mathewhe/aqua_rat huggingface dataset:
Question: The present ages of three persons are in the proportion of 4 : 7 : 9. Eight years ago, the sum of their ages was 16. Find their present ages.
(A) 20,35,45
(B) 8,14,18
(C) 16,28,36
(D) 16,28,46
(E) None of these
Rationale: Let the present ages of three persons be 4K,7K and 9K respectively.
(4K - 8) + (7K - 8) + (9K - 8) = 16
20K = 40
K = 2
Therefore, then present ages are 8,14,18.
ANSWER:B
Answer: (B) 8,14,18
Question: The length of a rectangle is 18 cm and its breadth is 10 cm. When the length is increased to 25 cm, what will be the breadth of the rectangle if the area remains the same ?
(A) 7 cm
(B) 7.1 cm
(C) 7.2 cm
(D) 7.3 cm
(E) None of these
Rationale: Solution
Let the breadth be b. Then,
⇒ 25b = 18 × 10 ⇒ b = (18x10/25)cm= 7.2 cm Answer C
Answer: (C) 7.2 cm
Question: Statement: According to a survey, the current water reservoir will deplete by 50% by 2050
Action:
I. Government of all the countries should appeal to all the citizens to use water carefully and avoid wastage.
II. Scientists should start finding an alternative solution to water.
(A) Only I follows
(B) Only II follows
(C) Either I or II follows
(D) Neither I nor II follows
(E) Both I and II follow
Rationale: Explanation:
Second option is not at all justifiable. Water is a basic necessity for survival. So, wasting money and efforts for finding something which doesn’t even exist makes no sense. 2nd option would have been a good and preferable option if it would have been something other than water like petrol or any such thing.
ANSWER IS A
Answer: (A) Only I follows
Question: The ratio of the cost price and the selling price is 4:5. The profit percent is:
(A) 10%
(B) 20%
(C) 25%
(D) 30%
(E) 40%
Rationale: Let C.P. = Rs. 4x. Then, S.P. = Rs. 5x
Gain = (5x - 4x) = Rs. x
Gain % = (x * 100)/ 4x = 25%.
ANSWER:C
Answer: (C) 25%
Question: Which of the following is true about 0<|x|-3x<5?
(A) -1<x<0
(B) 0<x<1
(C) 1<x<2
(D) 2<x<3
(E) 3<x<4
Rationale: when can be |x|-4x be greater than 0..
NEVER when x is positive..
ONLY A is left..
you can also substitute any value within the given range to check for answer
Example - put x as -0.5 for A. -1<x<0..
so |x|-3x = |-0.5|- 3*(-0.5) = 0.5+15. = 2 and it satisfies 0<|x|-4x<5
A
Answer: (A) -1<x<0
Question: A father said to his son, "I was as old as you are at the present at the time of your birth". If the father's age is 44 years now, the son's age 10 years back was:
(A) 10 years.
(B) 14 years.
(C) 17 years.
(D) 16 years.
(E) 12 years.
Rationale: Let the son's present age be x years. Then, (44 - x) = x
2x = 44.
x = 22
Son's age 10 years back (22 - 10) = 12 years.
ANSWER :E
Answer: (E) 12 years.
Question: If x is negative and y is positive, which of the following cannot be positive?
(A) x^2+y
(B) x/-y
(C) x/y
(D) -xy
(E) x^4+y
Rationale: -/+ = - x/y is not positive
Answer : C
Answer: (C) x/y
Question: There are 10 books on a shelf: 6 English books, 3 Spanish books and 2 Portuguese books. What is the probability of choosing 2 books in different languages?
(A) 31/90
(B) 3/10
(C) 4/5
(D) 31/45
(E) 28/90
Rationale: Probability = Favourable outcome / Total Outcome = 1- (Unfavourable outcome / Total Outcome)
Favourable Outcomes
Case-1: One book is English (out of 6 English books) and one book is Spanish (out of 3 Spanish books) i.e. 6C1*3C1
Case-2: One book is Spanish (out of 3 Spanish books) and one book is Portuguese (out of 2 Portuguese books) i.e. 3C1*2C1
Case-3: One book is English (out of 6 English books) and one book is Portuguese (out of 2 Portuguese books) i.e. 6C1*2C1
Total favourable Outcomes = 6C1*3C1+3C1*2C1+6C1*2C1 = 18+6+12 = 36
Total Possible Outcomes = 10C2 = 45
i.e. Probability = 36/45=4/5
C
Answer: (C) 4/5
Question: A man, a woman or a boy can do a job in 20 days, 30 days or 60 days respectively. How many boys must assist 2 men and 8 women to do the work in 2 days?
