mathewhe/aqua_rat huggingface dataset:
Question: How much time will it take for an amount of Rs. 400 to yield Rs. 60 as interest at 12% per annum of simple interest?
(A) 2.35 years
(B) 4.25 years
(C) 7 years
(D) 1.25 years
(E) 2 years
Rationale: Explanation:
Time = (100 x 60)/(400 x 12) years
= 1.25 years.
Answer: D
Answer: (D) 1.25 years
Question: For every positive even integer n, the function h(n) is defined to be the product of all the even integers from 2 to n, inclusive. If p is the smallest prime factor of h(100) +2, then p is?
(A) between 2 and 20
(B) between 10 and 20
(C) between 20 and 30
(D) between 30 and 40
(E) 2
Rationale: h(100)+2=2∗4∗6∗...∗100+2h(100)+2=2∗4∗6∗...∗100+2 . Notice that we can factor out 2 from h(100)+2, thus the smallest prime factor of h(100)+2 is 2: h(100)+2=2∗(4∗6∗...∗100+1)h(100)+2=2∗(4∗6∗...∗100+1).
Answer: E.
Answer: (E) 2
Question: If a particular is never chosen, in how many ways can a cricketbe chosen out of 15 players?
(A) 250
(B) 320
(C) 364
(D) 390
(E) 430
Rationale: A particular players is never chosen, it means that 11 players are selected out of 14 players.
=> Required number of ways = 14C11
= 14!/11!x3! = 364
C
Answer: (C) 364
Question: The operation is defined for all integers a and b by the equation ab = (a - 1)(b - 1). If x9 = 160, what is the value of x ?
(A) 18
(B) 15
(C) 17
(D) 19
(E) 21
Rationale: ab = (a - 1)(b - 1)
x9 = (x-1)(9-1) = 160 --> x-1=20 --> x=21
Answer: E
Answer: (E) 21
Question: If money is invested at r percent interest, compounded annually, the amount of investment will double in approximately 70/r years. If Pat's parents invested $ 5000 in a long term bond that pays 4 percent interest, compounded annually, what will be the approximate total amount of investment 36 years later, when Pat is ready for college?
(A) $20000
(B) $15000
(C) $12000
(D) $10000
(E) $9000
Rationale: Since investment doubles in 70/r years then for r=4 it'll double in 70/4=~18 years (we are not asked about the exact amount so such an approximation will do). Thus in 36 years investment will double twice and become ($5,000*2)*2=$20,000 (after 18 years investment will become $5,000*2=$10,000 and in another 18 years it'll become $10,000*2=$20,000).
Answer: A.
Answer: (A) $20000
Question: A train has a length of 150 meters . it is passing a man who is moving at 7 km/hr in the same direction of the train, in 3 seconds. Find out the speed of the train.
(A) 182 km/hr
(B) 180 km/hr
(C) 152 km/hr
(D) 169 km/hr
(E) 187 km/hr
Rationale: Explanation:
Length of the train, l = 150m
Speed of the man , Vm= 7 km/hr
Relative speed, Vr = total distance/time = (150/3) m/s = (150/3) × (18/5) = 180 km/hr
Relative Speed = Speed of train, Vt - Speed of man (As both are moving in the same direction)
=> 180 = Vt - 7
=> Vt = 180 + 7 = 187 km/hr
Answer: Option E
Answer: (E) 187 km/hr
Question: A man cycles at a rate of 4 kmph. He cycles for 45 minutes and then takes a 15 minute break. Determine the total time taken to cover 12 kms by him.
(A) 3 hours 48 minutes
(B) 3 hours 49 minutes
(C) 3 hours 25 minutes
(D) 3 hours 45 minutes
(E) 8 hours 45 minutes
Rationale: Explanation:
Speed of man = 4kmph
Time for which he cycled = 45 minutes.
Distance covered = speed*time
=> 4*45/60
=> 3km
Total time to cover 3 km = 45 minutes + 15 minutes = 60 minutes = 1 hour
Thus 3 km is covered in 1 hour
Required distance to be covered = 12 km
Beginning from origin point, he covers 9 km in 3 hours taking 15 minutes rest after every 45 minutes. To complete 12 kms he goes another 3 km in 45 minutes.
Thus, total time he takes is 3 hours 45 minutes.
