mathewhe/aqua_rat huggingface dataset:
Question: If x and y are positive odd integers, then which of the following must also be an odd integer? I. x^(y+2) II. x(y+3) III. (y+1)^(x-1) + 1
(A) I only
(B) I,III only
(C) II only
(D) III only
(E) II,III only
Rationale: let x= 5, y= 3
I. 5^5 = > Odd
II. 5*6 = > even
III. 4^4 +1 = > Odd
Answer : B
Answer: (B) I,III only
Question: Bills' school is 10 miles from his home. He travels 4 miles from school to football practice, and then 2 miles to friend's house. If he is then x miles from home, what is the range of possible values for x?
(A) 2≤x≤10
(B) 4≤x≤10
(C) 4≤x≤12
(D) 4≤x≤16
(E) 6≤x≤16
Rationale: 1.If his football ground and his friend's house lie on the way to his house.
then the distance can be minimum .
10 -(4+2) = 4
2.If his football ground and his friends house lie in the opposite direction from the way to his house.
this will then give us the maximum distance.
10+(4+2) = 16
therefore , x will lie between 4 and 16
So, Correct answer will d) 4≤x≤164≤x≤16
ANSWER:D
Answer: (D) 4≤x≤16
Question: A man whose speed is 4 kmph in still water rows to a certain upstream point and back to the starting point in a river which flows at 1 kmph, find his average speed for the total journey?
(A) 5
(B) 4
(C) 4.5
(D) 3.75
(E) 3
Rationale: M = 4
S = 1
DS = 5
US = 3
AS = (2 * 5 * 3) /8 = 3.75
Answer: D
Answer: (D) 3.75
Question: If a shirts can be purchased for c rupees, how many shirts can be purchased for t rupees?
(A) at/c
(B) a/c
(C) ac/t
(D) t/(ac)
(E) c/(at)
Rationale: Ans = A
Answer: (A) at/c
Question: A certain sum of money is invested for one year at a certain rate of simple interest. If the rate of interest is 3% higher, then the invest earned will be 25% more than the interest earned earlier. What is the earlier rate of interest?
(A) 11
(B) 787
(C) 17
(D) 12
(E) 77
Rationale: If the interest earned is 25% more than the earlier interest then the rate of interest also should be 25% higher than the earlier rate.
Let the earlier rate of interest be x%.
Now it will be (x + 3)%
% increase = (x + 3) - x/x * 100 = 25
=> x = 12
Answer: D
Answer: (D) 12
Question: How many 4 digit numbers can be formed with the digits 0, 1, 2, 3, 4, 5, 6, 7 and 6?
(A) a. 220
(B) b. 249
(C) c. 432
(D) d. 216
(E) e. 288
Rationale: Taking Question with it's same language as given
To make number divisible by 5, the unit digit should be either 0 or 5 only
Case 1: If unit digit is fixed as zero
With two6s The choice to fill the remaining three digits = 3C2 x 5 = 15
With all remaining 3 digits different, The choice to fill the remaining three digits = 6 x 5 x 4= 120
Total Such cases = 120+15 = 135
Case 2: If unit digit is fixed as Five
With two6s and one0The choice to fill the remaining three digits = 2 [6605 or 6065]
With two6s and without0The choice to fill the remaining three digits = 3C2 x 4 = 12
With all remaining 3 digits different, and one0The choice to fill the remaining three digits = 2 (ways to place zero) x 5 x 4= 40
With all remaining 3 digits different, and without0The choice to fill the remaining three digits = 3 x 5 x 4= 60
Total Such cases = 2+12+40+60 = 114
Total numbers = 135+114 = 288
ANSWER OPTION D
Answer: (D) d. 216
Question: A basketball coach is making the starting lineup for his team of 10 players. There are 4 guards on the team and 6 post players. How many different groups of 5 players could he choose assuming he must pick 2 guards and 3 post players?
(A) 100
(B) 120
(C) 140
(D) 160
(E) 180
Rationale: (4c2)*(6c3)
[4!/(2!*2!)]*[6!/(3!*3!)]
