mathewhe/aqua_rat huggingface dataset:
Question: The calendar for the year 2007 will be the same for the year
(A) 2017
(B) 2018
(C) 2014
(D) 2016
(E) None of these
Rationale: Explanation :
For a year to have the same calendar with 2007 ,the total odd days from 2007 should be 0.
Year	2007	2008	2009	2010	2011	2012
Odd Days	1	2	1	1	1	2
Year	2013	2014	2015	2016	2017
Odd Year	1	1	1	2	1
Take the year 2014 given in the choice.
Total odd days in the period 2007-2013 = 5 normal years + 2 leap year
= 5 x 1 + 2 x 2 = 9 odd days
= 2 odd day (As we can reduce multiples of 7 from odd days which will not change anything)
Take the year 2016 given in the choice.
Number of odd days in the period 2007-2015 = 7 normal years + 2 leap year
= 7 x 1 + 2 x 2 = 11 odd days
= 4 odd days
(Even if the odd days were 0, calendar of 2007 will not be same as the calendar of 2016 because 2007 is not a leap year whereas 2016 is a leap year. In fact, you can straight away ignore this choice due to this fact without even bothering to check the odd days)
Take the year 2017 given in the choice.
Number of odd days in the period 2007-2016 = 7 normal years + 3 leap year
= 7 x 1 + 3 x 2 = 13 odd days
= 6 odd days
Take the year 2018 given in the choice.
Number of odd days in the period 2007-2017 = 8 normal years + 3 leap year
= 8 x 1 + 3 x 2 = 14 odd days
= 0 odd day (As we can reduce multiples of 7 from odd days which will not change anything)
Also, both 2007 and 2018 are not leap years.
Since total odd days in the period 2007-2017 = 0 and both 2007 and 2018 are of same type, 2018 will have the same calendar as that of 2007. Answer : Option B
Answer: (B) 2018
Question: The rate of increase of the price of sugar is observed to be two percent more than the inflation rate expressed in percentage. The price of sugar, on January 1, 1994, is Rs. 18 per kg. The inflation rate for the years 1994 and 1995 are expected to be 6% each. The expected price of sugar on January 1, 1996 would be
(A) 20.99
(B) 21.9
(C) 25.4
(D) 20.19
(E) None of these
Rationale: Explanation :
Increase in the price of sugar = (6+2)= 8%
Hence, price of the sugar on Jan 1, 1996
=> (18 * 108 * 108)/( 100 * 100 ) = Rs 20.99.
Answer : A
Answer: (A) 20.99
Question: If [P] denotes the least integer greater than or equal to P and [P] = 0, which of the following statements must be true?
(A) P = 0
(B) -1 < P <= 0
(C) 0 < P <= 1
(D) -1 <= P < 0
(E) 0 <= P < 1
Rationale: The answer for this is 0 < = P < = 1
However it is not available in the options. The match to the above is-1 < P <= 0
Answer = B
Answer: (B) -1 < P <= 0
Question: A man can row 24 kmph in still water. It takes him thrice as long to row up as to row down the river. Find the rate of the stream?
(A) 6
(B) 12
(C) 18
(D) 15
(E) 20
Rationale: Let man's rate upsteam be X kmph
Then his rate of downstream = 3X kmph
Rate still water = 1/2 (3X + X) = 2X
2X = 24
X = 12
Rate of upstream = 12
Rate of downstream = 36
Rate of stream 1/2 ( 36 - 12) = 12 kmph
Answer is B.
Answer: (B) 12
Question: Two trains are moving in the same direction at 72 kmph and 36 kmph. The faster train crosses a girl sitting at window seat in the slower train in 32 seconds. Find the length of the faster train ?
(A) 170 m
(B) 100 m
(C) 270 m
(D) 320 m
(E) None of these
Rationale: Explanation:
Relative speed = (72 - 36) x 5/18 = 2 x 5 = 10 mps.
Distance covered in 32 sec = 32 x 10 = 320 m.
The length of the faster train = 320 m.
ANSWER IS D
Answer: (D) 320 m
Question: If a man can cover 10 metres in one second, how many kilometres can he cover in 3 hours 45 minutes?