ANSWER: D
Answer: (D) 3 hours 45 minutes
Question: The area of a square garden is A square feet and the perimeter is p feet. If a=2p+20, what is the perimeter of the garden, in feet?
(A) 28
(B) 36
(C) 40
(D) 56
(E) 64
Rationale: Perimeter of square = P
Side of square = P/4
Area of Square = (P^2)/16 =A
Given that A = 2P + 20
(P^2)/16 = 2P + 20
P^2 = 32P + 320
P^2 -32P -320 = 0
P^2 -40P +8P -320 = 0
P(P-40)+8(P+40) = 0
(P-40)(P+8) = 0
P = 40 or - 8
Discarding negative value , P = 40
Answer is C
Answer: (C) 40
Question: The inner circumference of a circular race track, 14 m wide, is 440 m. Find radius of the outer circle.
(A) 84
(B) 86
(C) 82
(D) 80
(E) None of them
Rationale: Let inner radius be r metres. Then, 2(22/7)r = 440 = r = (440 x (7/44))= 70 m.
Radius of outer circle = (70 + 14) m = 84 m.
Answer is A
Answer: (A) 84
Question: In how many different ways can the letters of the word 'LEADING' be arranged such that the vowels should always come together?
(A) 650
(B) 720
(C) 420
(D) 122
(E) 450
Rationale: Explanation:
The word 'LEADING' has 7 letters. It has the vowels 'E','A','I' in it and these 3 vowels should always come together. Hence these 3 vowels can be grouped and considered as a single letter. that is, LDNG(EAI).
Hence we can assume total letters as 5 and all these letters are different. Number of ways to arrange these letters
=5!=5Ã—4Ã—3Ã—2Ã—1=120=5!=5Ã—4Ã—3Ã—2Ã—1=120
In the 3 vowels (EAI), all the vowels are different. Number of ways to arrange these vowels among themselves
=3!=3Ã—2Ã—1=6=3!=3Ã—2Ã—1=6
Hence, required number of ways
=120Ã—6=720
ANSWER IS B
Answer: (B) 720
Question: If a and b is a positive integer, then 2^a + 2^(b + 1) =
(A) cannot be determined
(B) 2^(a + b)
(C) 2a+b
(D) 2^(a + 1+b)
(E) none
Rationale: If a and b is a positive integer, then 2^a + 2^(b + 1) =
2^a + 2^(b+ 1)
2^(1+a+b)
Answer:option D
Answer: (D) 2^(a + 1+b)
Question: By selling an article at Rs.600, a profit of 30% is made. Find its cost price?
(A) 400
(B) 267
(C) 287
(D) 480
(E) 811
Rationale: SP = 600
CP = (SP)*[100/(100+P)]
= 600 * [100/(100+50)]
= 600 * [100/150] = Rs.400
Answer: A
Answer: (A) 400
Question: In a certain sequence of 6 numbers, each number after the first is 1 more than the previous number. If the first number is −5, how many of the numbers in the sequence are positive?
(A) None
(B) One
(C) Two
(D) Three
(E) Four
Rationale: Non - Negative ( zero to positive infinity )
Solution to the question :
-5,-4,-3,-2,-1,0
Hence ans is 0 ..option A
Answer: (A) None
Question: P says to Q "I am thrice as old as you were when i was as old as you are". If the sum of their present age is 100 years, then the present age of Q?
(A) 35.5
(B) 36.5
(C) 37.5
(D) 38.5
(E) 39.5
Rationale: let the present age of q be x
the age of q years back(to be defined) is x/3
as the age of p will be x by then .
Years passed= x-x/3=2x/3(subtracting age of q)
so p acurrent age is x+2x/3
and q current age is x
adding them to 100
we get x =37.5
ANSWER:C
Answer: (C) 37.5
Question: Excluding stoppages, the average speed of a bus is 60 km/hr and including stoppages, the average speed of the bus is 15 km/hr. For how many minutes does the bus stop per hour?
(A) 22
(B) 88
(C) 77
(D) 20
(E) 45
Rationale: In 1hr, the bus covers 60 km without stoppages and 15 km with stoppages.
Stoppage time = time take to travel (60 - 15) km i.e 45 km at 60 km/hr.
stoppage time = 45/60 hrs = 45 min.