(A) 15 boys
(B) 8 boys
(C) 10 boys
(D) 11 boys
(E) None of these
Rationale: Man’s two day’s work = 2 × 1⁄20 th work = 1⁄10 th work
Woman’s two days’s work
= 2 × 1⁄30 th work = 1⁄15 th work
Boy’s two day’s work = 2 × 1⁄60 th work = 1⁄30 th work
Now, let 2 men, 8 women and x boys can complete work in 2 days. Then ,
2 men’s work + 8 women’s work + x boy’s work = 1
2(1⁄10) + 8(1⁄15) + x(1⁄30) = 1
⇒ x = (1 - 1⁄5 - 8⁄15) × 30 ⇒ x = 8 boys
Answer B
Answer: (B) 8 boys
Question: An amount of Rs.20,000 is to be distributed amongst P, Q, R and S such that “P” gets twice as that of “Q” and “S” gets four times as that of “R”. If “Q” and “R” are to receive equal amount, what is the difference between the amounts received by S and P?
(A) Rs. 5000
(B) Rs. 4570
(C) Rs. 2750
(D) Rs. 2950
(E) None of these
Rationale: Explanation:
We have, P = 2Q & S = 4R
Further Q = R & P + Q + R + S = 20,000
Thus we get, 2Q + Q + Q + 4Q = 20,000
8Q = 20,000 or Q = Rs. 2500
Thus, R = Rs. 2500, P = 5000 & S = Rs. 10000
Hence, the required difference = (S – P) = (10000 – 5000) = Rs. 5000
ANSWER:A
Answer: (A) Rs. 5000
Question: ?% of 360 = 115.2
(A) 277
(B) 36
(C) 64
(D) 32
(E) None of these
Rationale: ?% of 360 = 115.2
or, ? = 115.2×100/360=32
Answer D
Answer: (D) 32
Question: How many multiples of 3 are there between 10 and 100, exclusive ?
(A) 30
(B) 29
(C) 28
(D) 31
(E) 33
Rationale: 3 * 4 = 12
3 * 33 = 99
Total multiples = (33 - 4) + 1 = 30
Exclude 10 and 100 = 30
Answer is A
Answer: (A) 30
Question: In a two-digit number, if it is known that its unit's digit exceeds its ten's digit by 3 and that the product of the given number and the sum of its digits is equal to 517, then the number is:
(A) 14
(B) 36
(C) 47
(D) 58
(E) 63
Rationale: Let the ten's digit be x. Then, unit's digit = x + 3. Number = 10x + (x + 3) = 11x + 3
(11x + 3)(2x + 3) = 517
22(x)(x)+ 39x- 508 = 0
(x - 4)(22x + 127) = 0
x = 4
Hence, required number = 11x + 3 = 47.
ANSWER:C
Answer: (C) 47
Question: There is an increase of 30% in the production of milk chocolates in Amul Dairy in one month. If now it is 9,100 milk chocolates per month, what was it one month ago?
(A) 10,000 chocolates
(B) 9000 chocolates
(C) 8000 chocolates
(D) 7000 chocolates
(E) None of these
Rationale: Let one month ago, production be x chocolates.
Then, 130 % of x = 9100
⇒ x = 9100×100/130=7000 chocolates
Answer D
Answer: (D) 7000 chocolates
Question: Which of the following cannot be the range of a set consisting of 5 odd multiples of 13?
(A) 52
(B) 100
(C) 104
(D) 208
(E) 416
Rationale: Solution: sequence of 13 lets say sequence is 13n, 13(n+1), 13(n+2), 13(n+3), 13(n+4)
so range is 13n+52-13n = 52
if we put the different values of n we will get different but the range will be multiple of 52
and only 100 is not multiple of 52
Answer : B
Answer: (B) 100
Question: A and B started a business with an investment of Rs.26000 and Rs.28000. After two months C joined in the business with an investment of Rs.32000, what is share of C in the half year profit of Rs.9040 ?
