mathewhe/aqua_rat huggingface dataset:
Question: If (18^a) * 9^(3a – 1)= (2^2)(3^b) and a and b are positive integers, what is the value of a?
(A) 22
(B) 11
(C) 9
(D) 6
(E) 2
Rationale: (18^a) * 9^(3a – 1)= (2^2)(3^b)
= 2^a . 9^a . 9^(3a – 1) = (2^2)(3^b)
Just compare powers of 2 from both sides
Answer = 2 = E
Answer: (E) 2
Question: A tradesman by means of his false balance defrauds to the extent of 20%? in buying goods as well as by selling the goods. What percent does he gain on his outlay?
(A) 18%
(B) 23%
(C) 44%
(D) 65%
(E) 34%
Rationale: g%
= 20 + 20 + (20*20)/100
= 44%
Answer:C
Answer: (C) 44%
Question: The Natural Woman, a women's health food store, offers its own blends of trail mix. If the store uses 4 different ingredients, how many bins will it need to hold every possible blend, assuming that each blend must have at least four ingredients? (Also assume that each bin can hold one and only one blend.)
(A)  1
(B)  4
(C)  7
(D)  11
(E)  10
Rationale: We're told that there are 4 ingredients (we'll call them A, B, C and D); we're told that each 'mix' must include AT LEAST 4 ingredients...
4 ingredient blends:
ABCD
Total blends = 1
A
Answer: (A)  1
Question: Fox jeans regularly sell for $15 a pair and Pony jeans regularly sell for $20 a pair. During a sale these regular unit prices are discounted at different rates so that a total of $9 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 22 percent, what is the discount rate on Pony jeans?
(A) 9%
(B) 10%
(C) 11%
(D) 12%
(E) 18%
Rationale: x discount on Pony jeans, (0.22-x) discount on Fox jeans.
Set the equation: 3*15(0.22-x)+2*20x=9 --> x=0.18=18%
Answer: E.
Answer: (E) 18%
Question: The sum of first five prime numbers is?
(A) 12
(B) 23
(C) 24
(D) 28
(E) 30
Rationale: Required sum = (2 + 3 + 5 + 7 + 11) = 28.
Note: 1 is not a prime number.
Definition: A prime number (or a prime) is a natural number that has exactly two distinct natural number divisors: 1 and itself.
D
Answer: (D) 28
Question: Which of the following are/is prime?
I. 146
II. 147
III. 149
(A)  II only
(B)  III only
(C)  III
(D)  IIII
(E)  I, II,III
Rationale: 1) 143 = 13*11 so we know it is not prime quickly eliminate all options having 1 as a choice
which leaves us with 2 ) and 3) as possible answers
From here on we find 147 = 3* 49 so we eliminate 147 which leaves us with 149 as the only possible solution
E
Answer: (E)  I, II,III
Question: What distance will be covered by a bus moving at 108 kmph in 30 seconds?
(A) 287
(B) 600
(C) 289
(D) 276
(E) 900
Rationale: 108 kmph = 108 * 5/18
= 30 mps
D = Speed * time = 30 * 30
= 900 m.
Answer:E
Answer: (E) 900
Question: If x^2 + y^2 = 18 and xy = 3, then (x − y)^2 =
(A) 8
(B) 11
(C) 14
(D) 12
(E) 20
Rationale: but you cannot take xy+ 3 to mean xy=-3..
only if xy+3=0, it will mean xy=-3..
rest your solution is perfect and you will get your correct answer as 18-2*3=12..
Answer D
Answer: (D) 12
Question: How many words can be formed by using all letters of the word ‘ILLINOIS’ ?
(A) 40230
(B) 40320
(C) 30420
(D) 20340
(E) 40240
Rationale: Solution
The word ILLINOIS contains 8 different letters.
Required number of words = 8P8 = 8 ! = (8 x 7 x 6 x 5 x 4 x 3 x 2 x 1) = 40320
Answer B
Answer: (B) 40320
Question: The maximum numbers of students among them 561 toys and 510 pencils can be distributed in such a way that each student gets the same number of toys and same number of pencils is
(A) 91
(B) 910
(C) 1001
(D) 51
(E) None
Rationale: olution
Required number of students.
= H.C.F of 561 and 510.
