mathewhe/aqua_rat huggingface dataset:
Question: Tough and Tricky questions: Coordinate Geometry.
Line L contains the points (2,3) and (p,c). If c = 2, which of the following could be the equation of line m, which is perpendicular to line L?
(A)  2x + y = px + 7
(B)  2x + y = –px
(C)  x + 2y = px + 7
(D)  y – 7 = x ÷ (p – 2)
(E)  2x + y = 7 – px
Rationale: So we need m=p-2, so we should get y=mx+b form in answer choices
(A) 2x+y=px+7 => y=px-2x+7 => y=x(p-2)+7. It is what we need
(B) 2x + y = –px => y=-px-2x => y=x(-p-2). Wrong
(C) x + 2y = px + 7 => y=x(p-1/2)+7/2. Wrong
(D) y – 7 = x ÷ (p – 2) => y=(1/p-2)x+7. Wrong
(E) 2x + y = 7 – px => y=-px-2x+7 => y=x(-p-2)+7. Wrong
A
Answer: (A)  2x + y = px + 7
Question: The C.P of 15 books is equal to the S.P of 22 books. Find his gain% or loss%?
(A) 16 2/3%
(B) 31 9/11%
(C) 16 2/5%
(D) 16 2/1%
(E) 16 1/3%
Rationale: 15 CP = 22 SP
22 --- 7 CP loss
100 --- ? => 31 9/11% loss.Answer: B
Answer: (B) 31 9/11%
Question: Suddenly one boy tossed 3 coins. What is the probability of getting at most two heads?
(A) 2/7
(B) 3/11
(C) 7/8
(D) 4/13
(E) 3/16
Rationale: Here S = {TTT, TTH, THT, HTT, THH, HTH, HHT, HHH}
Let E = event of getting at most two heads.
Then E = {TTT, TTH, THT, HTT, THH, HTH, HHT}.
P(E) =	n(E)	=	7/8
n(S)
C
Answer: (C) 7/8
Question: Ele, the circus Elephant, is currently three times older than Lyn, the circus Lion. In 8 years from now, Lyn the circus Lion will be exactly half as old as Ele, the circus Elephant. How old is Ele today?
(A) 24
(B) 25
(C) 26
(D) 28
(E) 29
Rationale: Ele, the circus Elephant, is currently three times older than Lyn, the circus Lion.
Ele = 3*Lyn
Usually, ages are integers so there is a good possibility that the age of Ele is 24 (the only option that is a multiple of 3).
Then age of Lyn would be 8. In 8 yrs, Ele would be 32 and Lyn would be 16 - so Lyn would be half as old as Ele.
Answer (A)
Answer: (A) 24
Question: What is the value of 1/2 of 2/3 of 3/4 of 4/5 of 5/6 of 6/7 of 7/8 of 8/9 of 9/10 of 1000?
(A) 150
(B) 130
(C) 154
(D) 100
(E) 220
Rationale: D
100. Looks hard? Don't worry, just work it backwards and you'll find it very easy.
Answer: (D) 100
Question: The sum of ages of 5 children born 4 years different each is 70 yrs. What is the age of the Elder child?
(A) 8
(B) 9
(C) 22
(D) 17
(E) 18
Rationale: Let the ages of children be x, (x + 4), (x + 8), (x + 12) and (x + 16) years.
Then, x + (x + 4) + (x + 8) + (x + 12) + (x + 16) = 70
5x = 30
x = 6
x+16= 6+16= 22
Answer : C
Answer: (C) 22
Question: here are 6 periods in each working day of a school. In how many ways can one organize 5 subjects such that each subject is allowed at least one period?
(A) 1800
(B) 2130
(C) 2231
(D) 4510
(E) 3560
Rationale: 5 subjects can be arranged in 6 periods in 6P5 ways.
Any of the 5 subjects can be organized in the remaining period (5C1 ways).
Two subjects are alike in each of the arrangement. So we need to divide by 2! to avoid overcounting.