6*20
120
B
Answer: (B) 120
Question: A, B and C invests Rs.2000, Rs.3000 and Rs.4000 in a business. After one year A removed his money; B and C continued the business for one more year. If the net profit after 2 years be Rs.3200, then A's share in the profit is?
(A) 222
(B) 287
(C) 277
(D) 400
(E) 281
Rationale: 2*12 : 3*12 : 4*24
1: 3: 4
1/8 * 3200 = 400
Answer: D
Answer: (D) 400
Question: A white paper 2 inches wide is placed around a rectangular black paper with dimensions 8 inches by 12 inches. What is the area of the white paper, in square inches?
(A) 96
(B) 196
(C) 128
(D) 144
(E) 168
Rationale: This question is an example of a 'punch out' question - we have to find the area of EVERYTHING, then 'punch out' the part that we don't want.
We're told that a white paper 2 inches wide is placed around a rectangular black paper with dimensions 8 inches by 12 inches. We're asked for the area of the frame, in square inches.
Area of a rectangle = (length)(width)
So the area of the black paper is... (8)(12) = 96
The white paper 'adds' 2 inches to the top, bottom, left and right 'sides' of the picture, so the area of EVERYTHING is...
(8+2+2)(12+2+2) = (12)(16) = 196
When we 'punch out' the area of the black paper, we'll be left with the area of the white paper:
192 - 96 = 96
Final Answer:
B
Answer: (B) 196
Question: A number exceeds by 25 from its 3/8 part. Then the number is?
(A) 38
(B) 29
(C) 27
(D) 40
(E) 91
Rationale: Explanation:
x â€“ 3/8 x = 25
x = 40
Answer: D
Answer: (D) 40
Question: As x Decreases from 169 to 166, which of the following must increase?
I. 2x - 5
II. 1 - 1/x
III. 1/(x^2 - x)
(A)  I only
(B)  III only
(C)  I and II
(D)  I and III
(E)  II and III
Rationale: I. 2x - 5 --> x decreases from 169 to 166 --> 2x decreases --> 2x - 5 decreases.
II. 1 - 1/x --> x decreases from 169 to 166 --> 1/x increases --> 1 -1/x decreases.
III. 1/(x^2 - x) --> x decreases from 169 to 166 --> x^2-x decreases --> 1/(x^2 - x) increases.
Answer: B.
Answer: (B)  III only
Question: If a is the sum of p consecutive positive integers and b is the sum of q consecutive positive integers. For which of the following values of p and q is it impossible that a = b?
(A) p = 2; q = 6
(B) p = 3; q = 6
(C) p = 10; q = 4
(D) p = 7; q = 9
(E) p = 10; q = 7
Rationale: I approached this in a different way, although may be longer but it's certainly more intuitive
It is impossible that a = b if one of them is necessarily even while the other is necessarily odd
for two consecutive integers the sum is necessarily odd
for six consecutive integers the sum is necessarily odd (sum of 3two consecutive integerswhich are all odd)
Thus A is incorrect.
The sum of 3 consecutive integers can be even or odd (an odd integer from the first 2 + an additional integer which can be even or odd). Thus B is incorrect. You can do a similar approach for D and E (it follows that the sum of a specified odd number of consecutive integers can be odd or even).
Leaving us with C to be the only not-wrong answer. To confirm, you can easily deduce that the sum of 4 consecutive integers (sum of 2 odd integers) is necessarily even while the sum of 10 consecutive integers (sum of 5 odd integers) is necessarily odd. Thus C is the right answer.
Answer: (C) p = 10; q = 4
Question: The least perfect square, which is divisible by each of 21, 36 and 66 is:
(A) 213444
(B) 214344
(C) 214434
(D) 231444
(E) 233444
Rationale: Explanation:
L.C.M. of 21, 36, 66 = 2772.
Now, 2772 = 2 x 2 x 3 x 3 x 7 x 11
To make it a perfect square, it must be multiplied by 7 x 11.