â€¹=â€º 51.
Answer D
Answer: (D) 51
Question: On a certain road 10% of the motorists exceed the posted speed limit and receive speeding tickets, but 15% of the motorists who exceed the posted speed limit do not receive speeding tickets. What percent of the motorists on the road exceed the posted speed limit?
(A) 11.7%
(B) 12.5%
(C) 15%
(D) 22%
(E) 30%
Rationale: Answer is A.
This question is in the OG and thus well explained by ets.
those who exceed : X
so X = 10%+0,15X
id est X = 11,7%
Answer: (A) 11.7%
Question: Find the odd man out.
6, 9, 15, 21, 24, 28, 30
(A) 28
(B) 27
(C) 26
(D) 98
(E) 12
Rationale: Explanation:
Each of the numbers except 28, is a multiple of 3.
Answer: A) 28
Answer: (A) 28
Question: How many numbers between 0 and 1470 have a prime tens digit and a prime units digit?
(A) 228
(B) 236
(C) 244
(D) 252
(E) 260
Rationale: From 1-9 there are 4 prime numbers {2, 3, 5, 7}. The 10s and 1s of the number must be made with these numbers. The total number of combinations is 4*4 = 16. Thus every set of 100 consecutive positive integers has 16 such numbers.
From 0 to 1400, there 16*14 = 224 such numbers.
From 1401 to 1470, the 10s units can only use 3 numbers {2, 3, 5}. 3*4 =12.
The total number is then 224+12 = 236
The answer is B.
Answer: (B) 236
Question: A box contains 20 machine parts, 5 of them being standard. A worker takes out 3 parts at random. Find the probability that at least 1 of 3 turns out to be standard.
(A) 137/228
(B) 13/228
(C) 91/228
(D) 41/228
(E) None of these
Rationale: Explanation :
Let, E ≡ at least 1 of the 3 parts turns out to be standard.
P(E) = 1 - P(none is standard)
= 1 - (15C3 / 20C3 ).
= 1 - (15 x 14 x 13) / ( 20 x 19 x 18).
= 137/228.
Answer : A
Answer: (A) 137/228
Question: In a class of 42 students, 2 students did not borrow any books from the library, 12 students each borrowed 1 book, 10 students each borrowed 2 books, and the rest borrowed at least 3 books. If the average number of books per student was 2, what is the maximum number of books any single student could have borrowed?
(A) 1
(B) 5
(C) 8
(D) 13
(E) 15
Rationale: Total # of students = 42
Avg # of books per student = 2
Total # of books = 42*2 = 84
# of student borrowed at least 3 books = 42-2-12-10 =18
# of books borrowed by above 18 students =84-(12*1)+(10*2) = 52
Considering that 17 out of above 18 students borrowed only 3 books, # of books borrowed = 17*3 = 51
So maximum # of books borrowed by any single student = 52-51 = 1
Option A
Answer: (A) 1
Question: In 19 years time the combined ages of my three brothers will be 94. What will it be in nine years time?
(A) 45
(B) 62
(C) 82
(D) 97
(E) 56
Rationale: C
82
Combined age in 9 years time will 94 – (3 x (13 – 9))
94 – 12 = 82.
Answer: (C) 82
Question: The population of City A for each of three years is shown in the table above. If the population grew by m percent from 1970 to 1980 and n percent from 1980 to 1990, then m exceeds n by how much?
(A) 37.5
(B) 20
(C) 17.5
(D) 15
(E) 12.5
Rationale: 70 - 80
m = (55-40)/40 = 3/8
80 - 90
n = (66-55)/55 = 1/5
m - n
3/8 - 1/5 = 7/40 = 17.5%
ANSWER:C
Answer: (C) 17.5
Question: Two pipes A and B can fill a tank in 12 and 24 minutes respectively. If both the pipes are used together, then how long will it take to fill the tank?
(A) 6 minutes
(B) 8 minutes
(C) 5 minutes
(D) 2 minutes
(E) 7 minuteS
Rationale: Required time =12*24/12+12=12*24/36
=24/3=8 minutes
ANSWER:B
Answer: (B) 8 minutes
Question: A group of 55 adults and 70 children go for trekking. If there is meal for either 70 adults or 90 children and if 7 adults have their meal, find the total number of children that can be catered with the remaining food.