Answer: E
Answer: (E) 45
Question: The sum of the squares of two consecutive positive integers exceeds their product by 91. Find the integers?
(A) 6,5
(B) 5,8
(C) 2,3
(D) 9,8
(E) 9,10
Rationale: Explanation:
Let the two consecutive positive integers be x and x + 1
x2 + (x + 1)2 - x(x + 1) = 91
x2 + x - 90 = 0
(x + 10)(x - 9) = 0 => x = -10 or 9.
As x is positive x = 9
Hence the two consecutive positive integers are 9 and 10.
Answer E
Answer: (E) 9,10
Question: A student got 72% in math and 82% in history. To get an overall average of 75%, how much should the student get in the third subject?
(A) 69%
(B) 71%
(C) 73%
(D) 75%
(E) 77%
Rationale: 72 + 82 + x = 3*75
x = 71
The answer is B.
Answer: (B) 71%
Question: A 260 m long train running at the speed of 120 km/hr crosses another train running in opposite direction at the speed of 80 km/hr in 9 sec. What is the length of the other train?
(A) 230
(B) 240
(C) 267
(D) 256
(E) 298
Rationale: Relative speed = 120 + 80 = 200 km/hr.
= 200 * 5/18 = 500/9 m/sec.
Let the length of the other train be x m.
Then, (x + 260)/9 = 500/9 => x = 240.
Answer: B
Answer: (B) 240
Question: A technician makes a round-trip to and from a certain service center by the same route. If the technician completes the drive to the center and then completes 10 percent of the drive from the center, what percent of the round-trip has the technician completed?
(A) 5%
(B) 10%
(C) 25%
(D) 40%
(E) 55%
Rationale: Assuming that the technician makes a round-trip of 40 miles (each way is 20 miles), then the technician would have completed 20 miles + 2 miles (10% of the remaining 20 miles). Therefore, the total is 22 miles. 22miles/40 miles is 55% of the entire trip.
ANSWER:E
Answer: (E) 55%
Question: A train consists of 12 boggies, each boggy 15 metres long. The train crosses a telegraph post in 9 seconds. Due to some problem, two boggies were detached. The train now crosses a telegraph post in
(A) 18 sec
(B) 7.5 sec
(C) 15 sec
(D) 20 sec
(E) None of these
Rationale: Length of train = 12 Ã— 15 = 180 m.
Then, speed of train = 180â„9 = 20 m/s
Now, length of train = 10 Ã— 15 = 150m
âˆ´ Required time = 150â„20 = 7.5 sec.
Answer B
Answer: (B) 7.5 sec
Question: There are 2 kinds of staff members in a certain company, PART TIME AND FULL TIME. 25 percent of the total members are PART TIME members others are FULL TIME members. The work time of part time members is 3/5 of the full time members. Wage per hour is same. What is the ratio of total wage of part time members to total wage of all members.
(A) A.1/4
(B) B.1/5
(C) 1/6
(D) 1/7
(E) 1/8
Rationale: Just plug in
Assuming there are 100 employees
25% are PT = 25
75% FT = 75
Assume that the total number of hrs FT employees have to work = 10
PT will work = 3/5*10 = 6
since the wages are same , there will no affect on ratios
total number of hrs FT employees work = 75*10 = 750
PT = 25*6 = 150
now the ratio is 150/900 = 1/6 answer is C
Answer: (C) 1/6
Question: A cistern can be filled by a tap in 4 hours while it can be emptied by another tap in 9 hours. If both the taps are opened simultaneously, then after how much time will the cistern get filled?
(A) 7.3 hrs
(B) 7.9 hrs
(C) 7.1 hrs
(D) 7.2 hrs
(E) 7.8 hrs
Rationale: Net part filled in 1 hour
= (1/4 - 1/9) = 5/36
The cistern will be filled in 36/5 hrs i.e., 7.2 hrs.
Answer:D
Answer: (D) 7.2 hrs
Question: How long does a train 100 m long traveling at 72 kmph takes to cross a tunnel of 1400 m in length?