(A) 288
(B) 162
(C) 145
(D) 135
(E) 130
Rationale: 10 m/s = 10 * 18/5 kmph
3 hours 45 minutes = 3 3/4 hours = 15/4 hours
Distance = speed * time = 10 * 18/5 * 15/4 km = 135 km.
Answer: D
Answer: (D) 135
Question: A certain fraction is equivalent to 2/5. If the numerator of the fraction is increased by 4 and the denominator is doubled, the new fraction is equivalent to 1/3. What is the difference of the numerator and denominator of the original fraction?
(A)  49
(B)  9
(C)  28
(D)  26
(E)  21
Rationale: x/y = 2/5 -> 1
(x+4)/2y = 1/3 -> 2
Divide 1 by 2 :
=> 2x/(x+4) = 6/5
=> 5x = 3x + 12
=> x = 6
=> y = 5/2 * 6 = 15
so x - y = 9
The answer is B
Answer: (B)  9
Question: A five-digit number divisible by 3 is to be formed using numerical 0, 1, 2, 3, 4 and 5 without repetition. The total number R of ways this can be done is:
(A) 122
(B) 210
(C) 216
(D) 217
(E) 225
Rationale: We should determine which 5 digits from given 6, would form the 5 digit number divisible by 3.
We have six digits: 0, 1, 2, 3, 4, 5. Their sum=15.
For a number to be divisible by 3 the sum of the digits must be divisible by 3. As the sum of the six given numbers is 15 (divisible by 3) only 5 digits good to form our 5 digit number would be 15-0={1, 2, 3, 4, 5} and 15-3={0, 1, 2, 4, 5}. Meaning that no other 5 from given six will total the number divisible by 3.
Second step:
We have two set of numbers:
1, 2, 3, 4, 5 and 0, 1, 2, 4, 5. How many 5 digit numbers can be formed using these two sets:
1, 2, 3, 4, 5 --> 5! as any combination of these digits would give us 5 digit number divisible by 3. 5!=120.
0, 1, 2, 4, 5 --> here we can not use 0 as the first digit, otherwise number won't be any more 5 digit and become 4 digit. So, desired # would be total combinations 5!, minus combinations with 0 as the first digit (combination of 4) 4! --> 5!-4!=4!(5-1)=4!*4=96
120+96=216=R
Answer: C.
Answer: (C) 216
Question: Two employees A and B are paid a total of Rs. 550 per week by their employer. If A is paid 120 percent of the sum paid to B, how much is B paid per week?
(A) Rs.130
(B) Rs.140
(C) Rs.150
(D) Rs.250
(E) Rs.280
Rationale: Let the amount paid to A per week = x
and the amount paid to B per week = y
Then x + y = 550
But x = 120% of y = 120y/100 = 12y/10
∴12y/10 + y = 550
⇒ y[12/10 + 1] = 550
⇒ 22y/10 = 550
⇒ 22y = 5500
⇒ y = 5500/22 = 500/2 = Rs.250
D)
Answer: (D) Rs.250
Question: wo passenger trains start at the same hour in the day from two different stations and move towards each other at the rate of 16 kmph and 21 kmph respectively. When they meet, it is found that one train has traveled 60 km more than the other one. The distance between the two stations is?
(A) 227
(B) 444
(C) 277
(D) 298
(E) 212
Rationale: 1h ----- 5
? ------ 60
12 h
RS = 16 + 21 = 37
T = 12
D = 37 * 12 = 444
Answer: B
Answer: (B) 444
Question: Five years ago, the average age of A, B, C and D was 45 years. With E Joining them now, the average of all the five is 49 years. The age of E is?
(A) 45
(B) 47
(C) 48
(D) 49
(E) 46
Rationale: Solution
5 years ago average age of A,B,C,D = 45 years
=> 5 years ago total age of A, B, C, D = 45 x 4 = 180 years
=> Total present age of A, B, C, D = 180 + 5x4 = 200 years
If E's present age is x years = 200+x/5= 49
x=45 years. Answer A
Answer: (A) 45
Question: A luxury liner, Queen Marry II, is transporting several cats as well as the crew (sailors, a cook, and one-legged captain) to a nearby port. Altogether, these passengers have 16 heads and 45 legs. How many cats does the ship host?