(A) 33
(B) 54
(C) 81
(D) 17
(E) 01
Rationale: Explanation:
As there is meal for 70 adults and 7 have their meal, the meal left can be catered to 63 adults.
Now, 70 adults = 90 children
7 adults = 9 children
Therefore, 63 adults = 81 children
Hence, the meal can be catered to 81 children.
ANSWER: C
Answer: (C) 81
Question: The length of a rectangular landscape is 12 times its breadth. There is a playground in it whose area is 1200 square mtr & which is 1/4rd of the total landscape. What is the length of the landscape?
(A) 90
(B) 120
(C) 240
(D) 180
(E) 110
Rationale: Sol. x *12x = 4 * 1200
x = 20
Length = 12 * 20 = 240
C
Answer: (C) 240
Question: The compound ratio of 2:3, 3:2 and 4:5?
(A) 1:9
(B) 1:7
(C) 1:2
(D) 4:5
(E) 1:4
Rationale: 2/3 * 3/2 * 4/5
= 4/5
=4:5
Answer: D
Answer: (D) 4:5
Question: A person lent a certain sum of money at 6% per annum at simple interest and in 8 years the interest amounted to $520 less than the sum lent. What was the sum lent?
(A) 800
(B) 1000
(C) 1200
(D) 1400
(E) 1600
Rationale: P - 520 = (P*6*8)/100
P = 1000
The answer is B.
Answer: (B) 1000
Question: After an ice began to melt out from the freezer, in the first hour lost 3/4, in the second hour lost 3/4 of its remaining. If after two hours, the volume is 0.4 cubic inches, what is the original volume of the cubic ice, in cubic inches?
(A) 2.5
(B) 3.0
(C) 4.0
(D) 6.4
(E) 8.0
Rationale: Let initial volume of ice be = x
Ice Remaining after 1 hour = x - 0.75x = 0.25x
Ice Remaining after 2 hour = (1/4)x - (3/4 * 1/4 * x) = (1/16)x
(1/16)x = 0.4
x = 6.4
Alternate solution: Try to backsolve.
Initial volume = 6.4
After one hour --> (1/4)6.4 = 1.6
After two hours --> (1/4)1.6 = 0.4
Answer: D
Answer: (D) 6.4
Question: Lucy deposited $62500 in an investment fund that provided 24 percent annual return compounded half yearly.If she made no other transactions with the fund, in how much time, in months, did her investment earn a total interest of $10400?
(A) 0.5
(B) 2
(C) 12
(D) 6
(E) 6.1
Rationale: A = P + I = 62500 + 10400 = 72900
72900 = 62500(1 + 24/2*100)^(2t)
(676/625) = (112/100)^(2t)
(27/25)^2 = (27/25)^2t
t = 1yrs = 12 months
Answer: C
Answer: (C) 12
Question: How much time will a train of length 280 m moving at a speed of 72 kmph take to cross another train of length 360 m, moving at 36 kmph in the same direction?
(A) 50
(B) 99
(C) 64
(D) 76
(E) 12
Rationale: The distance to be covered = Sum of their lengths = 280 + 360 = 640 m.
Relative speed = 72 -36 = 36 kmph = 36 * 5/18 = 10 mps.
Time required = d/s = 640/10 = 64 sec.
Answer:C
Answer: (C) 64
Question: If José reads at a constant rate of 2 pages every 5 minutes, how many seconds will it take him to read N pages?
(A) 2/5*N
(B) 2N
(C) 5/2*N
(D) 24N
(E) 150N
Rationale: Jose would read 1 page in 5/2 min
Jose would read N page in (5/2)*N min i.e. (5/2)*N*60 Seconds = 150N Seconds.
ANSWER:E
Answer: (E) 150N
Question: A, B and C invested Rs.6300, Rs.4200 and Rs.10500 respectively, in a partnership business. Find the share of A in profit of Rs.12100 after a year?