So, required number = 22 x 32 x 72 x 112 = 213444
ANSWER IS A
Answer: (A) 213444
Question: In a square box of side 16 centimeters small square boxes of side 4 centimeters are arranged. How many small square boxes fit into the large square box?
(A) 12
(B) 25
(C) 16
(D) 30
(E) 20
Rationale: The 4 centimeter side should be aligned to the 16 centimeter side ( 4 layer)
4 centimeter side should be aligned to the 16 centimeter side. (4 layer)
Maximum number of squares =4*4=16
Answer is C
Answer: (C) 16
Question: Two pipes A and B can fill a cistern in 20 and 30 minutes respectively, and a third pipe C can empty it in 40 minutes. How long will it take to fill the cistern if all the three are opened at the same time?
(A) 17 1/9
(B) 17 1/0
(C) 17 1/7
(D) 17 1/2
(E) 17 1/3
Rationale: 1/20 + 1/30 - 1/40 = 7/120
120/7 = 17 1/7
Answer: C
Answer: (C) 17 1/7
Question: The average temperature for Monday, Tuesday, Wednesday and Thursday was 48 degrees and for Tuesday, Wednesday, Thursday and Friday was 46 degrees. If the temperature on Monday was 42 degrees. Find the temperature on Friday?
(A) 99
(B) 277
(C) 27
(D) 34
(E) 77
Rationale: M + Tu + W + Th = 4 * 48 = 192
Tu + W + Th + F = 4 * 46 = 184
M = 42
Tu + W + Th = 192 -42 = 150
F = 184 – 150 = 34
Answer:D
Answer: (D) 34
Question: A four-character password consists of one letter of the alphabet and three different digits between 2 and 9, inclusive. The letter must appear as the second or third character of the password. How many different passwords are possible?
(A) 5,040
(B) 17,472
(C) 26,000
(D) 37,440
(E) 52,000
Rationale: 4 character password: DLDD
First digit can be chosen in 8 ways.
The letter can be chosen in 26 ways.
Next digit can be chosen in 7 ways.
Next digit can be chosen in 6 ways.
This gives us 8*26*7*6ways
Now, the letter can also be DDLD so there will be another 8*26*7*6 ways
Total = 8*26*7*6*2 = 17,472 ways B
Answer: (B) 17,472
Question: if remainder is 19 , quotient is 61 and dividend is 507 then what is divisor ?
(A) 8
(B) 18
(C) 10
(D) 12
(E) 14
Rationale: we know
dividend = divisor * quotient + remainder===> 507 = divisor * 61 + 19 =====> 488/61 = divisor ===> divisor = 8 Ans - A
Answer: (A) 8
Question: Train X crosses a stationary train Y in 60 seconds and a pole in 25 seconds with the same speed. The length of the train X is 300 m. What is the length of the stationary train Y?
(A) 187 m
(B) 420 m
(C) 197 m
(D) 167 m
(E) 186 m
Rationale: Let the length of the stationary train Y be LY
Given that length of train X, LX = 300 m
Let the speed of Train X be V.
Since the train X crosses train Y and a pole in 60 seconds and 25 seconds respectively.
=> 300/V = 25 ---> ( 1 )
(300 + LY) / V = 60 ---> ( 2 )
From (1) V = 300/25 = 12 m/sec.
From (2) (300 + LY)/12 = 60
=> 300 + LY = 60 (12) = 720
=> LY = 720 - 300 = 420 m
Length of the stationary train = 420 m
Answer: B
Answer: (B) 420 m
Question: What is the present worth of Rs. 176 due in 2 years at 5% simple interest per annum
(A) 110
(B) 120
(C) 150
(D) 160
(E) None of these
Rationale: Explanation:
Let the present worth be Rs.x
Then,S.I.= Rs.(176 - x)
= (x*5*2/100) = 176 - x
= 10x = 17600 - 100x
= 110x = 17600
x= 160
Answer:D
Answer: (D) 160
Question: if Juan takes 10 seconds to run y yards, how many seconds will it take him to run x yards at the same rate?
(A) 11x/y
(B) 10x/y
(C) x/11y
(D) 11/xy
(E) xy/11
Rationale: Answer is B.