Total number of arrangements
= 6P5× 5C1 /2!=1800
Ans: A
Answer: (A) 1800
Question: Keats Library purchases a number of new books, all in the category of biography, and the library does not acquire any other books. With the addition of the new biographies, the biography collection of the library amounts to 25% of the total number of books in the library. If prior to the purchase, only 20% of the books in Keats Library were biographies, by what percent has the number of biographies in the library increased?
(A) 23%
(B) 28%
(C) 33%
(D) 38%
(E) 43%
Rationale: Let x be the number of new biographies added to the library.
Let b be the original number of biographies, so the original number of books was 5b.
0.25(5b+x) = b+x
0.25b = 0.75x
x = 0.33b
The answer is C.
Answer: (C) 33%
Question: A sum fetched a total simple interest of 4016.25 at the rate of 9 %.p.a. in 5 years. What is the sum?
(A) 4462.5
(B) 8032.5
(C) 8925
(D) None of these
(E) Cannot be determined
Rationale: Explanation: Principal = (100 x 4016.25)/(9 x 5)
= 401625/45
= 8925
Answer: Option C
Answer: (C) 8925
Question: Find the middle one when The sum of three consecutive even numbers is 72?
(A) 70
(B) 60
(C) 78
(D) 72
(E) 62
Rationale: 3 consecutive numbers can be a - 1, a, a + 1
So sum of numbers = 3a = 72.
Hence a = 72.
D
Answer: (D) 72
Question: A man has a savings account of $500. if he receives $50.6 for every $100 as interest and pays a tax of $15.5 on every $100 how many years will it take for his savings to double.
(A) 2.85
(B) 5
(C) 4.1
(D) 3.5
(E) 5.6
Rationale: Annual increase is (100 + 50.6 - 15.5)*5=675.5
Hence every year there is an increase of 175.5
for his saving to double he needs additional $500
therefore $500/175.5=2.85
correct option is A)
Answer: (A) 2.85
Question: What is the units digit of the product of the first 2 primes?
(A) 1
(B) 2
(C) 0
(D) 4
(E) 5
Rationale: 1*2*=2
Answer : B
Answer: (B) 2
Question: John makes $60 a week from his job. He earns a raise andnow makes $84 a week. What is the % increase?
(A) 16.12%
(B) 16.66%
(C) 16.56%
(D) 40%
(E) 18.1%
Rationale: Increase = (24/60)*100 = (4/10)*100 = 40%.
D
Answer: (D) 40%
Question: What is the sum of all possible 3-digit numbers that can be constructed using the digits 2, 4, and 5 if each digit can be used only once in each number?
(A) 2442
(B) 2552
(C) 2662
(D) 2772
(E) 2882
Rationale: There are 6 possible arrangements of the three numbers.
Then each number will be in the hundreds, tens, and ones place two times each.
The sum is 2(222) + 2(444) + 2(555) = 2442
The answer is A.
Answer: (A) 2442
Question: Elena purchased Brand X pens for $4.00 apiece and brand Y for $2.40 apiece. If Elena purchased a total of 12 of these pens for $42.00, how many brand X pens did she purchase?
(A) 4
(B) 5
(C) 6
(D) 7
(E) 8
Rationale: 4x+2.8y=42 --> multiply by 2.5 (to get the integers) --> 10x+7y=105 --> only one positive integers solutions x=5 and y=5 (how to solve: 7y must have the last digit of 5 in order the last digit of the sum to be 5).
Answer: B.
Answer: (B) 5
Question: Thefactor countof an integer n greater than 1 is the number of distinct prime factors of n. For example, the factor count of 36 is 2, since 2 and 3 are the distinct prime factors of 36 = 2 x 2 x 3 x 3. For which of the following integers is the factor count greatest T?
(A)  60
(B)  61
(C)  62
(D)  63
(E)  64
Rationale: 60 = 2*2*3*5 factor count =3
61= prime number
62 = 2*31 factor count=2
63=3*3*7 factor count=2
64=2*2*2*2*2*2 factor count=1=T
answer is A.
Answer: (A)  60
Question: A and B starts a business with Rs.8000 each, and after 4 months, B withdraws half of his capital . How should they share the profits at the end of the 18 months?