(A) 3630
(B) 4000
(C) 4200
(D) 4400
(E) 4500
Rationale: Explanation:
6300:4200:10500
3:2:5
3/10 * 12100 = 3630
A)
Answer: (A) 3630
Question: 862.68 âˆ’ 4.5 + 108.98 = ? âˆ’ 2132.54
(A) 6078.58
(B) 5225.9
(C) 6258.58
(D) 6088.58
(E) None
Rationale: Option 'D'
Answer: (D) 6088.58
Question: Mrs. Rodger got a weekly raise of $165. If she gets paid every other week, write an integer describing how the raise will affect her paycheck.
(A) $204
(B) $231
(C) $156
(D) $165
(E) $200
Rationale: Let the 1st paycheck be x (integer).
Mrs. Rodger got a weekly raise of $ 165.
So after completing the 1st week she will get $ (x+165).
Similarly after completing the 2nd week she will get $ (x + 165) + $ 165.
= $ (x + 165 + 165)
= $ (x + 330)
So in this way end of every week her salary will increase by $ 165.
D
Answer: (D) $165
Question: Mr. Thomas invested an amount of Rs. 13,900 divided in two different schemes A and B at the simple interest rate of 14% p.a. and 11% p.a. respectively. If the total amount of simple interest earned in 2 years be Rs. 3508, what was the amount invested in Scheme B?
(A) 6400
(B) 6500
(C) 7200
(D) 7500
(E) 7800
Rationale: Explanation :
Let the investment in scheme A be Rs.x
and the investment in scheme B be Rs.(13900 - x)
We know that SI = PRT/100
Simple Interest for Rs.x in 2 years at 14% p.a. = x×14×2/100=28x/100
Simple Interest for Rs.(13900 - x) in 2 years at 11% p.a. = (13900−x)×11×2/100
=22(13900−x)/100
Total interest = Rs.3508
28x/100+22(13900−x)/100=3508
28x+305800−22x=350800
6x=45000
x=45000/6=7500
Investment in scheme B = 13900 - 7500 = Rs.6400
Answer : Option A
Answer: (A) 6400
Question: The average age of 15 men is increased by years when two of them whose ages are 21 years and 23 years are replaced by two new men. The average age of the two new men is
(A) 22
(B) 37
(C) 99
(D) 38
(E) 27
Rationale: total age increased = (15 * 2) years = 30 years.
Sum of ages of two new men = (21 + 23 + 30) years = 74 years
Average age of two new men = (74/2) years = 37 years.
Answer: B
Answer: (B) 37
Question: A company pays project contractors a rate ofadollars for the first hour andbdollars for each additional hour after the first, where a > b.
In a given month, a contractor worked on two different projects that lasted 4 and 8 hours, respectively. The company has the option to pay for each project individually or for all the projects at the end of the month. Which arrangement would be cheaper for the company and how much would the company save?
(A) Per month, with savings of $(3a + 3b)
(B) Per month, with savings of $(3a - 3b)
(C) The two options would cost an equal amount.
(D) Per project, with savings of $(3a + 3b)
(E) Per project, with savings of $(3a - 3b)
Rationale: Per Project, company will pay as follows:
For 4 hours work = a+3b
For 8 hours work = a+7b
Total = 2a+10b
Per Month, company will pay for 12 hours work = a+11b
Total per contract - total per month
4a+8b - (a+11b)
3a-3b
Since a>b Amount 4a+8b(per contract amount) > a+11b (per project amount) by 3a-3b.
Hence per month payment will be cheaper by 3a-3b .
OA B
Answer: (B) Per month, with savings of $(3a - 3b)
Question: It takes six minutes to load a certain video on a cellphone, and fifteen seconds to load that same video on a laptop. If the two devices were connected so that they operated in concert at their respective rates, how many seconds would it take them to load the video?
(A) 13.8
(B) 14.1
(C) 14.4
(D) 14.6
(E) 14.8
Rationale: The laptop can load the video at a rate of 1/15 of the video per second.
The phone can load the video at a rate of 1/(60*6) = 1/360 of the video per second.
The combined rate is 1/15 + 1/360 = 25/360 of the video per second.
The time required to load the video is 360/25 = 14.4 seconds.
The answer is C.
Answer: (C) 14.4
Question: In a lake, there is a patch of lily pads. Every day, the patch doubles in size. If it takes 48 days for the patch to cover the entire lake, how long would it take for the patch to cover half of the lake?
