000 on repairs and sold it for Rs. 80000. What is his profit percent?
(A) 16%
(B) 17%
(C) 40%
(D) 58%
(E) 13%
Rationale: Total CP = Rs. 45000 + Rs. 12000
= Rs. 57000 and SP = Rs. 80000
Profit(%)
= (80000 - 57000)/57000 * 100
= 40%
Answer: C
Answer: (C) 40%
Question: A man can row his boat with the stream at 6 km/h and against the stream in 4 km/h. The man's rate is?
(A) 1 kmph
(B) 7 kmph
(C) 98 kmph
(D) 6 kmph
(E) 4 kmph
Rationale: DS = 6
US = 4
S = ?
S = (6 - 4)/2 = 1 kmph
Answer: A
Answer: (A) 1 kmph
Question: A hall 36m long and 15m broad is to be paved with stones, each measuring 5dm by 5 dm. The number of stones required is:
(A) 180
(B) 1800
(C) 18
(D) 2160
(E) 1.8
Rationale: Area of the hall= 3600*1500
Area of each stone= (50*50)
Therefore, number of stones= (3600*1500/ 50*50)= 2160
ANSWER:D
Answer: (D) 2160
Question: Using all the letters of the word "LETTERS", how many words can be formed, which begin with L and end with S?
(A) 50
(B) 120
(C) 160
(D) 100
(E) 124
Rationale: There are five letters in the given word.
Consider 7 blanks ....
The first blank and last blank must be filled with L and S all the remaining three blanks can be filled with the remaining 5 letters in 5! ways.
The number of words = 5! = 120.
Answer: B
Answer: (B) 120
Question: Find the invalid no.from the following series 2,3,12,37,86,166,288
(A) 2
(B) 3
(C) 166
(D) 288
(E) 37
Rationale: 3-2=1
12-3=9
37-12=25
86-37=49
166-86=80(this must be 81=167-86=81)
so wrong number in the sequence is 166
difference between two sucessive numbers sequence would be
1,9,25,49,81,121(square of 1,3,5,7,9,11)
C
Answer: (C) 166
Question: How many numbers amongst the numbers 8 to 52 are there which are exactly divisible by 5 but not by 3?
(A) Nil
(B) 1
(C) 2
(D) 3
(E) More than 3
Rationale: 10,15,20,25,30,35,40,45,50 are divisible by 5.
15,30,45 are divisible by 3 also.
So there are 6 numbers exactly divisible by 5 but not by 3
ANSWER:E
Answer: (E) More than 3
Question: In one hour a boat goes 14 km long the stream and 6 km against the stream.The speed of the boat in still water is?
(A) 7
(B) 10
(C) 12
(D) 11
(E) 13
Rationale: Speed in still water A = ½ ( 14+6) km/hr A= 10 kmph
Answer: B
Answer: (B) 10
Question: In the infinite sequence 27, 36, 45, 54, 63, . . . , where each term is 9 greater than the previous term, the 55th term is
(A) 783
(B) 513
(C) 198
(D) 963
(E) 741
Rationale: T(n) = a + (n-1) d
Here d =9, a=27, n=55
Solving we get T(n) = 513.
Answer: B
Answer: (B) 513
Question: If the positive integer y is divisible by 3, 8, and 16, then which of the following must y be divisible by?
I. 21
II. 32
III. 48
(A) III only
(B) II only
(C) I and II only
(D) II and III only
(E) I, II, and III
Rationale: Answer = A
LCM of 3, 8, 16 = 48
Answer = 48
Answer : A
Answer: (A) III only
Question: An article is bought for Rs.700 and sold for Rs.900, find the gain percent?
(A) 33 1/8%
(B) 33 8/3%
(C) 28 4/7%
(D) 35 1/3%
(E) 32 1/3%
Rationale: 700 ---- 200
100 ---- ? => 28 4/7%
Answer: C
Answer: (C) 28 4/7%
Question: What will be the cost of building a fence around a square plot with area equal to 289 sq ft, if the price per foot of building the fence is Rs. 57?