(A) 3
(B) 6
(C) 9
(D) 8
(E) 7
Rationale: a's +co +ca +cats = 16. sa's + 1 +1 +cats =16 or sa's +cats =14.
sa's(2) +2 +1 +cats*4 =45 sa's*2 +cats*4 = 42 or sa's +cats*2 =21 or 14-cats +cat*2 =21
then cats =7
E
Answer: (E) 7
Question: When the positive integer k is divided by the positive integer n , the remainder is 11. If k/n = 61.2 , what is the value of n?
(A) 9
(B) 20
(C) 65
(D) 70
(E) 81
Rationale: Here's an approach that's based on Number Properties and a bit ofbrute forcemath:
We're told that K and N are both INTEGERS.
Since K/N = 61.2, we can say that K = 61.2(N)
N has tomultiply outthe .2 so that K becomes an INTEGER. With the answers that we have to work with, N has to be a multiple of 5. Eliminate A and E.
With the remaining answers, we can TEST THE ANSWERS and find the one that fits the rest of the info (K/N = 81.2 and K/N has a remainder of 11)
Answer B: If N = 20, then K = 1624; 1624/20 has a remainder of 4 NOT A MATCH
Answer C: If N = 55, then K = 4466; 4466/55 has a remainder of 11 MATCH.
Final Answer:
C
Answer: (C) 65
Question: The surface area of a sphere is 4πR^2, where R is the radius of the sphere. If the surface area of sphere A is eight times as large as the surface area of sphere B, then the radius of sphere A is how many times the radius of sphere B?
(A) 2
(B) 2√2
(C) 4
(D) 2π
(E) π·√8
Rationale: R1 : Radius of sphere A
R2 : Radius of sphere B
As per question,4πR1^2=8∗4πR2^2
or R12=8∗R2^2
or R1 = 2√2R2. Hence, B
Answer: (B) 2√2
Question: A sum of Rs. 2717 is lent into two parts so that the interest on the first part for 8 years at 3% per annum may be equal to the interest on the second part for 3 years at 5% per annum. Find the second sum?
(A) 1642
(B) 1672
(C) 1632
(D) 2789
(E) 6386
Rationale: (x*8*3)/100 = ((2717 - x)*3*5)/100
24x/100 = 40755/100 - 15x/100
39x = 40755 => x = 1045
Second sum = 2717 – 1045
=1672
Answer:B
Answer: (B) 1672
Question: A multiple choice test consists of 4 questions, and each question has 5 answer choices. In how many Q ways can the test be completed if every question is unanswered?
(A) 24
(B) 120
(C) 625
(D) 720
(E) 1024
Rationale: 5 choices for each of the 4 questions, thus total Q of 5*5*5*5 = 5^4 = 625 ways to answer all of them.
Answer: C.
Answer: (C) 625
Question: Salad dressing P is made up of 30% vinegar and 70% oil, and salad dressing Q contains 10% vinegar and 90% oil. If the two dressings are combined to produce a salad dressing that is 20% vinegar, dressing P comprises what percentage of the new dressing?
(A) 60%
(B) 50%
(C) 40%
(D) 30%
(E) 20%
Rationale: Let x be the percentage of dressing P in the new dressing.
0.3x + 0.1(1-x) = 0.20
0.2x = 0.10
x = 0.5 = 50%
The answer is B.
Answer: (B) 50%
Question: A small company reduced its faculty by approximately 13 percent to 195 employees. What was the original number of employees?
(A) 182
(B) 208
(C) 220
(D) 224
(E) 302
Rationale: If x is the original number of employees, then after 13% reduction in employees number is .87x
but we are given .87x = 195
x = 224
So the original number of employees is 224
Correct Answer - D
Answer: (D) 224
Question: A factory has a fixed cost of $43,000 a month, and a cost of $2.5 for every item produced. If the selling price of a single item is $5, what is the number of items must be sold monthly for the factory to cover its cost exactly?