(A) 45
(B) 56
(C) 47
(D) 57
(E) 49
Rationale: Explanation: With all the talk of doubling and halves, your brain jumps to the conclusion that to solve the problem of when the lily patch covers half the lake, all you have to do is divide the number of days it took to fill the lake (48) in half. It's understandable but wrong.
The problem says that the patch DOUBLES in size every day, which means that on any day, the lily patch was half the size the day before. So if the patch reaches the entire size of the lake on the 48th day, it means the lily pad was half the size of the lake on day 47.
correct answer is C)47
Answer: (C) 47
Question: The sum of two numbers is 16 and the sum of their squares is 113. Find the
numbers.
(A) 1 and 2
(B) 4 and 5
(C) 7 and 8
(D) 2 and 3
(E) 6 and 7
Rationale: Let the numbers be x and (15 - x).
Then, x2 + (15 - x)2 = 113 =>	x2 + 225 + X2 - 30x = 113
=> 2x2 - 30x + 112 = 0 => x2 - 15x + 56 = 0
=> (x - 7) (x - 8) = 0 => x = 7 or x = 8.
So, the numbers are 7 and 8.
Answer is C
Answer: (C) 7 and 8
Question: The area of a circular field is 17.56 hectares. Find the cost of fencing it at the rate of Rs. 6 per metre approximately
(A) 4457
(B) 4567
(C) 4235
(D) 4547
(E) 8915
Rationale: Explanation:
Area = (17.56 x 10000) m2= 175600 m2.
ΠR2 = 175600 ⇔ (R)2 = (175600 x (7/22)) ⇔ R = 236.37 m.
Circumference = 2ΠR = (2 x (22/7) x 236.37) m =1485.78 m.
Cost of fencing = Rs. (1485.78 x 6) = Rs. 8915.
Answer: Option E
Answer: (E) 8915
Question: Kamal started a business investing Rs. 9000. After five months, Sameer joined with a capital of Rs. 8000. If at the end of the year, they earn a profit of Rs. 7380, then what will be the share of Sameer in the profit?
(A) s.2323
(B) s.2380
(C) s.2329
(D) s.2329
(E) s.2520
Rationale: Kamal : Sameer = (9000 * 12) : (8000 * 7)
= 108:56 = 27:14
Sameer's share = 7380 * 14/41
= Rs.2520.
Answer: E
Answer: (E) s.2520
Question: In how many ways can the letters of the word 'LEADER' be arranged?
(A) 90
(B) 180
(C) 360
(D) 60
(E) 240
Rationale: The word 'LEADER' contains 6 letters, namely 1L, 2E, 1A, 1D and 1R.
Therefore, Required number of ways = 6!/(1!)(2!)(1!)(1!)(1!)= 360.
Answer is C.
Answer: (C) 360
Question: If x and y are integers and x=50y + 49, which of the following must be odd?
(A) xy
(B) x + y
(C) x + 4y
(D) 3x-1
(E) 3x+1
Rationale: x = 50y + 69, since y is integer, 50y will always be even hence 50y + 69 will be odd hence x = odd
you don't know whether Y is even or odd, so you need to try.
A: odd * even = even ; odd*odd= odd ->not true
B: odd + odd = even ; odd+even = odd -> not true
C: odd + 4*odd = odd ; odd + 2*even = odd -> TRUE, stop here.
D&E -- EVEN
Answer C
Answer: (C) x + 4y
Question: John and David work at a hospital with 4 other workers. For an internal review, 2 of the 4 workers will be randomly chosen to be interviewed. What is the probability that John and David will both be chosen?
(A) 1/14
(B) 1/20
(C) 1/13
(D) 1/7
(E) 1/6
Rationale: Probability that John and David will both be chosen out of 8 workers
= (2/4)*(1/3)
= 1/6
Answer E
Answer: (E) 1/6
Question: In a test, sixty percent students passed in Maths and 65% in History, 40% passed in both of these subjects. If 90 students failed in maths and history both, then what is the total number of students?
(A) 600
(B) 650
(C) 700
(D) 750
(E) None of these
Rationale: Explanation :
Solution: let the total number of students be x.
Number passed in one or both is given by : n( A U B) = n(A)+n(B) -n( A ^ B).
= 60% of x+65% of x-40% of x
= (60/100 * x + 65/100 * x - 40/100 * x)
= 85x/100 = 17x/20.