(A) Rs.3360
(B) Rs.3120
(C) Rs.2940
(D) Rs.2560
(E) Rs.3550
Rationale: Investment x Time.
A = 26000 x 6 = 156000.
B = 28000 x 6 = 168000.
C = 32000 x 4 = 128000.
Ratio of shares A : B : C = 39 : 42 : 32 = [ Total 113 units ]
Share of C in the profit = 9040 × 32 / 113 = 2560
Option D
Answer: (D) Rs.2560
Question: A shopkeeper has 280 kg of apples. He sells 40% of these at 10% profit and remaining 60% at 30% profit. Find his % profit on total.
(A) 22%
(B) 25%
(C) 26%
(D) 28%
(E) 35%
Rationale: If the total quantity was 100
Then 40X 10% + 60 X30%= 22
This profit will remain same for any total quantity unless the % of products remains the same. Hence 'A' is the answer
Answer: (A) 22%
Question: There is a rectangular prism made of 1 in cubes that has been covered in tin foil. There are exactly 128 cubes that are not touching any tin foil on any of their sides. If the width of the figure created by these 128 cubes is twice the length and twice the height, what is the measure y in inches of the width of the foil covered prism?
(A) 4
(B) 6
(C) 8
(D) 9
(E) 10
Rationale: If the width is w, then length and height would be w/2.
So, w*w/2*w/2 = 128 => w^3 = (2^3)*64 = (2^3) * (4^3)
=> w = 2*4 = 8 in.
Along the width of the cuboid, 8 cubes don't touch the tin foil. So the actual width will be non-touching cubes + touching cubes
= 8 +2 =y=10
Ans E.
Answer: (E) 10
Question: A sales representative receives a salary of $150 per week and earns a commission of 15% on all sales she makes. How many dollars’ worth of sales does she need to make in order to bring her total weekly income to $900?
(A) $3,000
(B) $3,150
(C) $4,000
(D) $4,150
(E) $5,000
Rationale: We're told that a sales representative receives a salary of $150 per week and earns a commission of 15% on all sales she makes. We're asked how many dollars’ worth of sales will bring her total weekly income to $900.
Since the salesperson receives a $150 salary, the remaining $750 has to be accounted for by the 15% commission. Since those numbers are rather specific, we're likely dealing with a 'round number' for total sales.
Let's TEST Answer C: $4,000
Since 15% of $1,000 = $150
15% of $4,000 = 4($150) = $600
This is TOO HIGH (it's supposed to be $450), so we need a LOWER total sales figure.
Let's TEST Answer E: $5,000
Since 15% of $1,000 = $150
15% of $5,000 = 5($150) = $750
This is an exact MATCH for what we were told, so this MUST be the answer.
Final Answer:
E
Answer: (E) $5,000
Question: The probability that A speaks truth is 3/5 and that of B speaking truth is 4/7. What is the probability that they agree in stating the same fact?
(A) 18/35
(B) 18/39
(C) 18/128
(D) 18/30
(E) 18/32
Rationale: Explanation:
If both agree stating the same fact, either both of them speak truth of both speak false.
Probability = 3/5 * 4/7 + 2/5 * 3/7
= 12/35 + 6/35 = 18/35
Answer:A
Answer: (A) 18/35
Question: Machine X takes 10 hours longer than machine Y to produce 1080 Widgets. Machine Y produces 20 percent more widgets in an hour than machine x does in an hour. How many widgets per hour does machine X produce
(A) 100
(B) 65
(C) 25
(D) 11
(E) 18
Rationale: Machine Y produces 20 percent more widgets in an hour than machine x does in an hour.
So if machine X produces 100 widgets, then machine Y produces 120 widgets.
Ratio of 120/100 = 6/5.
This is their speed of work (Y:X).
i.e. speed of their work (X:Y) = 5/6
Now, time is inversely proportional to speed.
Hence the ratio of the time spent (X:Y)= 6/5
Let us assume that they spend 6x and 5x hours.
Given that 6x-5x = 10
So, x = 10.
Hence 6x = 6*10 = 60 hours.
Hence X takes 120 hours to produce 1080 widgets.
So, in 1 hour, it can produce (1 * 1080)/60
= 18
Hence option (E).
Answer: (E) 18
Question: In a kilometer race, A beats B by 50 meters or 10 seconds. What time does A take to complete the race?