(A) 18:11
(B) 18:18
(C) 98:18
(D) 18:10
(E) 18:12
Rationale: A invests Rs.8000 for 18 months, but B invests Rs.8000 for the first 4 months and then withdraws Rs.4000. So, the investment of B for remaining 14 months is Rs.4000 only.
A : B
8000*18 : (8000*4) + (4000*14)
14400 : 88000
A:B = 18:11
Answer: A
Answer: (A) 18:11
Question: If the price of sugar rises from Rs. 3 per kg to Rs. 5 per kg, a person, to have no increase in the expenditure on sugar, will have to reduce his consumption of sugar by
(A) 15%
(B) 20%
(C) 25%
(D) 30%
(E) 40%
Rationale: Sol.
Let the original consumption = 100 kg and new consumption = x kg.
So, 100 x 3 = x × 5 = x = 60 kg.
∴ Reduction in consumption = 40%.
Answer E
Answer: (E) 40%
Question: Three cubes of sides 5 m, 4 m, and 3 m are melted to form a new cube. Find the surface of the new cube?
(A) 236
(B) 256
(C) 216
(D) 246
(E) 206
Rationale: Volume of the new cube = [ 5(power)3 + 4(power)3 + 3(power)3 ] Cm(power)3
= 125 + 64 + 27 = 216 Cm(power)3 => a(power)3 = 216 Cm(power)3
Answer is C.
Answer: (C) 216
Question: A person was asked to state his age in years.His reply was,”Take my age three years hence,multiply it by 3 and then subtract three times my age three years ago and you will know how old I am”.What was the age of the person ?
(A) 18 years
(B) 20 years
(C) 24 years
(D) 32 years
(E) 43 years
Rationale: Solution
Let the present age of the person be x years.
Then,3(x+3)-3(x-3)=x ⇔ (3x + 9)-(3x-9)=x ⇔ x = 18.. Answer A
Answer: (A) 18 years
Question: The percentage profit earned by selling an article for Rs. 1920 is equal to the percentage loss incurred by selling the same article for Rs. 1280. At what price should the article be sold to make 25% profit?
(A) Rs. 2000
(B) Rs. 2200
(C) Rs. 2400
(D) Rs. 3400
(E) Data inadequate
Rationale: Explanation:
Let C.P. be Rs. x.
Then,	1920 - x	/ x	x 100 =	x - 1280/ x	x	100
=> 1920 - x = x - 1280
=> 2x = 3200
=> x = 1600
Required S.P. = 125% of Rs. 1600 = Rs.(125/100 x1600)=Rs 2000.
ANSWER IS A
Answer: (A) Rs. 2000
Question: How many two-element subsets of {2,4,6,8} are there that do not contain the element 4?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: Required subsets are = {2,6}, {2,8}, {6,8}= 3
Answer: C
Answer: (C) 3
Question: A man swims downstream 48 km and upstream 42 km taking 6 hours each time; what is the speed of the current?
(A) 3 kmph
(B) 0.5 kmph
(C) 13 kmph
(D) 6.5 kmph
(E) 7:3kmph
Rationale: Explanation:
48 --- 6 DS = 8
? ---- 1
42 ---- 6 US = 7
? ---- 1 S = ?
S = (8 - 7)/2 = 0.5
Answer: Option B
Answer: (B) 0.5 kmph
Question: A train running at the speed of 50 km/hr crosses a pole in 9 seconds. Find the length of the train?
(A) 125
(B) 272
(C) 278
(D) 277
(E) 112
Rationale: Speed =50*(5/18) m/sec = 125/9 m/sec
Length of Train (Distance) = Speed * Time
(125/9) * 9
= 125 meter
Answer: A
Answer: (A) 125
Question: 6 workers should finish a job in 8 days. After 3 days came 4 workers join them. How many days Z do they need to finish the same job?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
Rationale: Let Rate of one worker be R
=> (6*R)*8 = 1 (Rate * Time = work)
=> R = 1/48
=> Work remaining after 3 days
1 - (3*6)/48 = 30/48
After 4 ppl joined in
((6+4)*Time)/48 = 30/48
Time Z= 3 days to finish the task
IMO A
Answer: (A) 3
Question: The average weight of a class is x pounds. When a new student weighing 50 pounds joins the class, the average decreases by 1 pound. In a few months the student’s weight increases to 110 pounds and the average weight of the class becomes x + 4 pounds. None of the other students’ weights changed. What is the value of x?
