mathewhe/aqua_rat huggingface dataset:
Question: The output of a factory was increased by 10% to keep up with rising demand. To handle the holiday rush, this new output was increased by 20%. By approximately what percent would the output now have to be decreased in order to restore the original output?
(A) 20%
(B) 24%
(C) 30%
(D) 32%
(E) 79%
Rationale: Let initial output is O then after 10% increase it will be 1.1O and after 20% increase on this new output the latest output will be 1.1O * 1.20 = 1.32O
Now we have to decrease the output by some percentage so that the new output is same as the starting output (O)
so, 1.32O * (1-x/100) = O
=> x = 24.24%
So, answer will be B
Answer: (B) 24%
Question: In a graduate physics course, 70 percent of the students are male and 30 percent of the students are married. If two-sevenths of the male students are married, what fraction of the male students is single?
(A) 2/7
(B) 1/3
(C) 1/2
(D) 2/3
(E) 5/7
Rationale: let assume there are 100 students of which 70 are male and 30 are females
if 30 are married then 70 will be single.
now its given that two-sevenths of the male students are married that means 2/7 of 70 = 20 males are married
if 30 is the total number of students who are married and out of that 20 are males then the remaining 10 will be females who are married.
total females = 70
married males = 20
then single males = 70-20 = 50
we need to find the fraction of male students who are single i.e single male students / total male student
= 50/70 = 5/7 [E]
Answer: (E) 5/7
Question: The cost of painting the whole surface area of a cube at the rate of 13 paise per Sq.cm is Rs. 343.98. Then the volume of the cube is
(A) 8500 cm3
(B) 9000 cm3
(C) 9250 cm3
(D) 9261 cm3
(E) None
Rationale: Solution
Surface area	= (34398 / 13)
‹=›2646cm3
‹=›6a2= 2646
‹=›a2= 441
‹=›a = 21.
So,volume =(21x21x21)cm3= 9261cm3.
Answer D
Answer: (D) 9261 cm3
Question: A man sold 20 articles for $60 and gained 20%. How many articles should he sell for $50 to incur a loss 20%?
(A) 25
(B) 36
(C) 40
(D) 50
(E) 48
Rationale: Production cost per article: $60*(100%-20%) / 20 = $2.40
Required production costs for a loss of 20%: $50*(100% + 20%) = $60
Number of articles to be sold for $60 to incur a 20% loss: $60 / $2.40 = 25
Thus, solution A is correct.
Answer: (A) 25
Question: A man invests some money partly in 9% stock at 96 and partly in 12% stock at 120. To obtain equal dividends from both, he must invest the money in the ratio:
(A) 3:5
(B) 2:1
(C) 16:15
(D) 4:5
(E) None of these
Rationale: Explanation:
For an income of Re. 1 in 9% stock at 96, investment = Rs. 96/9 = Rs.32/3
For an income Re. 1 in 12% stock at 120, investment = Rs. 120/12 = Rs. 10.
Ratio of investments =(32/3) : 10 = 32 : 30 = 16 : 15.
Answer: C
Answer: (C) 16:15
Question: A, B, C rent a pasture. A puts 10 oxen for 7 months, B puts 12 oxen for 5 months and C puts 15 oxen for 3 months for grazing. If the rent of the pasture is Rs. 175, how much must C pay as his share of rent?
(A) Rs. 45
(B) Rs. 50
(C) Rs. 55
(D) Rs. 60
(E) Rs. 65
Rationale: Explanation:
A : B : C = (10 x 7) : (12 x 5) : (15 x 3) = 70 : 60 : 45 = 14 : 12 : 9.
C's rent = Rs.(175 x	9/35)= Rs. 45.
ANSWER IS A
Answer: (A) Rs. 45
Question: A train 500 m long can cross an electric pole in 20 sec and then find the speed of the train?
(A) 95 Kmph
(B) 90 Kmph
(C) 92 Kmph
(D) 95 Kmph
(E) 98 Kmph
Rationale: Length = Speed * time
Speed = L/T
S = 500/20
S = 25 M/Sec
Speed= 25*18/5 (To convert M/Sec in to Kmph multiply by 18/5)
Speed = 90 Kmph
ANSWER:B
Answer: (B) 90 Kmph
Question: The smallest number when increased by " 1 " is exactly divisible by 6,9,15,35,45 is:
(A) 631
(B) 630
(C) 359
(D) 629
(E) 600
Rationale: LCM = 630
630 - 1 = 629
ANSWER:D
Answer: (D) 629
Question: How many keystrokes are needed to type the numbers from 1 to 500?