The rate of running hards: 10 minutes per y hards.
Thus the time for running x hards = x hards * 10 minutes/y hards = 10x/y
Answer: (B) 10x/y
Question: The weight of four dogs is determined to be 25 pounds, 31 pounds, 43 pounds and 41 pounds respectively. The weight of a fifth dog is determined to be y pounds. If the average (arithmetic mean) weight of the first four dogs is the same as that of all five dogs what is the value of y?
(A) 31
(B) 33
(C) 35
(D) 37
(E) 39
Rationale: Total weight of the 4 dogs = (25+31+43+41) = 140
Avg = 140/4 = 35
Total weight of 5 dogs = 140+y or 4(35)+y
Average of 5 dogs as per Question = 35
Equation:
4(35) + y = 5 (35), or y = 35.
Choose C
Answer: (C) 35
Question: What is the slope of a line on a standard
xy-plane that passes through the point
(1, 3) and (4, –3)?
(A) -1
(B) 2
(C) -2
(D) 1/2
(E) -1/2
Rationale: Plug the values for the coordinates into the formula for the slope of a line:
Slope=y2-y1/x2-x1=-3-3/4-1=-6/3=-2
correct answer C)-2
Answer: (C) -2
Question: A can run a kilometer race in 4 1/2 min while B can run same race in 5 min. How many meters start can A give B in a kilometer race, so that the race mat end in a dead heat?
(A) 200 m
(B) 700 m
(C) 800 m
(D) 100 metre
(E) 400 m
Rationale: Explanation:
A can give B (5 min - 4 1/2 min) = 30 sec start.
The distance covered by B in 5 min = 1000 m.
Distance covered in 30 sec = (1000 * 30)/300 = 100 m.
A can give B 100m start.
Answer:D
Answer: (D) 100 metre
Question: Simplify: (4 – 5) – (13 – 18 + 2).
(A) 5
(B) 4
(C) -3
(D) 2
(E) -1
Rationale: (4 – 5) – (13 – 18 + 2).
= -1-(13+2-18).
= -1-(15-18).
= -1-(-3).
= -1+3.
= 2.
correct answer D
Answer: (D) 2
Question: I chose a number and divide it by 5. Then I subtracted 154 from the result and got 6. What was the number I chose?
(A) 600
(B) 700
(C) 800
(D) 900
(E) None
Rationale: Solution:
Let xx be the number I chose, then
x/5−154=6
x/5=160
x=800
Answer C
Answer: (C) 800
Question: A rower can row upstream at 7 km/hr and downstream at 13 km/hr. What is the rower's rate in still water?
(A) 8 km/hr
(B) 9 km/hr
(C) 10 km/hr
(D) 11 km/hr
(E) 12 km/hr
Rationale: The rate in still water is 1/2 * (13 + 7) = 10 km/hr
The answer is C.
Answer: (C) 10 km/hr
Question: A work as fast as B. If B can complete a work in 12days independently,the number of days in which A and B can together finish the work in?
(A) 2days
(B) 3days
(C) 4days
(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 = 1/6
B's 1day work = 1/12
A+B 1day work = 1/6 + 1/12 = 3/12 = 1/4
A and B can finish the work in 4days
Answer is C
Answer: (C) 4days
Question: The equation of line f is y = 4/3*x - 100. What is the smallest possible distance in the xy-plane from the point with coordinates (0, 0) to any point on line f?
(A) 48
(B) 50
(C) 60
(D) 75
(E) 100
Rationale: This can be solve in two steps and without any complex calculation.
Given : equation of line f as y=(4/3)x -100. So the line intercept the axes at (0,-100) and (75,0).
This can be considered a right angle triangle with right angle at (0,0) . So Base=100 , Height=75 and Hypotenuse =125 (By Pythagoras triplet)
So a perpendicular from the (0,0) to hypotenuse will be the answer.