(A) 277 sec
(B) 190 sec
(C) 667 sec
(D) 167 sec
(E) 176 sec
Rationale: Time taken by B run 1000 meters = (1000 * 10)/50 = 200 sec.
Time taken by A = 200 - 10 = 190 sec.Answer: B
Answer: (B) 190 sec
Question: In a race of length L metres, Johnson beats Lewis by P metres and Greene by Q metres, By how many metres does Lewis beat Greene in the same race ? (P<Q)
(A) L(L-Q) / L-P
(B) L(Q-P) / L-P
(C) L-Q
(D) P-Q
(E) P+Q
Rationale: As the time is constant, the ratio of distances will be the same as the ratio of speeds.
If Sj,Sl,Sg are the speeds of Johnson, Lewis, and Greene respectively, then
Sj/Sl = L/(L-P)
and Sj/Sg = L/(L-Q)
=> Sg/Sl = (L-Q)/(L-P)
Therefore the speeds of Lewis and Greene are in the ratio (L-P)/(L-Q)
When Lewis finishes the race, the time run by him and Greene are same
=> The ratio of the speeds of Lewis and Greene will be the same as the ratio of distances run by them.
=> Distance run by Greene when Lewis finishes the race = (L-Q)/(L-P) * L
=> Lewis beats Greene by L - L*(L-Q)/(L-P) = L [ 1 - (L-Q)/(L-P)] = L (Q-P) / (L-P)
Option (B) is therefore correct.
Answer: (B) L(Q-P) / L-P
Question: The age of father 5 years ago was four times the age of his son. Five years hence, father's age will be twice that of his son. The ratio of their present ages is:
(A) 5 : 4
(B) 7 : 4
(C) 5 : 2
(D) 5 : 3
(E) 7 : 5
Rationale: Let the ages of father and son 5 years ago be 4x and x years respectively.
Then, (4x + 5) + 5= 2[(x + 5) + 5]
4x + 10 = 2x + 20
x = 5.
Required ratio = (4x + 5) : (x + 5) = 25: 10= 5 : 2.
Answer: Option C
Answer: (C) 5 : 2
Question: A baker filled with a measuring cup with 1/2 cup water. He poured 1/2 of the water into the batter, and then spilled 1/8 of the water on the floor. How much water will the baker needed to add what is left in the cup to have 50% more than what he started with?
(A) 1/8 cup
(B) 3/8 cup
(C) 1/4 cup
(D) 1/2 cup
(E) 5/8 cup
Rationale: 1/2 is the original water in cup .half in batter.So left is 1/4 out which 1/8 is spilled out.So again left with 1/8.
so 50% more than what he started was = 1/2+1/2*(1/2)=3/4
Amount of water needed to add = 6/8 - 1/8=5/8
E
Answer: (E) 5/8 cup
Question: The perimeters of two squares are 40 cm and 32 cm. Find the perimeter of a third square whose area is equal to the difference of the areas of the two squares
(A) 22 cm
(B) 24 cm
(C) 26 cm
(D) 28 cm
(E) None of these
Rationale: Explanation:
We know perimeter of square = 4(side)
So Side of first square = 40/4 = 10 cm
Side of second square = 32/4 = 8 cm
Area of third Square = 10*10 - 8*8
= 36 cm
So side of third square = 6 [because area of square = side*side]
Perimeter = 4*Side = 4*6 = 24 cm
Option B
Answer: (B) 24 cm
Question: If the price of a certain bond on May 1st was 3/4 the price of the bond on June 1st and the price of the bond on July 1st was 50% greater than the price of the bond on May 1st. then the price of the bond on June 1st st was what percent of the average (arithmetic mean) price of the bond on May 1st and July 1st?
(A) 50%
(B) 114.28%
(C) 120%
(D) 133 1/3%
(E) 150%
Rationale: The price on June 1st = 12 (assume);
The price on May 1st = 3/4*12 = 9;
The price on July 1st = 8*1.5 = 12.
The average price of the bond on May 1st and July 1st = (9+12)/2 = 10.5.
The price of the bond on June 1st (12) is 24/21 times (114.28%) the average price of the bond on May 1st and July 1st.
Answer: B.