(A) 1156
(B) 1392
(C) 1480
(D) 1562
(E) 1788
Rationale: There are 9 one-digit numbers from 1 to 9.
There are 90 two-digit numbers from 10 to 99.
There are 401 three-digit numbers from 100 to 500.
9 + 90(2) + 401(3) = 1392
The answer is B.
Answer: (B) 1392
Question: In a two-digit number, the digit in the unit's place is four times the digit in ten's place and the sum of the digits is equal to 10. What is the number?
(A) 82
(B) 41
(C) 14
(D) 56
(E) 28
Rationale: Let the ten's digit be x. then, unit's digit = 4x
therefore x + 4x = 10 ==> 5x = 10 ==> x = 2
so ten's digit is 2 and unit's digit is 8, so the number is 28
so the correct answer is option E) 28
Answer: (E) 28
Question: The edge of a cube is 7a cm. Find its surface?
(A) 24a8
(B) 24a4
(C) 24a1
(D) 24a2
(E) 294a2
Rationale: 6a2 = 6 * 7a * 7a = 294a2
Answer:E
Answer: (E) 294a2
Question: A shop sells chocolates It is used to sell chocolates for Rs.2 each but there were no sales at that price.When it reduced the price all the chocolates sold out enabling the shopkeeper to realize Rs 164.90 from the chocolates alone If the new price was not less than half the original price quoted How many chocolates were sold?
(A) 1.9
(B) 1.7
(C) 1.2
(D) 1.5
(E) 1.6
Rationale: 16490 = 2 × 5 × 17 × 97
Now now chocolate price should be greater than 1 and less than 2. So 2 x 5 x 17 = 170
So Total chocolates sold = 97 and New chocolate price = Rs.1.7
Answer:	B
Answer: (B) 1.7
Question: A board 7ft. 9 inches long is divided into 3 equal parts . What is the length of each part?
(A) 31 inches
(B) 32 inches
(C) 33 inches
(D) 34 inches
(E) 35 inches
Rationale: 7 ft 9 in is 84 + 9 = 93 inches. so 93/3 = 31 inches or 2 ft. 7 inch.
ANSWER:A
Answer: (A) 31 inches
Question: Find the number of zeroes in the expression 15*32*25*22*40*75*98*112*125
(A) 12
(B) 9
(C) 14
(D) 7
(E) 6
Rationale: (3*5)*(2*2*2*2*2)*(5*5)*(2*11)*(2*2*2*2*5)*(5*5*3)*(2*7*7)*(2*2*2*2*7)*(5*5*5)
there are 9 (5*2) pairs which gives zero
so.no of zeros 9
ANSWER:B
Answer: (B) 9
Question: The diagonals of a rhombus are 18 cm and 22 cm. Find its area?
(A) 277
(B) 266
(C) 198
(D) 288
(E) 212
Rationale: 1/2 * 18 * 22 = 198
Answer: C
Answer: (C) 198
Question: If rupee one produces rupees nine over a period of 40 years, find the rate of simple interest?
(A) 22 1/8 %
(B) 22 3/2 %
(C) 28 1/2 %
(D) 22 1/2 %
(E) 32 1/2 %
Rationale: 9 = (1*40*R)/100
R = 22 1/2 %
Answer:D
Answer: (D) 22 1/2 %
Question: A and B invests Rs.6000 and Rs.12000 in a business. After 4 months, A withdraws half of his capital and 2 months later, B withdraws one-third of his capital. In what ratio should they share the profits at the end of the year?
(A) 32:99
(B) 8:21
(C) 32:45
(D) 34:89
(E) 35:21
Rationale: A : B
(6000*4)+(3000*8) : (12000*6)+(9000*6)
48000 : 126000
8 : 21
Answer:B
Answer: (B) 8:21
Question: A train covers a distance of 10km in 10 min. If it takes 6 sec to pass a telegraph post, then the length of the train is?