(A) 85
(B) 86
(C) 88
(D) 90
(E) 92
Rationale: When the student weighs 80 pounds the average weight is x - 1 pounds;
When the student weighs 110 pounds the average weight is x + 4 pounds.
So, the increase in total weight of 110 - 80 = 30 pounds corresponds to the increase in average weight of (x + 4) - (x - 1) =5 pounds, which means that there are 30/5 = 6 students (including the new one). So, initially there were 5 student.
Total weight = 5x + 80 = 6(x-1) --> x = 85 pounds.
Answer: A.
Answer: (A) 85
Question: There are 10 pairs of socks and 2 socks are worn from that such that the pair of socks worn are not of the same pair. what is the number of pair that can be formed.
(A) 90
(B) 85
(C) 75
(D) 95
(E) 82
Rationale: First of all you should remember that there is a difference in left and right sock.
now no. of way to select any of the sock = 10
and for second = 9
so total methods = 10*9 = 90
ANSWER:A
Answer: (A) 90
Question: How many two-digit numbers are there whose remainder when divided by 10 is 1, and whose remainder when divided by 7 is 6?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
Rationale: 2 digit numbers whose remainder when divided by 10 is 1 are
11 , 21 , 31 , 41 , 51 , 61 , 71 , 81 , 91
Out of above , numbers whose remainder when divided by 6 is 5 are
11 , 41 and 71
Answer D
Answer: (D) 6
Question: Car A travels at three times the average speed of car B. Car A started to travel at 12:00 o'clock, car B started to travel at 16:00 o'clock. What is the speed of car B (in Km/h) if the total distance that both cars traveled until 18:00 was 1000 Km?
(A) 10.
(B) 25.
(C) 30.
(D) 38
(E) 50.
Rationale: Total distance - 1000KM
Time ratio A:B - 3:1
Speed Ratio A : B - 3 : 1
So distance(speed*time) ratio will be - 3*3 : 1*1 - 9:1
So total distance traveled by B - 100 KM
Time taken by B (18:00-16:00 =2) - 2 hours
Speed of B - 50 KMPH
ANSWER:E
Answer: (E) 50.
Question: A shopkeeper buys two articles for Rs.1000 each and then sells them, making 20% profit on the first article and 20% loss on second article. Find the net profit or loss percent?
(A) 200
(B) 88
(C) 77
(D) 66
(E) 51
Rationale: Profit on first article = 20% of 1000 = 200.
This is equal to the loss he makes on the second article. That, is he makes neither profit nor loss.
Answer: A
Answer: (A) 200
Question: If A and B are positive integers, and the remainder obtained when A is divided by B is the same as the remainder obtained when B is divided by A, which of the following is a possible value of AB?
(A)  62
(B)  55
(C)  49
(D)  34
(E)  24
Rationale: I am not too sure on this. I guess it is possible only when A and B are both same. If they are both same, AB must be a perfect square.
49 is a perfect square.
Ans:C
Answer: (C)  49
Question: Farm A had an average output of 300 kgs of wheat per acre. Farm B had an average output of 350 kgs of wheat per acre. It is known that Farm B's area is 15 acres less than Farm A's. It is also known that Farm B in total harvested 3000 kgs of wheat more than Farm A. What is the area of Farm A?
(A)  130 acres
(B)  135 acres
(C)  145 acres
(D)  164 acres
(E)  180 acres
Rationale: The area of Farm A = x acres;
The area of Farm B = x-15 acres.
Total output of Farm A = 300x kgs;
Total output of Farm B = 350(x-15) kgs.
Farm B in total harvested 3000 kgs of wheat more than Farm A: 300x+3000=350(x-15) --> x=164 acres.
Answer: D.
Answer: (D)  164 acres
Question: The true discount on a bill due 9 months hence at 16% per annum is Rs. 162.The amount of the bill is
(A) Rs. 1386
(B) Rs. 1350
(C) Rs. 1575
(D) Rs. 2268
(E) None of these
Rationale: Solution
32.5
Let P.W. be Rs. x.Then,S.I. on Rs.x at 16% for 9 months =Rs.162.