Answer: (B) 114.28%
Question: The area of a square field 3136 sq m, if the length of cost of drawing barbed wire 3 m around the field at the rate of Rs.2.50 per meter. Two gates of 1 m width each are to be left for entrance. What is the total cost?
(A) s.1014
(B) s.1140
(C) s.999
(D) s.1665
(E) s.1020
Rationale: a2 = 3136 => a = 56
56 * 4 * 3 = 672 – 6 = 666 * 2.5 = 1665
ANSWER:D
Answer: (D) s.1665
Question: Two trains are traveling on a collision course. If train A is traveling at a speed of 350 mph and train B is traveling 28% slower, how much time will it take the trains to collide if the initial distance between the two is 1806 miles?
(A) Two hours and 30 minutes.
(B) One hour and 10 minutes.
(C) Two hours and 25 minutes.
(D) Three hours and 0 minutes.
(E) Four hours and 20 minutes.
Rationale: Answer is D. Three hours and 0 minutes.
Since they are racing towards each other, the speed is accumulative, ie. 350 mph + 350*0.72 = 602 (0.72 because the second train is 28% slower)
So time before collision is total distance / total speed = 1806/602 = 3 hours and 00 mins
Answer: (D) Three hours and 0 minutes.
Question: How long will a man take to go, walking at 4 km per hour, twice round a circular garden of 70 m radius
(A) 11
(B) 28
(C) 26
(D) 18
(E) 111
Rationale: Answer:B
Answer: (B) 28
Question: In each of the following questions a number series is given with one term missing. Choose the correct alternative that will continue the same pattern and fill in the blank spaces.
2, ?, 14, 23, 34, 47
(A) 31
(B) 7
(C) 36
(D) 31
(E) 33
Rationale: B
7
The given sequence is +5, +7, +9, ——
ie. 2+ 5 = 7, 7 + 7 = 14, 14 + 9 = 23
Answer: (B) 7
Question: The average of first ten prime numbers which are odd is?
(A) 15.2
(B) 15.7
(C) 15.4
(D) 15.8
(E) 15.5
Rationale: Sum of first 10 prime no. which are odd = 158
Average = 158/10
= 15.8
Answer:D
Answer: (D) 15.8
Question: The perimeter of a triangle is 28 cm and the inradius of the triangle is 2.5 cm. What is the area of the triangle?
(A) 30
(B) 32
(C) 34
(D) 31
(E) 35
Rationale: Area of a triangle = r * s
Where r is the inradius and s is the semi perimeter of the triangle.
Area of triangle = 2.5 * 28/2 = 35 cm2
Answer: Option E
Answer: (E) 35
Question: 10 men, working 6 hours a day can complete a work in 18 days. How many hours a day must 15 men work to complete the work in 12 days ?
(A) 2hours a day
(B) 7hours a day
(C) 6hours a day
(D) 3hours a day
(E) 2hours a day
Rationale: Explanation:
More Men, Less Hours {Indirect Proportion}
Less Days, More Hours {Indirect Proportion}
\inline {\color{Blue} \begin{bmatrix} Men &15 & 10\\ Days &12 & 18 \end{bmatrix}::6:x}
=> x * 15 * 12 = 10 * 18 * 6
=> x = (10 *18 *6)/(12*15)
=>x = 6
Answer: C
Answer: (C) 6hours a day
Question: By selling a house for Rs.72000, it was found that 1/5 of the outlay was gained, what ought the selling to price to have been in order to have lost 5 p.c?
(A) 38020
(B) 57000
(C) 38028
(D) 38019
(E) 38192
Rationale: CP + CP/5 = 72000
CP = 60000
SP = 60000*(95/100)
=57000
Answer: B
Answer: (B) 57000
Question: How many negative numbers are there in an alternating sequence of positive and negative numbers, if the sequence contains b numbers, where b is an odd number greater than 12. The first number of the sequence is a negative number.
(A) (b-1)/2
(B) (b+1)/2
(C) b/2
(D) b/(2-1)
(E) b/(2+1)
Rationale: Lets put values for b, say b=13 since it's odd and it is grater than 12,
and first number is neg so sequence will be {neg,pos,neg,pos,neg,pos,neg,pos,neg,pos,neg,pos,neg} we can see that it has 7 positive terms
so putting bx=13 in the options,
option B = (b+1)/2 => (13+1)/2 = 7 , the number of positive integers
So, B is the answer
Answer: (B) (b+1)/2
Question: The base of a parallelogram is twice its height. If the area of the parallelogram is 72 sq.cm. Find its height?