(A) s.3876
(B) s.3948
(C) s.3942
(D) s.3965
(E) s.3929
Rationale: Let the side of the square plot be a ft.
a2 = 289 => a = 17
Length of the fence = Perimeter of the plot = 4a = 68 ft.
Cost of building the fence = 68 * 57
= Rs.3876.
Answer: A
Answer: (A) s.3876
Question: The paragraph can start only with the sentence E. The opening words of the sentence of ‘B’ – ‘these two parties’ is a continuation of the last words of the sentence E– ‘two parties’. There are only two options with EB; in the option 4, D follows B; but whom the opening pronoun ‘he’ of D does refer to? F is the further explanation of B. Hence EBFCAD.
(A) 11
(B) 77
(C) 26
(D) 99
(E) 171
Rationale: Answer:	B
Answer: (B) 77
Question: 1604 x 1604 = ?
(A) A)2572816
(B) B)3624216
(C) C)3624316
(D) D)3625116
(E) E)3625216
Rationale: 1604 x 1604 = (1604)2
= (1600 + 4)2
= (1600)2 + (4)2 + (2 x 1600 x 4)
= 2560000 + 16 + 12800.
= 2572816.
A)
Answer: (A) A)2572816
Question: Arrange 4boys and 4girls in a row such that all the 4 girls are together.
(A) 1240
(B) 1440
(C) 2880
(D) 3200
(E) 3260
Rationale: Treat all the 4 girls as G
4boys and G can be arranged in 5!ways
G can be arranged among them in 4!ways
total = 5!*4! = 2880
correct option is C
Answer: (C) 2880
Question: If s and t are positive integers such that s/t = 43.18, which of the following could be the remainder when s is divided by t ?
(A) 44
(B) 17
(C) 54
(D) 20
(E) 47
Rationale: s/t= 43.18
s = 43.18t
s = (43 + 0.18)t
s = 43t + (18/100)t
s = 43t + (9/50)t
So remainder will be multiple of 9. The only multiple of 9 is 54.
Ans. C
Answer: (C) 54
Question: he number of sequences in which 8 players can throw a ball, so that the youngest player may not be the last is?
(A) 43288
(B) 23770
(C) 43200
(D) 35280
(E) 27820
Rationale: x Not younger_______ ↑
The last ball can be thrown by any of the remaining 7 players. The first 7 players can throw the ball in 7p7₆ ways.
The required number of ways = 7(7!) = 35280
Answer:D
Answer: (D) 35280
Question: Find the number of square tiles to cover the floor of a room measuring 6 m * 11 m leaving 0.50 m space around the room. A side of square tile is given to be 50 cms?
(A) 187
(B) 476
(C) 200
(D) 208
(E) 276
Rationale: Area of the room =5 * 10 =50
Area of the tile = 0.5 *0.5=0.25
No. of tiles =50/0.25 =200
Answer : C
Answer: (C) 200
Question: The H.C.F. of two numbers is 23 and the other two factors of their L.C.M. are 13 and 14. The larger of the two numbers is:
(A) 276
(B) 299
(C) 322
(D) 345
(E) 354
Rationale: Clearly, the numbers are (23 x 13) and (23 x 14).
Larger number = (23 x 14) = 322.
Answer: Option C
Answer: (C) 322
Question: The sector of a circle has radius of 14 cm and central angle 108o. Find its perimeter?
(A) 52cm
(B) 54.4cm
(C) 60cm
(D) 65cm
(E) 70cm
Rationale: Perimeter of the sector = length of the arc + 2(radius)
= (108/360 * 2 * 22/7 * 14) + 2(14)
= 26.4 + 28 = 54.4 cm
Answer:B
Answer: (B) 54.4cm
Question: A number increased by 25% gives 520. The number is?