∴ x 16 x9/ 12x 1/100}= 162 or x = 1350.
∴ P.W. = Rs. 1350.
Answer B
Answer: (B) Rs. 1350
Question: If the length of a certain rectangle is decreased by 4 cm and the width is increased by 3 cm, a square with the same area as the original rectangle would result. Find the perimeter of the original rectangle?
(A) 76
(B) 27
(C) 19
(D) 50
(E) 11
Rationale: Let x and y be the length and breadth of the rectangle respectively.
Then, x - 4 = y + 3 or x - y = 7 ----(i)
Area of the rectangle =xy; Area of the square = (x - 4) (y + 3)
(x - 4) (y + 3) =xy <=> 3x - 4y = 12 ----(ii)
Solving (i) and (ii), we get x = 16 and y = 9.
Perimeter of the rectangle = 2 (x + y) = [2 (16 + 9)] cm = 50 cm.
Answer: D
Answer: (D) 50
Question: In one hour,a boat goes 11 km along the stream and 5 km against the stream.The speed of the boat in still water (in km/hr) is :
(A) 3
(B) 5
(C) 8
(D) 9
(E) 10
Rationale: Solution
Speed in still water =1/2(11+5)kmph.= 8 kmph. Answer C
Answer: (C) 8
Question: Shawn invested one half of his savings in a bond that paid simple interest for 2 years (20% per anum) and received $600 as interest. He invested the remaining in a bond that paid compound interest, interest being compounded annually, for the same 2 years at the same rate of interest and received $655 as interest. What was the value of his total savings before investing in these two bonds?
(A) 3000
(B) 5000
(C) 6000
(D) 8000
(E) 9000
Rationale: So, we know that Shawn received 20% of the amount he invested in a year. We also know that in one year Shawn received $300, thud 0.2x = $300 --> x = $1,500.
Since, he invested equal sums in his 2 bonds, then his total savings before investing was 2*$1,500 = $3,000.
Answer: A
Answer: (A) 3000
Question: A father said his son , " I was as old as you are at present at the time of your birth. " If the father age is 38 now, the son age 5 years back was
(A) 14
(B) 17
(C) 11
(D) 19
(E) 99
Rationale: Let the son's present age be x years .Then, (38 - x) = x x= 19.
Son's age 5 years back = (19 - 5) = 14 years
Answer: A
Answer: (A) 14
Question: A certain company employs 6 senior officers and 3 junior officers. If a committee is to be created, that is made up of 3 senior officers and 1 junior officer, how many different committee are possible?
(A) 8
(B) 24
(C) 58
(D) 60
(E) 210
Rationale: Number of ways to select 3 senior officers from 6 of them = 6C3 = (6 x 5 x 4)/3! = 20 ways
Next we can determine the number of ways to select 1 junior officer.
number of ways to select 1 junior officer from 3 of them = 3C1 = 3 ways
Thus the number of ways to select 3 senior officers and 1 junior officer is 20 x 3 = 60 ways.
Answer: D
Answer: (D) 60
Question: Two persons start running simultaneously around a circular track of length 300 m from the same point at speeds of 15 km/hr and 25 km/hr. When will they meet for the first time any where on the track if they are moving in opposite directions?
(A) 12
(B) 15
(C) 24
(D) 27
(E) 52
Rationale: Time taken to meet for the first time anywhere on the track
= length of the track / relative speed
= 300 / (15 + 25)5/18 = 300* 18 / 40 * 5 = 27 seconds.
Answer:D
Answer: (D) 27
Question: A certain tax rate is $82 per $100.00. What is the rate, expressed as a percent?
(A) 82%
(B) 8.2%
(C) 0.82%
(D) 0.082%
(E) 0.0082%
Rationale: Here in question it is asking $.82 is what percent of $ 100.Suppose $ .82 is x% of 100 means
100* (x/100) = 82
Hence x = 82 %
So answer is A
Answer: (A) 82%
Question: A number when divided b the sum of 555 and 445 gives two times their difference as quotient and 30 as the remainder. The number is:
(A) 1220
(B) 1250
(C) 22030
(D) 220030
(E) None of these
Rationale: Required number = (555+445)*2*110+30 = 220000+30= 220030.