(A) 70 sec
(B) 60sec
(C) 82 sec
(D) 75 sec
(E) 62 sec
Rationale: D = 1400+100 = 1500 m
S = 72 * 5/18 = 20
T = 1500 * 1/20 = 75 sec
ANSWER:D
Answer: (D) 75 sec
Question: In a triangle ABC, AB = 6, BC = 8 and AC = 10. A perpendicular dropped from B, meets the side AC at D. A circle of radius BD (with centre B) is drawn. If the circle cuts AB and BC at P and Q respectively, then AP : QC is equal to
(A) 1:1
(B) 3:2
(C) 4:1
(D) 3:8
(E) 2:5
Rationale: Explanation :
Triangle ABC and Triangle ADB are similar,
AC/AB= BC/BD
10/6=8/r
r=24/5
BP=BQ=BD=r=24/5
AP=AB-r= 6-24/5 = 6/5
CQ=BC-r=8-24/5=16/5
AP:CQ= 6/16 = 3:8
Answer : D
Answer: (D) 3:8
Question: Maddie has 6 apples, if she give 3 to mike, how many does she have left?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: 6-3=3
C. 3
Answer: (C) 3
Question: Three pipes, A, B, & C are attached to a tank. A & B can fill it in 20 & 30 minutes respectively while C can empty it in 20 minutes. If A, B & C are kept open successively for 1.5 minute each, how soon will the tank be filled?
(A) 2 hours
(B) 4 hours
(C) 5 hours
(D) 2 hours 15 min
(E) 3 hours
Rationale: in three minute 1/20+1/30-1/20=2/60 = 1/30 part is filled
4.5 min--------1/30 parts
x min--------- 1 part(full)
x=135 min =2 hours 15 min
ANSWER:D
Answer: (D) 2 hours 15 min
Question: If the time is currently 1:30 pm, what time will it be in exactly 644 hours?
(A) 7:30 am
(B) 8:30 am
(C) 9:30 am
(D) 10:30 am
(E) 11:30 am
Rationale: 644 = 26(24) + 20/24
The time will be 20 hours later than 1:30 pm which is 9:30 am.
The answer is C.
Answer: (C) 9:30 am
Question: A no.when divided by 220 gives a remainder 43, what remainder will be obtainedby dividingthe same no.17?
(A) 5
(B) 6
(C) 9
(D) 11
(E) 15
Rationale: 221 + 43 = 264/17 = 9 (Remainder)
C
Answer: (C) 9
Question: A river 5m deep and 35 m wide is flowing at the rate of 2 kmph, calculate the amount of water that runs into the sea per minute?
(A) 5832.75
(B) 5839.75
(C) 5837.75
(D) 5222.75
(E) 5835.75
Rationale: Rate of water flow-2kmph--2000/60--33.33 m/min
depth of river--5m
width of river--35m
vol of water per min--33.33 *5*35---5832.75
Answer A
Answer: (A) 5832.75
Question: Dawson purchased a house for Rs.78000 and a site for Rs.12000 respectively, if he sold the house for Rs.79000 and the site for Rs.15000, then find the resultant percentage of gain?
(A) 4.43%
(B) 4.44%
(C) 4.45%
(D) 4.46%
(E) 4.47%
Rationale: Sol.
Total CP = 90000 & total SP = 94000 ⇒ gain = SP/CP = 94000/90000 = 1.0444 = 4.44%.
Answer B
Answer: (B) 4.44%
Question: Marketing executives for a certain chewing gum company projected a 25 percent increase in revenue this year over that of last year, but revenue this year actually decreased by 25%. What percent of the projected revenue was the actual revenue ?
(A) 53%
(B) 58%
(C) 60%
(D) 64%
(E) 75%
Rationale: Last year revenue = 100 (assume);
This year revenue = 75;
Projected revenue = 125.
Actual/Projected*100=75/125*100 = 60%.
Answer: C.
Answer: (C) 60%
Question: A batsman makes a score of 87 runs in the 17th inning and thus increases his average by 3. Find his average after 17th inning?
(A) 38
(B) 178
(C) 39
(D) 27
(E) 11
Rationale: Let the average after 7th inning = x
Then average after 16th inning = x - 3
16(x-3)+87 = 17x
x = 87 - 48 = 39
ANSWER:C
Answer: (C) 39
Question: The average of first five multiples of 6 is?
(A) 6
(B) 18
(C) 9
(D) 5
(E) 7
Rationale: Average = 6(1 + 2 + 3 + 4 + 5)/5
= 90/5
= 18.