(A) 9,000
(B) 14,000
(C) 17,200
(D) 22,500
(E) 27,000
Rationale: selling price - Cost price = 2.5 so per unit profit =2.5
cost to recover =43000
no of items required = 43000/2.5 = 17200
Answer: C
Answer: (C) 17,200
Question: 85% of the employees in a multinational corporation have VCD players, 75 percent have microwave ovens, 80 percent have ACs and 85 percent have washing machines. At least what percentage of employees has all four gadgets?
(A) (a) 15%
(B) (b) 5%
(C) (c) 10%
(D) (d) 20%
(E) (e) 25%
Rationale: so 15% employees don't have VCD devices.
25% employees don't have MO
20% employees don't have ACs
15% employees don't have WM
Summ of employees that don't have some device = 15%+25%+20%+15% = 75% < 100%
So definitely at least 25% employees have 4 devices.
ans: E
Answer: (E) (e) 25%
Question: There are 17 stations between Hyderabad and Bangalore. How many second class tickets have to be printed, so that a passenger can travel from any station to any other station?
(A) 156
(B) 167
(C) 157
(D) 342
(E) 380
Rationale: The total number of stations = 19
From 19 stations we have to choose any two stations and the direction of travel (i.e., Hyderabad to Bangalore is different from Bangalore to Hyderabad) in 19P₂ ways.
²⁰P₂ = 19 * 18
= 342.
Answer: D
Answer: (D) 342
Question: In a room filled with 7 people, 4 people have exactly 1 sibling in the room and 3 people have exactly 2 siblings in the room. If two individuals are selected from the room at random, what is the probability that those two individuals are NOT siblings?
(A) 5/21
(B) 3/7
(C) 4/7
(D) 5/7
(E) 16/21
Rationale: # of selections of 2 out of 7 - C27=21C72=21;
# of selections of 2 people which are not siblings - C12∗C12C21∗C21 (one from first pair of siblings*one from second pair of siblings)+C12∗C13C21∗C31 (one from first pair of siblings*one from triple)+ C1^_2*C^1_3(one from second pair of siblings*one from triple) =4+6+6=16=4+6+6=16.
P=16/21
ANSWER:E
Answer: (E) 16/21
Question: Village X has a population of 78000, which is decreasing at the rate of 1200 per year. Village Y has a population of 42000, which is increasing at the rate of 800 per year .in how many years will the population of the two villages be equal?
(A) 15
(B) 19
(C) 11
(D) 18
(E) 13
Rationale: Let the population of two villages be equal after p years
Then, 78000-1200p=42000+800p
2000p=36000
p=18
Answer is D.
Answer: (D) 18
Question: Find the average of the series : 312, 162, 132, 147 and 122?
(A) 170
(B) 175
(C) 180
(D) 185
(E) 195
Rationale: Average = (312 + 162 + 132 + 147+ 122)/5 = 875/5 = 175
ANSWER:B
Answer: (B) 175
Question: In 1979 approximately 1/3 of the 38.3 million airline passengers traveling to or from the United States used Kennedy Airport. If the number of such passengers that used Miami Airport was 1/2 the number that used Kennedy Airport and 4 times the number that used Logan Airport, approximately how many millions of these passengers used Logan Airport that year?
(A)  18.6
(B)  9.3
(C)  6.2
(D)  3.1
(E)  1.6
Rationale: number of
passengers using Kennedy airport = 38/3 =~12.67
Passengers using Miami airport = 12.67/2=~6.3
passengers using logan airport = 6.3/4 =~1.58
so E
Answer: (E)  1.6
Question: 583 is related to 293 in the same way as 488 is related to
(A) 2338
(B) 378
(C) 277
(D) 299
(E) 271
Rationale: Explanation:
Sum of digits of the first number is 2 more than the sum of digits of the second number.
Answer: B) 378
Answer: (B) 378
Question: When the positive integer k is divided by the positive integer n , the remainder is 13. If k/n = 81.2 , what is the value of n?
(A) 9
(B) 20
(C) 55
(D) 70
(E) 81
Rationale: Here's an approach that's based on Number Properties and a bit ofbrute forcemath:
We're told that K and N are both INTEGERS.