(A) m
(B) m
(C) m
(D) m
(E) m
Rationale: Speed = (10/10 * 60) km/hr
= (60 * 5/18) m/sec = 50/3 m/sec.
Length of the train = 50/3 * 6
= 100 m.
Answer:C
Answer: (C) m
Question: The rental charge for a car is 34 cents for the first 1/4 mile driven and 6 cents for every 1/5 mile driven over the initial 1/4 mile. If a man paid $1.24 in rental charges, how many miles did he drive?
(A) 2.5
(B) 3.0
(C) 3.25
(D) 3.75
(E) 4.0
Rationale: Total Rent = Rent for the first 0.25 mile + Rent After 0.25 mile
Rent for the first 0.25 mile = 34 cents
Rent After 0.25 mile = [6 cent/(1/5 mile)]*(x - 0.25) = 30(x-0.25)
Therefore, Total Rent = 35 + 30(x - 0.25)
124 = 34 + 30(x - 0.25)
90 = 30(x - 0.25)
3 = x - 0.25
x = 3 + 0.25 = $3.25 C
Answer: (C) 3.25
Question: A question paper consists of three sections 4,5 and 6 questions respectively. Attempting one question from each section is compulsory but a candidate need not attempt all the questions. In how many ways can a candidate attempt the questions?
(A) 209
(B) (4!-1)*(5!-1)*(6!-1)
(C) 119
(D) 29295
(E) None
Rationale: Solution:
At least 1 question from each section is compulsory, so from the 1st section the candidate can attempt 1 or 2 or 3 or 4 questions.
In each section each question can be dealt with in 2 ways, i.e. either he attempts it or leaves it.
So far 4 question there are 2 *2 *2 *2 ways to attempt. As he has to attempt at least 1 question, the total number of ways in which he can attempt questions from 1st section is 24−1.
Similarly for the 2nd section there are 25−1 ways in which he can attempt and for the 3rd section there are 26−1 ways.
The ways in which the attempts one or more questions in any section is independent of the number of ways in which he attempts one or more questions from the other sections.
Thus, total number of ways
Answer: Option D
Answer: (D) 29295
Question: 10 women can complete a work in 9 days and 10 children take 12 days to complete the work. How many days will 6 women and 7 children take to complete the work?
(A) 4
(B) 5
(C) 7
(D) 8
(E) 2
Rationale: 1 women's 1 day work = 1/90
1 child's 1 day work = 1/120
(6 women + 7 children)'s 1 day work
= (6/90 + 7/120) = 1/8
6 women and 7 children will complete the work in 8 days.
D
Answer: (D) 8
Question: Three numbers are in the ratio 5 : 6 : 7. The sum of its longest and smallest numbers equals the sum of the third number and 54. Find the third number?
(A) A)37
(B) B)85
(C) C)48
(D) D)43
(E) E)54
Rationale: Let the numbers be 5x, 6x, 7x.
Largest number = 7x.
Smallest number = 5x.
Third number = 6x.
7x + 5x = 6x + 54
6x = 54 => third number is 54.
Answer: Option E
Answer: (E) E)54
Question: At the end of a business conference the nine people present all shake hands with each other once. How many handshakes will there be altogether ?
(A) 20
(B) 45
(C) 36
(D) 90
(E) 95
Rationale: number of handshakes = 9C2= 9*8/2 = 36
ANSWER:C
Answer: (C) 36
Question: Sum of the squares of three numbers is 351 and the sum of their products taken two at a time is 245. Find the sum?
(A) 20
(B) 22
(C) 25
(D) 26
(E) 29
Rationale: (a + b + c)2 = a2 + b2 + c2 + 2(ab +bc + ca) = 351 + 2* 245
a + b + c = √841 = 29
E
Answer: (E) 29
Question: What is the are of an equilateral triangle of side 16 cm?