Area of triangle= 0.5*100*75=0.5*125* x
=> x=60;
SO answer is 60=C
Answer: (C) 60
Question: seven children, Arya, Betsy, Chen, Daniel, Emily, and Franco, are to be seated in a single row of six chairs. If Betsy cannot sit next to Emily, how many different arrangements of the six children are possible?
(A) 240
(B) 480
(C) 540
(D) 720
(E) 840
Rationale: Since it is more time consuming and error prone to find ways Betsy and E not sitting together, It is better we find ways in which they will be together and then subtract from total ways..
total ways = 6!..
ways B and E will be sitting together..
take both B and E as one, then these two together with other 4 can sit in 5! ways ...
Also B and E can sit within themselves in 2! ways..
so the answer required = 6!-2*5!=540..
ans C
Answer: (C) 540
Question: There are 1000 doors that are of the open-close type. When a person opens the door he closes it and then opens the other. When the first person goes he opens-closes the doors in the multiples of 1 i.e., he opens and closes all the doors. when the second goes he opens and closes the doors 2, 4 6 8 respectively. Similarly when the third one goes he does this for 3 6 9 12 15th doors respectively. Find number of doors that are open at last.
(A) 29
(B) 31
(C) 32
(D) 24
(E) 21
Rationale: 31. only the perfect squares between 1 to 1k
ANSWER:B
Answer: (B) 31
Question: If the simple interest on a sum of money at nineteen percent per annum for two years is Rs.12000, compound interest on the same sum for the same period at the same rate of interest is
(A) 13,041.00
(B) 11,430.00
(C) 13,410.00
(D) 11,340.00
(E) 13,140.00
Rationale: S I for 2 years = 12000 ie for one year =6000
The compound interest for Rs.6000 for the second year = 6000*19/100 = 1140
The CI for two years 12000+1140 = 13,140.00
ANSWER:E
Answer: (E) 13,140.00
Question: How much time will take for an amount of Rs. 360 to yield Rs. 81 as interest at 4.5% per annum of simple interest?
(A) 8 years
(B) 4 years
(C) 3 years
(D) 9 years
(E) 5 years
Rationale: Time = (100 * 81) / (360 * 4.5)
= 5 years
Answer: E
Answer: (E) 5 years
Question: Two buses and a van were employed to transport a class of students on a field trip. 2/5 of the class boarded the first bus. 2/3 of the remaining students boarded the second bus, and the rest of the students boarded the van. When the second bus broke down, 1/2 of the students on the second bus boarded the first bus. What fraction of the class was on board the first bus?
(A) a) 1/2
(B) b) 2/3
(C) c) 11/15
(D) d) 6/10
(E) e) 4/5
Rationale: This is a pure ratio question (we aren't given any numbers for anything), so you can just choose any starting number you like, and use it to solve the problem. The best number to pick is almost always the product of all the denominators of your fractions, so here we could start with 30 students. Then we have:
• 2/5 of these, or 12 students, board the first bus
• there are 18 students left. 2/3 of these, or 12 students, board the second bus
• this bus breaks down, and 1/2 of the 12 students, or 6 students, board the first bus
• the first bus now contains 18 out of the original 30 students, so the answer is 18/30 = 6/10
Answer D
Answer: (D) d) 6/10
Question: Ravi purchased 20 dozens of toys at the rate of Rs. 380 per dozen. He sold each one of them at the rate of Rs. 33. What was his percentage profit?
(A) 23%
(B) 1.2%
(C) 5.6%
(D) 4.21%
(E) 12.2%
Rationale: D
C.P. of 1 toy = 380/12 = Rs. 31.6
S.P of 1 toy = Rs. 33
Profit = 1.33/31.25 * 100 = 4.21%
Answer is D
Answer: (D) 4.21%
Question: The ratio of the number of ladies to gents at a party was 1:2 but when 2 ladies and 2 gents left, the ratio became 1:3. How many people were at the party originally?
(A) 36
(B) 24
(C) 12
(D) 6
(E) 8
Rationale: x, 2x
(x-2):(2x-2) = 1:3
ANSWER C
Answer: (C) 12
Question: If (x-14)(x-3) < 0, which of the following must be true?