Since K/N = 81.2, we can say that K = 81.2(N)
N has tomultiply outthe .2 so that K becomes an INTEGER. With the answers that we have to work with, N has to be a multiple of 5. Eliminate A and E.
With the remaining answers, we can TEST THE ANSWERS and find the one that fits the rest of the info (K/N = 81.2 and K/N has a remainder of 11)
Answer B: If N = 20, then K = 1624; 1624/20 has a remainder of 4 NOT A MATCH
Answer C: If N = 55, then K = 4466; 4466/55 has a remainder of 11 MATCH.
Final Answer:
B
Answer: (B) 20
Question: How many odd three-digit integers greater than 800 are there such that all their digits are different?
(A) 40
(B) 56
(C) 72
(D) 81
(E) 104
Rationale: In the range 800 - 900:
1 choice for the first digit: 8;
5 choices for the third digit: 1, 3, 5, 7, 9 (as the number is odd);
8 choices for the second digit: 10 digits - first digit - third digit = 8 digits.
1*5*8 = 40.
In the range 900 - 999:
1 choice for the first digit: 9;
4 choices for the third digit: 1, 3, 5, 7 (9 is out as it's the first digit);
8 choices for the second digit: 10 digits - first digit - third digit = 8 digits.
1*4*8 = 32.
Total: 40+32 = 72.
Answer: C
Answer: (C) 72
Question: Square M is inscribed in circle N. If the perimeter of M is 20, what is the circumference of N?
(A) 33√ 2π
(B) 2√ 2π
(C) 6√ 2π
(D) 7√ 2π
(E) 5√ 2π
Rationale: square forms two right angled triangles.
Any time we have a right angle triangle inside a circle, the hypotenuse is the diameter.
hypotenuse here = diagonal of the square = 5 sqrt(2) = diameter
=> radius = 2.5 sqrt(2)
Circumference of the circle = 2pi r = 5 pi sqrt(2)
Answer is E.
Answer: (E) 5√ 2π
Question: Which of the following is non negative?
(A) (c-0.9)(c-1)
(B) (c+1)(c-1)
(C) (c-0.9)(c-0.9)
(D) (c-0.9)(c+0.9)
(E) c(c+1)
Rationale: 5-sec approach:
C. (c-0.9)(c-0.9) = (c-0.9)^2. The square of a number is always non-negative.
Answer: C.
Answer: (C) (c-0.9)(c-0.9)
Question: Evaluate: 40 - 12÷6×2 =
(A) A)24
(B) B)36
(C) C)48
(D) D)60
(E) E)72
Rationale: According to order of operations, 12÷6×2 (division and multiplication) is done first from left to right
12÷6×2 = 2 × 2 = 4
Hence
40 - 12÷6×2 = 40 - 4 = 36
correct answer is B) 36
Answer: (B) B)36
Question: The mall charges 50 cents for the first hour of parking and $3 for each additional hour until the customer reaches 4 hours, after that the parking fee is $1 per hour. If a certain customer parked his in the mall for 7 hours and 30 minutes, how much is he going to pay?
(A) $11.5.
(B) $12.
(C) $13.
(D) $14.5
(E) $15.
Rationale: Charges for 7 Hours = ( First hour @ $ 0.50 ) + ( 3 hours @ $ 3 ) + ( 3.5 hours @ $ 1 )
Charges for 7 Hours = ( 1 @ $ 0.50 ) + ( 3 hours @ $ 3 ) + ( 3.5 hours @ $ 1 )
Charges for 7 Hours = ( $ 0.50 ) + ( $ 9) + ( $ 3.5 )
Charges for 7 Hours = ( $ 0.50 ) + ( $ 9) + ( $ 3.50 )
Charges for 7 Hours = $ 13
Hence correct answer must be (C)
Answer: (C) $13.
Question: A particular library has 75 books in a special collection, all of which were in the library at the beginning of the month. These book are occasionally loaned out through an inter-library program. If, by the end of the month, 80 percent of books that were loaned out are returned and there are 66 books in the special collection at that time, how many books of the special collection were loaned out during that month?