Failed in both = (x - 17x/20) = 3x/20.
.'. 3x/20 =90
x = 90*20/3 = 600.
Answer : A
Answer: (A) 600
Question: Gold is 19 times as heavy as water and copper is 9 times as heavy as water. In what ratio should these be mixed to get an alloy 16 times as heavy as water?
(A) 1:2
(B) 7:3
(C) 4:1
(D) 5:2
(E) 6:5
Rationale: G = 19W
C = 9W
Let 1gm of gold mixed with x gm of copper to get 1+x gm of the alloy
1gm gold + x gm copper = x+1 gm of alloy
19W+9Wx = x+1 * 16W
19+9x = 16(x+1)
x = 3/7
Ratio of gold with copper = 1:3/7 = 7:3
Answer is B
Answer: (B) 7:3
Question: How many possible ways can 5 girls (Rebecca, Kate, Ashley) go on a date with 5 boys (Peter, Kyle, Sam)?
(A)  3
(B)  120
(C)  5
(D)  6
(E)  8
Rationale: Any one girl can go with 5 boys.
2nd girl can go with remaining 4 boys
3nd girl can go with remaining 3 boys
4nd girl can go with remaining 2 boys. 5nd girl can go with remaining 1 boys. 5! i.e 120 (B) is the answer
Answer: (B)  120
Question: The cost price of a radio is Rs.1500 and it was sold for Rs.1230, find the loss %?
(A) 18%
(B) 19%
(C) 28%
(D) 68%
(E) 48%
Rationale: 1500 ---- 270
100 ---- ? => 18%
Answer: A
Answer: (A) 18%
Question: In an examination a pupil's average marks were 63 per paper. If he had obtained 20 more marks for his Geography paper and 2 more marks for his History paper, his average per paper would have been 65. How many papers were there in the examination?
(A) 8
(B) 9
(C) 10
(D) 11
(E) 12
Rationale: Let the number of papers be x. Then,
63x + 20 + 2 = 65x
= 2x = 22
= x = 11.
ANSWER:D
Answer: (D) 11
Question: A trader sells 60 meters of cloth for Rs. 8400 at the profit of Rs. 12 per metre of cloth. What is the cost price of one metre of cloth?
(A) 128
(B) 140
(C) 123
(D) 110
(E) 150
Rationale: SP of 1m of cloth = 8400/60 = Rs. 140
CP of 1m of cloth = SP of 1m of cloth - profit on 1m of cloth
= Rs. 140 - Rs. 12 = Rs. 128.
Answer: A
Answer: (A) 128
Question: A person covers a distance in 6 minutes. If runs at a speed of 12 km per hour on an average. Find the speed at which he must run to reduce the time of journey to 5 minutes.
(A) 18 m/s
(B) 4 m/s
(C) 15 m/s
(D) 10 m/s
(E) 5 m/s
Rationale: Explanation:
T = 6 m
Spees = 12 kmph
= 12 x 5/18 = 10/3 m/s
Let new speed be "x"
6 x (10/3) = 5x
x = 4 m/s
Answer: Option B
Answer: (B) 4 m/s
Question: A train which has 500 m long, is running 100 kmph. In what time will it cross a person moving at 10 kmph in same direction ?
(A) 20 sec
(B) 25 sec
(C) 30 sec
(D) 35 sec
(E) 40 sec
Rationale: Time taken to cross a moving person = length of train/ relative speed
Time taken = 500/((100-10) (5/18) = 500/ 90*(5/18) = 500/25= 20 sec
Answer: A
Answer: (A) 20 sec
Question: The ratio of the volumes of two cubes is 125 : 216. What is the ratio of their total surface areas?
(A) 25:36
(B) 12:25
(C) 25:46
(D) 18:22
(E) 12:24
Rationale: Ratio of the sides = Â³âˆš125 : Â³âˆš216
= 5 : 6
Ratio of surface areas =25:36
Answer: A
Answer: (A) 25:36
Question: Calculate the cost of b bags of grains given that the cost of c bags of said grain is d rupees?
(A) Rs.(b/d*c)
(B) Rs.(d*c)
(C) Rs.(d/c)
(D) Rs.(bd/c)
(E) Rs.(b*c)
Rationale: Cost of c bags = Rs. d.