Answer: D
Answer: (D) 220030
Question: Twenty two years ago,a father was three times as old as his son.Now the father is only twice as old as his son. Then the sum of the present ages of the son and the father is :
(A) 132
(B) 76
(C) 108
(D) 105
(E) 86
Rationale: Let the present ages of the father and son be 2x and x years respectively.
then,(2x-22)=3 (x-22)
x=44.
Required sum =(2x+x)=3x=132 years.
Answer is A
Answer: (A) 132
Question: If 0.5% of A =75 paise, then the value of A is ?
(A) Rs. 150
(B) Rs. 17
(C) Rs. 1.70
(D) Rs. 4.25
(E) None
Rationale: Answer
∵ 0.5/100 of A = 75/100
∴ A = Rs. (75 / 0.5) = Rs. 150
Correct Option: A
Answer: (A) Rs. 150
Question: Two boys starting from the same place walk at a rate of
5kmph and 5.5kmph respectively.what time will they take to be
8.5km apart, if they walk in the same direction
(A) 17 hrs
(B) 11 hrs
(C) 19 hrs
(D) 7 hrs
(E) 21 hrs
Rationale: The relative speed of the boys = 5.5kmph – 5kmph = 0.5 kmph
Distance between them is 8.5 km
Time= 8.5km / 0.5 kmph = 17 hrs
Answer is A.
Answer: (A) 17 hrs
Question: It takes 35 identical printing presses 15 hours to print 500,000 papers. How many hours would it take 25 of these printing presses to print 500,000 papers?
(A) 18
(B) 20
(C) 21
(D) 24
(E) 25
Rationale: 35 printing presses can do 1/15 of the job each hour.
25 printing presses can do 5/7*1/15 = 1/21 of the job each hour.
The answer is C.
Answer: (C) 21
Question: In a company, 54 percent of the employees are men. If 60 percent of the employees are unionized and 70 percent of these are men, what percent of the non-union employees are women?
(A) 55%
(B) 60%
(C) 65%
(D) 70%
(E) 75%
Rationale: The percent of employees who are unionized and men is 0.7*0.6 = 42%
The percent of employees who are unionized and women is 60 - 42 = 18%
46% of all employees are women, so non-union women are 46%-18% = 28%
40% of all employees are non-union.
The percent of non-union employees who are women is 28%/40% = 70%
The answer is D.
Answer: (D) 70%
Question: Cost price of 12 mangoes is equal to the selling price of 9 mangoes and the discount on 10 mangoes is equal to the profit on 5 mangoes. What is the percentage point difference between the profit percentage and discount percentage?
(A) 1.5 %
(B) 1.75 %
(C) 1.85 %
(D) 2 %
(E) None of these
Rationale: Cost price of 12 mangoes is equal to the selling price of 9 mangoes,
Let the C.P. of one mango = Re. 1
C.P. of 9 mangoes = Rs. 9
S.P. of 9 mangoes = Rs. 12
Profit % of 9 mangoes = 3/9 x 100 = 33.33 %
Profit % of 1 mango = 33.33/9 = 3.703 %
Profit % of 5 mangoes = 3.703 x 5 = 18.51 %
Given, the discount on 10 mangoes is equal to the profit on 5 mangoes,
Discount on 10 mangoes = 18.51 %
Discount on 1 mango = 1.851 %
Therefore, Profit % of 1 mango - Discount on 1 mango = 3.703 - 1.851 = 1.85 %
ANSWER:C
Answer: (C) 1.85 %
Question: The area of a square pond is A square feet and the perimeter is p feet. If 2A=4p+18, what is the perimeter of the pond, in feet?
(A) 28
(B) 36
(C) 40
(D) 56
(E) 84
Rationale: You can also solve this via using the given numbers in the answer choices!