(A) 20
(B) 30
(C) 35
(D) 45
(E) 55
Rationale: there are 9 books less(75-66) which represents 20% of the loaned books (100-80)
So total loaned out books = 45
Answer D
Answer: (D) 45
Question: Find a 6-digit integer abcdef with the following properties:
Take the rightmost digit and place it in front of the integer to form a new number (abcdef --> fabcde).
The new one is the product of the old one and the shifted digit (fabcde = f*abcdef).
What was the original integer?
(A) 122564
(B) 102564
(C) 142564
(D) 102574
(E) 102566
Rationale: a=1 b=0 c=2 d=5 e=6 f=4
fabcde = f x abcdef
410256 = 4 x 102564
ANSWER:B
Answer: (B) 102564
Question: A sum of money at simple interest amounts to Rs. 825 in 3 years and to Rs. 840 in 4 years. The sum is?
(A) s. 780
(B) s. 638
(C) s. 650
(D) s. 730
(E) s. 735
Rationale: S.I. for 1 year = (840 - 825) = Rs. 2915
S.I. for 3 years = 15 * 3 = Rs. 45
Principal = (825 - 45) = Rs. 780.
ANSWER:A
Answer: (A) s. 780
Question: In how many different number of ways 3 boys and 2 girls can sit on a bench?
(A) 700
(B) 710
(C) 120
(D) 300
(E) 720
Rationale: npn = n!
5p5 = 5 × 4 × 3 × 2 × 1 = 120
C)
Answer: (C) 120
Question: A committee has 4 men and 7 women. What are the number of ways of selecting 2 men and 4 women from the given committee?
(A) 125
(B) 150
(C) 180
(D) 210
(E) 225
Rationale: The number of ways to select two men and four women = 4C2 * 7C4 = 6 * 35 = 210
The answer is D.
Answer: (D) 210
Question: A train is moving at a speed of 132 km/hr. If the length of the train is 110m, how long will it take to cross a railway platform 165m long?
(A) 8 sec
(B) 9 sec
(C) 7 1/2 sec
(D) 10 sec
(E) None
Rationale: Speed of the train=(132*5/18)m/sec=(110/3)m/sec
Distance covered in passing the platform= (110+65)m=275m
Therefore, Time taken=(275*3/110)sec =7 1/2 Sec
Answer: Option C
Answer: (C) 7 1/2 sec
Question: What percent is 70 of 280?
(A) 12 %
(B) 25 %
(C) 26 %
(D) 27 %
(E) 28 %
Rationale: 70/280 = 1/4
1/4 × 100 = 25 %
B
Answer: (B) 25 %
Question: An air conditioner can coo the hall in 25 minutes while another takes 30 minutes to cool under similar conditions. if both air conditioners are switched on at same instance then how long will it take to cool the room?
(A) about 16 minutes
(B) about 24 minutes
(C) about 14 minutes
(D) about 34 minutes
(E) about 4 minutes
Rationale: Take LCM of 25 and 30 = 150
25*6=150/ 30*5=150.
So if both are switched on together , room cooled in 150/(6+5)=150/11=13.64 minutes
13.64 can be round to 14 minutes , so about 14 minutes
ANSWER: C
Answer: (C) about 14 minutes
Question: A carpenter worked alone for 1 day on a job that would take him 6 more days to finish. He and another carpenter completed the job in 8 more days. How many days would it have taken the second carpenter to do the complete job working alone?
(A) 4 2/3
(B) 7
(C) 9
(D) 14
(E) 28
Rationale: A carpenter worked only 1 day on something that takes him 6 MORE days.
Means;
Carpenter finishes his work in 7 days.
Let his buddy finish the same task in x days.
Respective rates per day:
1/7 AND 1/x
To complete 1 work:
First guy worked for 5 days @ rate=1/7 per day.
Second one worked for 8 days @ rate=1/x per day
Expression:
Days*Rate=Work
5*1/7+8*1/x=1
5x+56=7x
2x=56
x=28 days.
Ans:E
Answer: (E) 28
Question: A man can row 8 kmph in still water. When the river is running at 2 kmph, it takes him 1 hour to row to a place and black. What is the total distance traveled by the man?