(A) x^2 + 5x + 6 < 0
(B) 14-x > 0
(C) 5 - x < 0
(D) x - 5 < 0
(E) 11 - x > 0
Rationale: (x-14)(x-3)<0 can be written as (14-x)(x-3)>0
So,to inequality hold true multiple of (14-x) and (x-3) must be positive and if I let both elements positive/negative then the range becomes 3<x<14
Answer Choice E matched which says 14-x>0 or x<14,which must be true (I started to look from E to A for making easy decision first)
Correct Answer B
Answer: (B) 14-x > 0
Question: A firm has 4 senior partners and 5 junior partners. How many different groups of 3 partners can be formed in which at least one member of the group is a senior partner. (2 groups are considered different if at least one group member is different)
(A) 66
(B) 74
(C) 82
(D) 90
(E) 98
Rationale: The total number of ways to form a group of 3 is 9C3 = 84
The number of groups without a senior partner is 5C3 = 10
The number of groups which include a senior partner is 84-10 = 74
The answer is B.
Answer: (B) 74
Question: 3251+587+369-?=3007
(A) 1250
(B) 1300
(C) 1375
(D) 1200
(E) None of them
Rationale: Let 4207-x=3007
then x=4207-3007
=1200
Answer is D
Answer: (D) 1200
Question: By mixing two brands of tea and selling the mixture at the rate of Rs. 177 per kg. a shopkeeper makes a profit of 18%. If to every 2 kg of one brand costing Rs. 200 per kg, 3 kg of the other brand is added, then how much per kg does the other brand cost?
(A) Rs. 110
(B) Rs. 120
(C) Rs. 140
(D) None of these
(E) Not determined
Rationale: Explanation:
Let the cost of the brand be Rs. X per kg.
C.P. of 5 kg = (2 * 200 + 3 * x) = Rs. (400 + 3x)
S.P of 5 kg = Rs. (5 * 177) = Rs. 885
[885 - (400 + 3x)]/(400 + 3x) * 100 = 18
24250 - 150x = 3600 + 27x
177x = 20650 => x = 116 2/3
So, cost of the other brand = Rs. 116.66.
Answer is D
Answer: (D) None of these
Question: A certain experimental mathematics program was tried out in 2 classes in each of 42 elementary schools and involved 55 teachers. Each of the classes had 1 teacher and each of the teachers taught at least 1, but not more than 3, of the classes. If the number of teachers who taught 3 classes is n, then the least and greatest possible values of n, respectively, are
(A) 0 and 13
(B) 0 and 14
(C) 1 and 10
(D) 1 and 9
(E) 2 and 8
Rationale: One may notice that greatest possible values differ in each answer choice in contrast to the least values, which repeat.
To find out the greatest value you should count the total classes (42*2=84), then subtract the total #of teachers since we know from the question that each teacher taught at least one class (84-55=29). Thus we get a number of the available extra-classes for teachers, and all that we need is just to count how many teachers could take 2 more classes, which is 29/2 = 14.5. So the greatest possible value of the # of teachers who had 3 classes is 14.
Only answer B has this option.
Answer: (B) 0 and 14
Question: If the number 617*324 is completely divisible by 3, then the smallest whole number in the place of * will be:
(A) 3
(B) 1
(C) 2
(D) 4
(E) 5
Rationale: Sum of digits = (6 + 1 + 7 + x + 3 + 2 + 4) = (23 + x), which must be divisible by 3.
x = 1.
B
Answer: (B) 1
Question: The compound interest on Rs.30,000 at 7% per annum is Rs.4347. The period (in years) is
(A) 2
(B) 2½
(C) 3
(D) 4
(E) 5
Rationale: Solution
Amount	=Rs(30000 + 4347)
= Rs.34347.
Let the time be n years.
Then, 30000(1+7/100)^n
= 34347.
=34347/3000
=11449/1000
=(107/100)^n
n= 2years.
Answer A
Answer: (A) 2
Question: A certain company had a total annual expenditure of 2.1∗10^7 on employee salaries last year. If the company employed 420 people, what was the average employee salary?