Of course you need to be aware of the basic properties as outlined by the other posts above (a = x^2 and p = 4x)
Starting with D you will notice that x=14 is way too big for your area (14^2) and will not satisfy: 2A=4p+18 or A=2p+9
--> Eliminate D and E
Now pick B (its either too big, then its A, or too small then you know its C or it is B itsself)
And picking B indeed solves the problem! (36/4 --> 9; a= 9^2 = 81 and 81=2x36+9)
Answer: (B) 36
Question: A train covers a distance of 18 km in 10 min. If it takes 6 sec to pass a telegraph post, then the length of the train is?
(A) 177
(B) 168
(C) 120
(D) 882
(E) 180
Rationale: Speed = (18/10 * 60) km/hr = (108 * 5/18) m/sec = 30 m/sec.
Length of the train = 30 * 6 = 180 m.Answer:E
Answer: (E) 180
Question: Arun is 4 years older than Sachin, and Jai is 5 times older than Arun. If S is Sachin’s age and J is Jai’s age, what is the relationship between S and J?
(A) J = 5S + 20
(B) J = 5S + 10
(C) J = 5S + 5
(D) J = 5S − 20
(E) J = 5S − 5
Rationale: A=S+4 and J=5A --> J=5S+20
Answer A
Answer: (A) J = 5S + 20
Question: The number of new words that can be formed by rearranging the letters of the word 'MOTHER' is
(A) 288
(B) 767
(C) 719
(D) 287
(E) 112
Rationale: Explanation:
Number of words which can be formed = 6! - 1 = 720 - 1 = 719.
Answer: C
Answer: (C) 719
Question: A trumpet section includes six musicians. If they hold an audition to determine chair order within the section, and there are to be no ties, how many distinct chair orders can result?
(A) 240
(B) 125
(C) 720
(D) 100
(E) 25
Rationale: We have a word problem using permutations. We must identify the number of total items in the group. There are six possible musicians who could be placed in the first chair, five possible musicians for the second, four for the third, three for the fourth, and two for the fifth and one for the sixth. To determine the number of possible orderings, we multiply these numbers, which we can express as 6!. Now 6! = (6)(5)(4)(3)(2)(1) = 720=C
Answer: (C) 720
Question: What approximate value should come in place of the question mark (?) in the following equation ?
1⁄7 of 1596 + 3015 = ? – 2150
(A) 7200
(B) 48000
(C) 5380
(D) 58000
(E) 6300
Rationale: ? ≈ 1 × 230 + 3000 + 2150
= 230 + 3000 + 2150 = 5380
Answer C
Answer: (C) 5380
Question: Fox jeans regularly sell for $15 a pair and Pony jeans regularly sell for $18 a pair. During a sale these regular unit prices are discounted at different rates so that a total of $6 is saved by purchasing 5 pairs of jeans: 3 pairs of Fox jeans and 2 pairs of Pony jeans. If the sum of the two discounts rates is 18 percent, what is the discount rate on Pony jeans?
(A) 9%
(B) 10%
(C) 11%
(D) 35%
(E) 15%
Rationale: You know that Fox jeans costs $15, and Pony jeans costs $18, you also know that 3 pairs of Fox jeans and 2 pairs of Pony jeans were purchased. So
3(15) = 45 - Fox
2(18) = 36 - Pony
The total discount discount is $6 and you are asked to find the percent discount of pony jeans,
so 45(18 - X)/100 + 36(X)/100 = 6 or 45*18 -45*x + 36*x =6*100 or 9x = -6*100 +45*18
x=210/6= 35%
D
Answer: (D) 35%
Question: if log 2 = 0.30103, the number of digits in 2128 is
(A) 22
(B) 39
(C) 88
(D) 28
(E) 11
Rationale: Explanation:
log(2128) = 128log(2) = 128 × 0.30103 ≈ 38.4
ie, its characteristic = 38
Hence, number of digits in 2128 = 38+1 = 39
Answer: Option B
Answer: (B) 39
Question: The perimeter of one face of a cube is 32 cm. Its volume will be:
(A) 125cm3
(B) 400cm3
(C) 512cm3
(D) 625cm3
(E) None of these
Rationale: Explanation:
Edge of cude = 32/4 = 8 cm
Volume = a*a*a = 8*8*8 = 512 cm cube
Option C
Answer: (C) 512cm3