Answer:B
Answer: (B) 18
Question: The 19th of September 1987 was a Saturday. If 1988 was a leap-year, what day of the week was the 25th of September 1990?
(A) Monday
(B) Tuesday
(C) Wednesday
(D) Thursday
(E) Friday
Rationale: 19th September
1987: Saturday
1988: Monday (due to leap year)
1989: Tuesday
1990: Wednesday
Hence 25th September was a Tuesday.
The answer is B.
Answer: (B) Tuesday
Question: The average marks obtained by 100 candidates in an examination is 50. Find how many candidates have passed in the examination, if the average marks of candidates who passed is 70 and that of failed candidates is 20.
(A) 90
(B) 75
(C) 60
(D) 58
(E) 65
Rationale: Explanation:
Let the number of students who passed the examination be X
Number of students failed = (100 - X)
Total marks of students who have passed = 70X
Total marks of 100 students = 100 * 50 = 5000
Total marks of students who have failed = 20(100 – X)
20(100 – X) + 70X = 5000
2000 – 20 X + 70X = 5000
50 X = 3000
X = 60
ANSWER:C
Answer: (C) 60
Question: What is the next number in this sequence:
1, 11, 21, 1211, 111221, 312211, 13112221, _________?
(A) 1113213211
(B) 1113213244
(C) 1113213233
(D) 1113213222
(E) 1113213255
Rationale: A
1113213211
The next number in sequence is 1113213211.
EXPLANATION-
The sequence goes like
You need to spell the no of digits.
e.g. take the no 1,11,21
Take 1. it spells as one 1 so we get the no 11,
take 11 we spell it as two ones‘ and we get 21
.so take the last given no in the sequence 13112221 so we spell it as one 1 one 3 two 1 three 2’s one 1.
So
the next no in sequence is 1113213211.
Answer: (A) 1113213211
Question: Divide Rs. 1500 among A, B and C so that A receives 1/3 as much as B and C together and B receives 2/3 as A and C together. A's share is?
(A) 297
(B) 268
(C) 375
(D) 367
(E) 363
Rationale: A+B+C = 1500
A = 1/3(B+C); B = 2/3(A+C)
A/(B+C) = 1/3
A = 1/4 * 1500 => 375
Answer: C
Answer: (C) 375
Question: which one is odd?
4377
3954
9865
8454
9831
(A) 4377
(B) 3954
(C) 9865
(D) 8454
(E) None
Rationale: Correct Answer : C
sum of digit of all other number is 21, but sum of digit of 9865 is 28
Answer: (C) 9865
Question: Two trains of equal length, running with the speeds of 60 and 40 kmph, take 55 seconds to cross each other while they are running in the same direction. What time will they take to cross each other if they are running in opposite directions?
(A) 10 sec
(B) 16 sec
(C) 13 sec
(D) 67 sec
(E) 11 sec
Rationale: RS = 60 -40 = 20 * 5/18 = 100/18
T = 55
D = 55 * 100/18 = 2750/9
RS = 60 + 40 = 100 * 5/18
T = 2750/9 * 18/500 = 11 sec
Answer: E
Answer: (E) 11 sec
Question: Mark bought a set of 6 flower pots of different sizes at a total cost of $8.25. Each pot cost 0.15 more than the next one below it in size. What was the cost, in dollars, of the largest pot?
(A) $1.75
(B) $1.85
(C) $2.00
(D) $2.15
(E) $2.30
Rationale: This question can be solved with a handful of different Algebra approaches (as has been shown in the various posts). Since the question asks for the price of the largest pot, and the answers are prices, we can TEST THE ANSWERS.
We're told that there are 6 pots and that each pot costs 25 cents MORE than the next. The total price of the pots is $8.25. We're asked for the price of the largest (most expensive) pot.
Since the total price is $8.25 (a 15-cent increment) and the the difference in sequential prices of the pots is 15 cents, the largest pot PROBABLY has a price that is a 15-cent increment. From the answer choices, I would then TEST Answer A first
IF....
The largest pot = $1.75
1
1.15
1.3
1.45
1.6
1.75
Total = $8.25
So this MUST be the answer.