(A) 3 cm
(B) 6 cm
(C) 7 cm
(D) 9 cm
(E) 10 cm
Rationale: Solution
Let the height of the parallelogram be x cm.Then base
= (2x) cm
=2x² = 72
x²=36
x = 6.
Answer B
Answer: (B) 6 cm
Question: How many ways can 10 friends be arranged around a circular dinner table?
(A) 6!
(B) 7!
(C) 8!
(D) 9!
(E) 10!
Rationale: The number of ways to order 10 people is 10!
However, around a circular table, each pattern would be repeated 10 times.
So the number of ways to seat 10 friends around a circular table is 9!
The answer is D.
Answer: (D) 9!
Question: Replace X with the appropriate number in
1 , 3 , 5 , 7 , 8 , 9 , 10 , X
(A) 2
(B) 11
(C) 4
(D) 6
(E) 30
Rationale: B
list of consecutive numbers that has an 'e' in the spelling
Answer: (B) 11
Question: What will come in place of the x in the following Number series? 2, 7, 32, 157, 782, x
(A) 3707
(B) 3790
(C) 3910
(D) 3907
(E) 3970
Rationale: 22 x 5 - 3 = 77 x 5 - 3 = 3232 x 5 - 3 = 157157 x 5 - 3 = 782782 x 5 - 3 = 3907D
Answer: (D) 3907
Question: In given series 582, 605, 588, 611, 634, 617, 600 only one number is incorrect. Find out that wrong number
(A) 615
(B) 634
(C) 600
(D) 620
(E) 617
Rationale: 582+23=605
605-17=588
588+23=611
611-17=594....so 634 is wrong.
594+23=617
617-17=600
ANSWER:B
Answer: (B) 634
Question: Find the value for x from below equation: x/3=-4?
(A) -12
(B) 1
(C) -2
(D) -3
(E) 4
Rationale: 1. Multiply both sides by 3:
x*3/3= -4/3
. Simplify both sides:
x = -12
A
Answer: (A) -12
Question: A college has classes from 10:00 AM until 1:40 PM. In this duration, there are five periods. If 5 minutes are provided between each period to leave one class and enter the next class, how many minutes long is each period?
(A) 38 min
(B) 41 min
(C) 40 min
(D) 42 min
(E) 52 min
Rationale: The total time is 220 minutes.
There are four breaks of five minutes between the classes for a total of 20 minutes.
The total class time is 200 minutes.
200 / 5 classes = 40 minutes per class
The answer is C.
Answer: (C) 40 min
Question: Rajan and Rakesh started a business and invested Rs. 20,000 and Rs. 25,000 respectively. After 4 months Rakesh left and Mukesh joined by investing Rs. 15,000. At the end of the year there was a profit of Rs. 4,600. What is the share of Rakesh ?
(A) 1000
(B) 1100
(C) 1125
(D) 1200
(E) 1050
Rationale: Ratio of share of Rajan, Rakesh nd Mukesh => 20000:25000:15000
=>4:5:3
=>4*12 : 5*4 : 3*8 [Since Rakesh left after 4 months nd Mukesh joined after 4 months...]
=> 12:5:6
Share of Rajan => 4600*12/23 = 2400
Share of Rakesh => 4600*5/23 = 1000
ANSWER:A
Answer: (A) 1000
Question: A man swims downstream 76 km and upstream 48 km taking 4 hours each time; what is the speed of the current?
(A) 3 kmph
(B) 1.5 kmph
(C) 3.5 kmph
(D) 6.5 kmph
(E) 7:3kmph
Rationale: Explanation:
76 --- 4 DS = 19
? ---- 1
48 ---- 4 US = 12
? ---- 1 S = ?
S = (19 - 12)/2 = 3.5
Answer: Option C
Answer: (C) 3.5 kmph
Question: How many multiples of 8 are less than 7600, and also multiples of 19?
(A) 104
(B) 100
(C) 50
(D) 89
(E) 90
Rationale: LCM of 8 & 19 = 152
Tried dividing 7600 by 152
Got quotient 50'So C is answer
Answer: (C) 50
Question: The value of log2(log5625) is
(A) 2
(B) 5
(C) 10
(D) 15
(E) 20
Rationale: Solution
Let log5625	= x.