(A) 64√6 cm2
(B) 64√3 cm2
(C) 64√9 cm2
(D) 34√3 cm2
(E) 24√3 cm2
Rationale: Area of an equilateral triangle = √3/4 S2
If S = 16, Area of triangle = √3/4 * 16 * 16
= 64√3 cm2;
Answer: D
Answer: (D) 34√3 cm2
Question: Each of the following equations W has at least one solution EXCEPT
(A) W=–2^n = (–2)^-n
(B) 2^-n = (–2)^n
(C) 2^n = (–2)^-n
(D) (–2)^n = –2^n
(E) (–2)^-n = –2^-n
Rationale: While it is possible to reason out which of these choices must not work, we may not have time or the confidence to do so. However, this problem has variable in its answer choice, and relatively simple math. Therefore, an easy alternative is picking numbers.
Since we're dealing with exponents, we want to keep things as easy as possible. Hence, we'll start with the easiest exponent possible: n = 1. A, B, and C are not solved (x^-n = 1/(x^n), so we're comparing integers to fractions), but choices D and E both end up valid, eliminating them from contention.
In the process of doing this, however, we've uncovered a major clue to our next step: A, B, and C, all compared integers to fractions, and the only integer equal to it's reciprocal is 1, which is equal to 1/1. This, in turn, tells us the we need to pick n = 0. Remember, for all non-zero x, x^0 = 1.
If we plug n = 0 into choices B and C, we end up with 1 = 1 both times. Choice A, however, results in the false 1 = -1. Thus, we conclude that the first choice has no valid solutions, and is therefore the correct answer.
Answer: (A) W=–2^n = (–2)^-n
Question: If the population of a certain country increases at the rate of one person every 40 seconds, by how many persons does the population increase in 1 hour?
(A) 90
(B) 120
(C) 150
(D) 180
(E) 160
Rationale: Answer = 1.5 * 60 = 90
Answer is A
Answer: (A) 90
Question: A train crosses a platform of 120 m in 15 sec, same train crosses another platform of length 180 m in 18 sec. then find the length of the train?
(A) 288
(B) 180
(C) 288
(D) 277
(E) 265
Rationale: Length of the train be ‘X’
X + 120/15 = X + 180/18
6X + 720 = 5X + 900
X = 180m .Answer: B
Answer: (B) 180
Question: Find the area of a rhombus whose side is 25 cm and one of the diagonals is 30 cm?
(A) 272 sq.cm
(B) 267 sq.cm
(C) 286 sq.cm
(D) 251 sq.cm
(E) 600 sq.cm
Rationale: Consider the rhombus ABCD. Let the diagonals intersect at E. Since diagonals bisect at right angles in a rhombus.
BE2 + AE2 = AB2
252 = 152 + AE2 AE
= √(625 - 225)
= √400 = 20,
AC = 20 + 20 = 40 cm.
Area of a rhombus
= 1/2 * d1d2
= 1/2 * 40 * 30
= 600 sq.cm.
Answer:E
Answer: (E) 600 sq.cm
Question: How long does a train 110 m long running at the speed of 72 km/hr takes to cross a bridge 132 m length?
(A) 12.8 sec
(B) 12.1 sec
(C) 12.2 sec
(D) 12.6 sec
(E) 11.1 sec
Rationale: Speed = 72 * 5/18 = 20 m/sec
Total distance covered = 110 + 132 = 242 m.
Required time = 242/20 = 12.1 sec.
Answer: B
Answer: (B) 12.1 sec
Question: The consumption of diesel per hour of a bus varies directly as square of its speed. When the bus is travelling at 60 kmph its consumption is 1 litre per hour. if each litre costs $60 and other expenses per hous is $ 60, then what would be the minimum expenditure required to cover a distance of 600 Km?
(A) 120
(B) 1250
(C) 1200
(D) 1100
(E) 1150
Rationale: 60 kmph consumption is 1 lt/hr
so 600 km will take 10 hrs and the consumption is 10 lt for entire distance.
1 lt costs $60
so 10 lt costs $600
extra expenses for 1 hr - $60
10 hrs - $600
total expense - $600 + $600 = $1200
Answer : C
Answer: (C) 1200
Question: From a group of 7 men and 6 women, five persons are to be selected to form a committee so that at least 3 men are there on the committee. What is the probability of having 0 woman in committee ?