A
Answer: (A) $1.75
Question: S is a set of 64 consecutive multiples of 4. If the smallest number in S is 68, then the greatest number in S is
(A) 198
(B) 297
(C) 320
(D) 402
(E) 405
Rationale: last term =first term +(total no. of terms-1)consecutive difference
S is a set of 64 consecutive multiples of 4. If the smallest number in S is 68, then the greatest number in S is
first term = 68 ; total terms =64 ; difference = 4
68+(63)4 = 320
Ans C
Answer: (C) 320
Question: Ajay buys 6 dozen eggs for Rs 10.80, and 12 eggs are found rotten and the rest are sold at 5 eggs per rupee. Find his percentage gain or loss.
(A) 11 1/9 % gain
(B) 11 1/9 % loss
(C) 9 1/11 % gain
(D) 9 1/11 % loss
(E) None of these
Rationale: 6 dozen egg cost = Rs 10.80
Since one dozen is rotten , he sells 5 dozen at 5 eggs per rupee.
Hence, S.P = Rs 12
Thus, Gain % = [(12 - 10.8) / 10.8] x 100 = 11 1/9%
ANSWER:A
Answer: (A) 11 1/9 % gain
Question: Given that there are 11 cricket players per team, how many ways can you select 3 cricket players from 4 teams if no more than one player can be selected from each team?
(A) 500
(B) 484
(C) 396
(D) 656
(E) 336
Rationale: First select 3 group out of available 4 groups. This cane be done in 4C3 ways = 4 ways
Now from each group we have to select one person only: 11C1 * 11C1= 11 * 11 = 121
Total ways: 121 * 4 = 484 ways.
Answer is B
Answer: (B) 484
Question: |-5| (|-20|-|4|)= ??
Source: Preparation Material MBA Center
(A) 64
(B) –60
(C) 44
(D) 75
(E) 100
Rationale: Absolute value will turn negatives into their positive 'equivalents', and will leave positives unchanged, so |-5| = 5, |-20| = 20, and |4| = 4. Getting rid of our absolute values we have:
|-5| (|-20|-|4|) = (5) (20 - 4) = 4*16 = 64
Answer: (A) 64
Question: A train crosses a platform of 150 m in 15 sec, same train crosses another platform of length 250 m in 20 sec. then find the length of the train?
(A) 150metres
(B) 157m
(C) 750m
(D) 850m
(E) 350m
Rationale: Length of the train be ‘X’
X + 150/15 = X + 250/20
4X + 600 = 3X + 750
X = 150m
Answer:A:
Answer: (A) 150metres
Question: The markup on a television set is 20 percent of the cost. The markup is what percent of the selling price?
(markup = selling price - cost)
(A) 8%
(B) 10%
(C) 12 1/2%
(D) 15%
(E) 16 2/3%
Rationale: SP = 1.2CP
markup/SP = 0.2CP/1.2CP = 1/6 * 100 = 50/3 = 16 2/3%
Answer - E
Answer: (E) 16 2/3%
Question: if (log5 5)(log4 9)(log3 2) is equal to
(A) -1
(B) 2
(C) 3
(D) 4
(E) 1
Rationale: =>1*log 9/log 4 * log 2/log 3
=>log 3^2/log 2^2 * log 2/log 3
=>2 log 3/2log 2*log 2/log 3=1
ANSWER A
Answer: (A) -1
Question: A company pays 12.5% dividend to its investors. If an investor buys Rs.40 shares and gets 25% on investment, at what price did the investor buy the shares?
(A) 20
(B) 66
(C) 18
(D) 19
(E) 01
Rationale: Explanation:
Dividend on 1 share = (12.5 * 40)/100 = Rs.5
Rs.25 is income on an investment of Rs.100
Rs.5 is income on an investment of Rs. (5 * 100)/25 = Rs.20
ANSWER: A
Answer: (A) 20
Question: If a and b are nonzero integers such that 6a = 15b, then each of the following must be true EXCEPT
(A) 0 < b/a < 1
(B) ab is positive.
(C) On the number line, b lies between 0 and a.
(D) The ratio of a to b is equivalent to 10/4.
(E) a – b is positive.
Rationale: This question can be solved by TESTing VALUES. Based on its wording, you would likely need to do 2 TESTs to get to the correct answer though.
We're told that a and b are NONZERO INTEGERS and that 6a=15b or 2a = 5b. We're told that each of the answer is always true EXCEPT for one of them...