Cost of 1 bag = Rs.	d/c
Cost of b bags = Rs.(d/c)* b= Rs.(bd/c)
Answer is D.
Answer: (D) Rs.(bd/c)
Question: A person got Rs.48 more when he invested a certain sum at compound interest instead of simple interest for two years at 8% p.a. Find the sum?
(A) Rs.7500
(B) Rs.7000
(C) Rs.8000
(D) Rs.6500
(E) None of these
Rationale: P = (d * 1002) / R2
=> (48 * 100 * 100) / 8 * 8 = Rs.7500
ANSWER:A
Answer: (A) Rs.7500
Question: If n is a positive integer, then n(n+1)(n+2) is even without any condition
(A) divisible by 3 only when n is odd
(B) divisible by 4 whenever n is even
(C) odd whenever n is odd
(D) even only when n is odd
(E) even only when n is even
Rationale: n*(n+1)*(n+2)= +ve even integer divisible by 4 ( e.g 6,7&8)
B
Answer: (B) divisible by 4 whenever n is even
Question: In a class everyone will play at least one sport viz table tennis, cricket and badminton. 73
students play table tennis, 79 play badminton, 75 play cricket and 25 students play both table
tennis and badminton, 28 play both table tennis and cricket 30 play. Badminton and cricket and
16 students play all the sports. How many students play only cricket ?
(A) 36
(B) 38
(C) 39
(D) 47
(E) 41
Rationale: PERSONS PLAY CRICKET ONLY=N(C)-N(B∩C)+N(C∩T)-2(N(B∩T∩C))
=75-30+28-(2*16)
=41
ANSWER:E
Answer: (E) 41
Question: A car covers a distance of 200 metres in 1 minute whereas a bus covers a distance of 100kms in 50minutes. The ratio of their speeds is?
(A) ratio 2:3
(B) ratio 1:5
(C) ratio 1:10
(D) ratio 9:13
(E) ratio 7:15
Rationale: Ratio of speeds = (200/60) 18/5 : 60*100/50 = 12:120 = 1:10
Answer is C
Answer: (C) ratio 1:10
Question: If 4 (A’s capital) = 6 (B’s capital) = 10 (C’s capital), then out of a profit of Rs.4650, C will receive:
(A) Rs.2250
(B) Rs.1550
(C) Rs.900
(D) Rs.465
(E) Rs.565
Rationale: 4A = 6B = 10C = k => A = k/4, B = k/6 and C = k/10.
Therefore, A : B : C = k/4 : k/6 : k/10 = 15 : 10 : 6
Therefore, C’s share = Rs. 4650* 6/31
= Rs.900.
ANSWER:C
Answer: (C) Rs.900
Question: Jim is now 18 years older than Betty. If in 8 years Jim will be twice as old as Betty, how old will Jim be in 4 years?
(A) 30
(B) 32
(C) 34
(D) 36
(E) 38
Rationale: J=B+18 so B=J-18.
J+8=2(B+8).
J+8=2(J-18+8).
J+8=2J-20.
J=28.
In 4 years, Jim will be 32 years old.
The answer is B.
Answer: (B) 32
Question: A car covers a distance of 642 km in 6 ½ hours. Find its speed?
(A) 104 kmph
(B) 176 kmph
(C) 298 kmph
(D) 186 kmph
(E) 107 kmph
Rationale: 642/6
= 107 kmph
Answer:E
Answer: (E) 107 kmph
Question: John and Lewis leave Chennai for Bangalore simultaneously at 6 P.M in the evening driving in two cars at speeds of 50 mph and 70 mph respectively. As soon as Lewis reaches Bangalore he returns back to Chennai along the same route and meets John on the way back. If the distance between the two cities is 140 miles, how far from Chennai did John and Lewis meet?
(A) 110 miles
(B) 130 miles
(C) 100 miles
(D) 125 miles
(E) 25 mlies
Rationale: Time taken by Lewis to reach Bangalore = 140/70 = 2 hours
In 2 hours, John travels 50*2 = 100 miles
So distance at which they meet should be greater than 100 miles.
Only C satisfies.
Answer is C.
Answer: (C) 100 miles