(A) 7/36
(B) 9/144
(C) 1/36
(D) 1/18
(E) 5/18
Rationale: We may have (3 men and 2 women) = (7C3 x 6C2) = 525
or (4 men and 1 woman) = (7C4 x 6C1) = 210
or (5 men only) = (7C5) = 21
Required ways = 756
Probability of having 0 woman in committee = 21 / 756 =1/36
ans - C
Answer: (C) 1/36
Question: A box contains nine bulbs out of which 4 are defective. If four bulbs are chosen at random, find the probability that exactly three bulbs are good.?
(A) 20/69
(B) 20/63
(C) 20/65
(D) 20/61
(E) 20/62
Rationale: Required probability = (10 * 4)/126 = 20/63.Answer: B
Answer: (B) 20/63
Question: A train passes a station platform in 32 sec and a man standing on the platform in 20 sec. If the speed of the train is 54 km/hr. What is the length of the platform?
(A) 228
(B) 240
(C) 887
(D) 166
(E) 180
Rationale: Speed = 54 * 5/18 = 15 m/sec.
Length of the train = 15 * 20 = 300 m.
Let the length of the platform be x m . Then,
(x + 300)/32 = 15 => x = 180 m.
Answer: E
Answer: (E) 180
Question: If |w|=−w, which of the following must be true?
(A) x≥0
(B) w≤0
(C) x2>x
(D) x3<0
(E) 2x<x
Rationale: |w| =-w means absolute value of w is equal to negative of w. Since absolute value cannot be negative hence negative of w should result in a non negative number. It means w is a non positive number i.e. w<0. Answer is B
Answer: (B) w≤0
Question: Two numbers are less than third number by 30% and 37% respectively. How much percent is the second number less than by the first
(A) 8%
(B) 9%
(C) 10%
(D) 11%
(E) 12%
Rationale: Explanation:
Let the third number is x.
then first number = (100-30)% of x
= 70% of x = 7x/10
Second number is (63x/100)
Difference = 7x/10 - 63x/100 = 7x/10
So required percentage is, difference is what percent of first number
=> (7x/100 * 10/7x * 100 )% = 10%Explanation:
Let the third number is x.
then first number = (100-30)% of x
= 70% of x = 7x/10
Second number is (63x/100)
Difference = 7x/10 - 63x/100 = 7x/10
So required percentage is, difference is what percent of first number
=> (7x/100 * 10/7x * 100 )% = 10%
Option C
Answer: (C) 10%
Question: How many numbers from 39 to 79 are exactly divisible by 11?
(A) 5
(B) 7
(C) 4
(D) 11
(E) 12
Rationale: 39/11 = 1 and 79/11 = 7 ==> 7 - 3 = 4 Numbers
Answer : C
Answer: (C) 4
Question: It is found that the volume of a cube is numerically equal to its surface area. Then the measure of its edge in meters is:
(A) 4
(B) 6
(C) 8
(D) 9
(E) cannot be determined
Rationale: if edge of cube = a
volume of cube = a^3
surface area = 6(a^2)
then
a^3 = 6(a^2)
a = 6
ANSWER:B
Answer: (B) 6
Question: if there are 30 cans out of them one is poisned if a person tastes very little he will die within 14 hours so if there are mice to test and 24 hours to test, how many mices are required to find the poisned can?
(A) 3
(B) 2
(C) 6
(D) 1
(E) 7
Rationale: as we know only one can is poisoned so try mice every can n notice the time
for ex suppose for ist can time was 12:05 then after 5 min test for can 2 means 12:10..n if 1st can contain poision then according to time it can be cleared..
ANSWER:D
Answer: (D) 1
Question: How long does a train 165 meters long running at the rate of 72 kmph take to cross a bridge 660 meters in length?
(A) 28
(B) 41.25
(C) 55
(D) 18
(E) 12
Rationale: T = (660 + 165)/72 * 18/5
T = 41.25
Answer: B
Answer: (B) 41.25
Question: A particular store purchased a stock of turtleneck sweaters and marked up its cost by 20%. During the New Year season, it further marked up its prices by 25% of the original retail price. In February, the store then offered a discount of 15%. What was its profit on the items sold in February?