(A) 5.75
(B) 5.7
(C) 7.5
(D) 5.74
(E) 5.71
Rationale: M = 8
S = 2
DS = 10
US = 6
x/10 + x/6 = 1
x = 3.75
D = 3.75 * 2 = 7.5 Answer: C
Answer: (C) 7.5
Question: For her customer feedback score, Jess wants to average at or above an 8.0 rating. For the month of June, she received the following scores: 5, 8, 8, 7, 9, 10, 6, 6, 8 and 7. By what percent did she fall short of her goal?
(A)  4%
(B)  7.5%
(C)  8%
(D)  10%
(E)  12%
Rationale: Expected minimum rating = 8
Deviation from the expected minimum rating = (-3 + 0 + 0 - 1 + 1 + 2 - 2 - 2 + 0 - 1)/10 = -6/10 = -0.6
Current rating is 0.6 less than 8.
Percentage = (0.6/8)*100 = 7.5%
Answer: B
Answer: (B)  7.5%
Question: The amount of water (in ml) that should be added to reduce 9 ml. Lotion, containing 50% alcohol, to a lotion containing 30% alcohol, is?
(A) 8 ml
(B) 5 ml
(C) 4 ml
(D) 6 ml
(E) 1 ml
Rationale: 4.5 4.5
30% 70%
30% ----- 4.5
70% ------? => 10.5 - 4.5 = 6 ml
Answer:D
Answer: (D) 6 ml
Question: The sale price sarees listed for Rs.280 after successive discount is 12% and 8% is?
(A) 288
(B) 226
(C) 250
(D) 230
(E) 262
Rationale: 280*(88/100)*(92/100)
= 226
Answer: B
Answer: (B) 226
Question: A person goes to his office at 1/3rd of the speed at which he returns from his office. If the avg speed during the whole trip is 24m/h. what is the speed of the person while he was going to his office?
(A) 8km/h
(B) 9km/h
(C) 10km/h
(D) 11km/h
(E) 16km/h
Rationale: u = k , v= 3k
\inline \therefore \frac{2uv}{u+v}\: \: \Rightarrow \frac{2\times k\times 3k}{(k+3k)}=24
\inline \Rightarrow 1.5k = 24
\inline \Rightarrow k=16km/h
E
Answer: (E) 16km/h
Question: A train 250 m long running at 72 kmph crosses a platform in 15 sec. What is the length of the platform?
(A) 50m
(B) 200m
(C) 250m
(D) 270m
(E) 300 m
Rationale: D = 72 * 5/18 = 15 = 300 â€“ 250 = 50m
ANSWER:A
Answer: (A) 50m
Question: A wholesaler wishes to sell 100 pounds of mixed nuts at $2.50 a pound. She mixes peanuts worth $3.50 a pound with cashews worth $4.00 a pound. How many pounds of cashews must she use?
(A) 40
(B) 45
(C) 50
(D) 55
(E) 60
Rationale: From the question stem we know that we need a mixture of 100 pounds of peanuts and cashews. If we represent peanuts as x and cashews as y, we get x + y = 100. Since the wholesaler wants to sell the mixture of 100 pounds @ $2.50, we can write this as: $2.5 * (x + y) = $1.5x + $4y
From the equation x + y = 100, we can rewrite y as y = 100 - x and substitute this into our equation to get:
$2.5 * (x + 100 - x) = $1.5x + $4(100 - x)
If you solve for x, you will get x = 60, and therefore y = 40. So the wholesaler must use 40 pounds of cashews.
You can substitute into the original equation to see that: $250 = $1.5(60) + $4(40)
Answer is E
Answer: (E) 60
Question: Tough and Tricky questions: Exponents.
If 3^m3^m3^m = 8^n, then m/n =
(A) 1/3
(B) 2/3
(C) 1
(D) 3/2
(E) 2
Rationale: I also soved it, but a bit differently. Thank you for reminding me of this much easier and logical way!
What I did was to test powers of 3 that would lead to 9.
So, we have 3 raised to the same power 3 times and 9 raised to another power one time: 3^m3^m3^m = 9^n
What I did was test 3 raised to the power of 2 like this:
3^2*3^2*3^2 = 9*9*9 = 9^3. This means that m=2 and n=3. So, m/n=2.E
Answer: (E) 2