(A) $20,000
(B) $25,000
(C) $35,000
(D) $40,000
(E) $50,000
Rationale: Given: Total annual expenditure of 2.1∗10^7 on employee salaries
Total employees = 420
Observe that 420*5 = 2100
Therefore try to bring the numerator in terms of 2100
Average salary = (2100*10^4) /420 = 5*10^4 = 50,000
Option E
Answer: (E) $50,000
Question: Three years ago the average age of a class of six members was 19 years. A boy have been added, the average age of the class is the same today. What is the age of the boy?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: 6 * 22 = 132
7 * 19 = 133
`1
A
Answer: (A) 1
Question: The average weight of 8 person's increases by 2.5 kg when a new person comes in place of one of them weighing 75 kg. What might be the weight of the new person?
(A) 95 kg
(B) 90 kg
(C) 85 kg
(D) Data inadequate
(E) None of these
Rationale: A
95 kg
Total weight increased = (8 x 2.5) kg = 20 kg.
Weight of new person = (75 + 20) kg = 95 kg.
Answer: (A) 95 kg
Question: If y > 0, which of the following could be true?
I. y^3 > y^2
II. y^2 = y
III. y^2 > y^3
(A) I only
(B) III
(C) IIIII
(D) All of the above
(E) None of the above
Rationale: 1. y^3 > y^2 Well this is true for all y > +1 (but not for values 0 < y < 1)
2. y^2 = y This is true for only one positive number, 1
3. y^2 > y^3 Again this is true only for values of x such that 0 < y < 1
So the answer is D, since there exists at least one value of y which satisfies the equation/ in equation(s)
Answer: (D) All of the above
Question: The length of a room is 5.5 m and width is 3.75 m. Find the cost of paving the floor by slabs at the rate of Rs. 600 per sq. metre.
(A) Rs. 12375
(B) Rs. 15550
(C) Rs. 15600
(D) Rs. 16500
(E) None of these
Rationale: Solution
Area of the floor = (5.5 × 3.75) m2 = 20.625 m2
∴ Cost of paving = Rs. (600 × 20.625) = 12375. Answer A
Answer: (A) Rs. 12375
Question: Bhajan Singh purchased 120 reams of paper at Rs.80 per ream. He spent Rs.280 on transportation, paid octroi at the rate of 40 paise per ream and paid Rs.72 to the coolie. If he wants to have a gain of 8% , what must be the selling price per ream ?
(A) Rs.86
(B) Rs.87.48
(C) Rs.89
(D) Rs.90
(E) None
Rationale: Explanation:
C.P of 120 reams = Rs.(120×80+280+72+120×0.40)= Rs.10000.
C.P. of 1 ream = 10000/120= Rs.250/3
S.P. of 1 ream = Rs.108/100×250/3=Rs.90
Correct Option : D
Answer: (D) Rs.90
Question: 2.205 divided by 0.3 gives
(A) 7.35
(B) 6.25
(C) 8.15
(D) 6.95
(E) None of these
Rationale: Explanation :
2.205/0.3 = 22.05/3 = 7.35. Answer : Option A
Answer: (A) 7.35
Question: The average of 11 results is 52, if the average of first six results is 49 and that of the last six is 52. Find the sixth result?
(A) A)46
(B) B)34
(C) C)66
(D) D)76
(E) E)74
Rationale: 1 to 11 = 11 * 52 = 572
1 to 6 = 6 * 49 = 294
6 to 11 = 6 * 52 = 312
6th = 294 + 312 – 572 = 34
Answer:B
Answer: (B) B)34
Question: A started a business with an investment of Rs. 70000 and after 6 months B joined him investing Rs. 120000. If the profit at the end of a year is Rs. 52000, then the share of B is?
(A) 34500
(B) 24000
(C) 24098
(D) 23007
(E) 24098
Rationale: Ratio of investments of A and B is (70000 * 12) : (120000 * 6) = 7 : 6
Total profit = Rs. 52000
Share of B = 6/13 (52000)
= Rs. 24000
Answer:B
Answer: (B) 24000