Before we get to the actual work, it's important to note a few details:
1) We are NOT told that a and b are positive - we're just told that they're NONZERO - that's interesting - it means that we have to consider the possibility that they're both NEGATIVE...
2) 4 of the answers will always be true, while one of them will EITHER be sometimes true OR never true. We'll have to keep working until we find 1 answer that is not true (for whatever reason) - that will be the solution to this question.
Since 2A = 5B, I'm going to run 2 pairs of TESTs at the same time...
A = 5
B = 2
AND
A = -5
B = -2
Answer A: 0 < B/A < 1
2/5 and -2/-5 both = 2/5. Answer A appears true.
Answer B: AB is positive
(2)(5) and (-2)(-5) both = +10. Answer B appears true.
Answer C: B is between 0 and A on the number line
0....2....5
-5....-2....0
Answer C appears true.
Answer D: A/B = 10/4
5/2 = -5/-2
10/4 = 5/2
Answer D appears true.
Answer E: A - B is positive
5 - 2 = 3
-5 - (-2) = -3 *****This is NOT always true.
Final Answer:
E
Answer: (E) a – b is positive.
Question: Find the area of the quadrilateral of one of its diagonals is 30 cm and its off sets 9 cm and 6 cm?
(A) 188 cm2
(B) 150 cm2
(C) 168 cm2
(D) 198 cm2
(E) 225 cm2
Rationale: 1/2 * 30(9 + 6)
= 220 cm2
Answer: E
Answer: (E) 225 cm2
Question: The simple interest on a sum of money is 4/9 of the principal. Find the rate percentage and time, if both are numerically equal.
(A) 6 1/3 % and 6 2/3 years
(B) 6 2/3 % and 6 1/3 years
(C) 6 2/3 % and 6 2/3 years
(D) 6 1/3 % and 6 1/3 years
(E) 6 % and 6 2/3 years
Rationale: Let sum = Rs. x. Then, S.l. = Rs. 4x/9
Let rate = R% and time = R years.
Then, (x*R*R)/100=4x/9 or R^2 =400/9 or R = 20/3 = 6 2/3.
Rate = 6 2/3 % and
Time = 6 2/3 years = 6 years 8 months
Answer is C
Answer: (C) 6 2/3 % and 6 2/3 years
Question: A sum of 25 was paid for a work which A can do in 32 days, B in 20 days, B and C in 12 days and D in 24 days.How much did C receive if all the four work together ?
(A) 14⁄3
(B) 16⁄3
(C) 15⁄3
(D) 17⁄3
(E) None of these
Rationale: A's one day's work = 1⁄32
B's one day's work = 1⁄20
(B + C)'s one day's work = 1⁄12
∴ C's one day's work = 1⁄12 - 1⁄20 = 1⁄30
D's one day's work = 1⁄24
∴ (A + B + C + D)'s one day's work
1/32+1/20+1/30+1/24=75+120+80+100/2400
= 375⁄2400 = 15⁄96 = 5⁄32
∴ Out of 5⁄32 of work done
1⁄30 of the work is done by C.
⇒ Out of 25 paid for the work, C will receive
1/30 /5/32×25, i.e, 1⁄30 × 32⁄5 × 25, i.e, 16⁄3
Answer B
Answer: (B) 16⁄3
Question: If x^2+(1/x^2)=7, x^4+(1/x^4)=?
(A) 10
(B) 11
(C) 12
(D) 14
(E) 47
Rationale: -> x^4+(1/x^4)=(x^2)^2+(1/x^2)^2=(x^2+1/x^2)^2-2x^2(1/x^2)=7^2-2=47.
Thus, the answer is E.
Answer: (E) 47
Question: A man can row at 6 kmph in still water. If the velocity of current is 2 kmph and it takes him 2 hour to row to a place and come back, how far is the place?
(A) 5.33 km
(B) 6.33 km
(C) 5.63 km
(D) 7.33 km
(E) 5.93 km
Rationale: Speed in still water = 6 kmph
Speed of the current = 2 kmph
Speed downstream = (6+2) = 8 kmph
Speed upstream = (6-2) = 4 kmph
Let the required distance be x km
Total time taken = 2 hour
x/8 +x/4 =2
x+2x/8 =2
3x/8=2
3x=16
x=5.33 km
ANSWER:A
Answer: (A) 5.33 km