(A) 216
(B) 316
(C) 616
(D) 516
(E) 416
Rationale: Formula = TOTAL=100% ,INCREASE = "+" DECREASE= "-"
A number means = 100 %
That same number increased by 25 % = 125 %
125 % -------> 520 (120 Ã— 4.16 = 520)
100 % -------> 416 (100 Ã— 4.16 = 416)
Option 'E'
Answer: (E) 416
Question: What percent is 520 gm of 1 kg?
(A) 25%
(B) 40%
(C) 52%
(D) 8%
(E) 12%
Rationale: 1 kg = 1000 gm
520/1000 Ã— 100 = 52000/1000
=52 %
Answer is C
Answer: (C) 52%
Question: In 10 years, A will be twice as old as B was 10 years ago. If A is now 9 years older than B, the present age of B is :
(A) 19
(B) 29
(C) 39
(D) 49
(E) None of these
Rationale: Explanation:
Let B's present age = x years. Then, A's present age = (x + 9) years.
(x + 9) + 10 = 2(x - 10)
=> x + 19 = 2x - 20
=> x =39. Answer: C
Answer: (C) 39
Question: Ramu bought an old car for Rs. 42000. He spent Rs. 13000 on repairs and sold it for Rs. 64900. What is his profit percent?
(A) 33
(B) 12
(C) 18
(D) 19
(E) 11
Rationale: Total CP = Rs. 42000 + Rs. 13000 = Rs. 55000 and SP = Rs. 64900
Profit(%) = (64900 - 55000)/55000 * 100 = 18%
Answer: C
Answer: (C) 18
Question: An amount of Rs. 85000 is invested in two types of shares. The first yields an interest of 9% p.a and the second, 11% p.a. If the total interest at the end of one year is 9 3/4 %, then the amount invested in each share was?
(A) s. 53125; Rs. 31875
(B) s. 62500; Rs. 37500
(C) s. 72500; Rs. 27500
(D) s. 82500; Rs. 17500
(E) s. 72500; Rs. 17500
Rationale: Let the sum invested at 9% be Rs. x and that invested at 11% be Rs. (85000 - x). Then,
(x * 9 * 1)/100 + [(85000 - x) * 11 * 1]/100 = (85000 * 39/4 * 1/100)
(9x + 935000 - 11x)/100 = 39000/4 = 16575/2
x = 53125
Sum invested at 9% = Rs. 53125
Sum invested at 11% = Rs. (85000 - 53125) = Rs. 31875.
ANSWER:A
Answer: (A) s. 53125; Rs. 31875
Question: Of the three numbers, the sum of the sum of the first two is 45; the sum of the second and the third is 55 and the sum of the third and thrice the first is 90. the third number is :
(A) 20
(B) 25
(C) 30
(D) 3
(E) None of these
Rationale: Solution
Let the numbers be x,y, and z. then, x + y = 45, y + x = 55 and 3 x + z = 90
⇒ y = 45 - x, z = 55 - y = 55 - (45 - x) = 10 + x.
∴ 3 x + 10 + x = 90 or x = 20.
y = (45 - 20) = 25 and z = (10 + 20) = 30.
∴ third number = 30
Answer C
Answer: (C) 30
Question: In a two digit number, the digit in the units place is three times the digit in ten's place and sum of the digits is equal to 8. What is the number?
(A) 26
(B) 28
(C) 32
(D) 36
(E) 38
Rationale: Solution
Let the ten digits be x. Then,units digit=3x
Therefore x + 3x = 8
‹=›4x = 8
‹=›x= 2.
So, ten's digit = 2, unit's digit = 6.
Hence, the required number is 26.
Answer A
Answer: (A) 26
Question: If 8m − n = p, then which of the following represents the average (arithmetic mean) of m, n, and p, in terms of m?
(A) 2m −1
(B) 3m
(C) 6m
(D) m/5
(E) 6m/5
Rationale: 8m - n = p
Add n to both sides:
8m = n + p
Add m to both sides:
9m = n + p + m
Now, divide both sides by 3
3m = (n + p + m)/3 = the average of n, p, and m
B
Answer: (B) 3m