Then, 5x	= 625
= 54
‹=› x=4.
Let log2( log5625)	= y.
Then, log 24= y
‹=› 2y= 4
y;2.
Answer A
Answer: (A) 2
Question: Solve x2 â€“ 3x â€“ 4 = 0.
(A) 1,4
(B) -1,4
(C) 2,3
(D) 2,4
(E) 2,6
Rationale: This one factors easily:
x2 â€“ 3x â€“ 4 = 0
(x + 1)(x â€“ 4) = 0
x + 1 = 0 or x â€“ 4 = 0
x = â€“1 or x = 4
The solution is x = â€“1, 4
ANSWER B
Answer: (B) -1,4
Question: What is the product of all the prime factors of 25?
(A) 25
(B) 30
(C) 35
(D) 40
(E) 45
Rationale: 25 , factors are 5,1. Now again prime Number is Only 5 , this time we would have 5*5=25
Answer : A
Answer: (A) 25
Question: Jackie has two solutions that are 2 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 12 percent solution will be required?
(A) 18
(B) 20
(C) 24
(D) 36
(E) 42
Rationale: let a=amount of 2% acid and b= amount of 12% acid.
Now, The equation translates to,
0.02a + .12b = .05(a+b)
but a+b= 60
therefore .02a + .12b = .05(60)
=> 2a + 12b = 300
but b=60-a
therefore
2a+ 12(60-a) = 300
=> 10a = 420
hence a = 42., B = 60-42 =18
Answer :A
Answer: (A) 18
Question: There are 6 people and 3 chairs. In how many different ways people can occupy the chairs?
(A) 90
(B) 120
(C) 150
(D) 100
(E) 140
Rationale: number of ways =6*5*4 = 120
Answer is B
Answer: (B) 120
Question: If (-12x)^(4x) = 12x^(15 - x) and x is an integer, what is the value of x ?
(A) 5
(B) 4
(C) 3
(D) 2
(E) -2
Rationale: Since x is an integer, (-12x)^(4x) is always positive.
So, 12x^4x = 12x^(15 - x)
4x = 15 - x
5x = 15
x = 3
Answer: C
Answer: (C) 3
Question: There are 100 wine glasses. I offered my servant to 3 paise for every broken glass to be delivered safely and forfeit 9 paisa for every glass broken at the end of day. He recieved Rs.2.40 .how many glass did he break.
a. 20 b. 73 c. 5 d. 8
(A) 22
(B) 281
(C) 29
(D) 28
(E) 191
Rationale: Answer:B
Answer: (B) 281
Question: In a single throw of a die, what is probability of getting a number greater than 4?
(A) 2/3
(B) 4/3
(C) 1/3
(D) 5/7
(E) 7/9
Rationale: E= {5,6}
n(E)=2
P(S)=n(E)/n(S)
=2/6
=1/3
Ans: C
Answer: (C) 1/3
Question: 4, 12, 48, 240, 1440, (...)
(A) 7620
(B) 6200
(C) 10020
(D) 10080
(E) 11000
Rationale: Go on multiplying the given numbers by 3, 4, 5, 6, 7
4 x 3 =12; 12 x 4 = 48 .....1440 x 7 = 10080
Answer is D.
Answer: (D) 10080
Question: A glass was filled with 15 ounces of water, and 0.05 ounce of the water evaporated each day during a 15-day period. What percent of the original amount of water evaporated during this period?
(A) 0.005%
(B) 0.05%
(C) 0.5%
(D) 5%
(E) 25%
Rationale: In 15 days 15*0.05=0.75 ounces of water evaporated, which is 0.75/15âˆ—100=5 of the original amount of water.
Answer: D.
Answer: (D) 5%
Question: A rectangular block 6cm by 12cm by 15cm is cut into an exact number of equal cubes. Find the least possible number of cubes?
(A) 20
(B) 25
(C) 40
(D) 50
(E) 35
Rationale: Volume of the block = 6*12*15 = 1080 cm^3
Side of the largest cube = H.C.F of 6,12,15 = 3cm
Volume of the cube = 3*3*3 = 27 cm^3
Number of cubes = 1080/27 = 40
Answer is C
Answer: (C) 40