(A) 27.5%
(B) 30%
(C) 35%
(D) 37.5%
(E) 40%
Rationale: Assume the total price = 100x
Price after 20% markup = 120x
Price after 25%further markup = 1.25*120x = 150x
Price after the discount = 0.85*150x = 127.5x
Hence total profit = 27.5%
Option A
Answer: (A) 27.5%
Question: Half of 2 percent written as decimal is
(A) 0.01
(B) 0.5
(C) 0.05
(D) 0.005
(E) None of these
Rationale: Explanation:
It will be 1/2(2%) = 1/2(2/100) = 2/200 = 0.01
Option A
Answer: (A) 0.01
Question: If books bought at prices ranging from Rs. 98 to Rs. 195 are sold at prices ranging from Rs. 120 to Rs 215, what is the greatest possible profit that might be made in selling 13 books ?
(A) Rs. 1650
(B) Rs. 3000
(C) Rs. 1521
(D) Rs. 1400
(E) Rs. 1560
Rationale: The greatest profit is possible only if the cost price of the books are minimum and selling prices are maximum.
Let lowest cost price of the 13 books = 98*13 = Rs. 1,274
Maximum selling price of 13 books = 215 *13 = Rs. 2,795
So, maximum profit = 2795 - 1274 = Rs. 1,521
ANSWER : OPTION C
Answer: (C) Rs. 1521
Question: Two trains A and B starting from two points and travelling in opposite directions, reach their destinations 9 hours and 4 hours respectively after meeting each other. If the train A travels at 60kmph, find the rate at which the train B runs.
(A) 40
(B) 90
(C) 120
(D) 80
(E) 100
Rationale: If two objects A and B start simultaneously from opposite points and, after meeting, reach their destinations in ‘a’ and ‘b’ hours respectively (i.e. A takes ‘a hrs’ to travel from the meeting point to his destination and B takes ‘b hrs’ to travel from the meeting point to his destination), then the ratio of their speeds is given by:
Sa/Sb = √(b/a)
i.e. Ratio of speeds is given by the square root of the inverse ratio of time taken.
Sa/Sb = √(4/9) = 2/3
This gives us that the ratio of the speed of A : speed of B as 2:3.
Since speed of A is 60 kmph, speed of B must be 60*(3/2) = 90 kmph
Answer B
Answer: (B) 90
Question: I bought three toys for my triplet boys (one for each). I placed the toys in the dark store. One by one each boy went to the store and pick the toy. What is the probability that no boy will choose his own toy?
(A) 1/3
(B) 2/3
(C) 3/3
(D) 4/3
(E) 5/3
Rationale: Solution:
1/3
Assuming T1 is the Toy for brother1, T2 is the toy for brother2 and T3 is the toy for brother3.
Following are the possible cases for toys distribution:
Boy1 Boy2 Boy3
T1 T2 T3
T1 T3 T2
T2 T1 T3
T2 T3 T1 .... (A)
T3 T1 T2 .... (B)
T3 T2 T1
In both steps (A) & (B), no one gets the correct toy.
Therefore probability that none brother can get the own toy is 2/6 = 1/3
Answer A
Answer: (A) 1/3
Question: A man, a woman and a boy can complete a job in 3 days, 4 days and 12 days respectively. How many boys must assist 1 man and 1 woman to complete the job in 1/4th of a day?
(A) 10
(B) 41
(C) 31
(D) 21
(E) 22
Rationale: Explanation:
1 man’s 1 day’s work = 1/3, ¼ day’s work = 1/3 × ¼ = 1/12
1 woman’s 1 day’s work = ¼, ¼ day’s work = ¼ × ¼ = 1/16
1 boy’s 1 day’s work = 1/12, ¼ day’s work = 1/12 × ¼ = 1/48
Let ‘x’ be the No. of boys required.
Then, (1 man + 1 woman + x boy)’s ¼ day’s work 1/12 + 1/16 + x/48 = 1
= (4 + 3 + x)/48 = 1
i.e. 7 + x= 48 and x = 41.
Answer: Option B
Answer: (B) 41
Question: At present, the ratio between the ages of Amit and Dhiraj is 5 : 4. After 6 years, Amit’s age will be 26 years. What is the age of Dhiraj at present?
(A) 16
(B) 77
(C) 566
(D) 197
(E) 161
Rationale: Explanation:
Let the present ages of Amit and Dhiraj be 5x years and 4x years respectively. Then,
5x + 6 = 26
5x = 20
x = 4
Dhiraj’s age = 4x = 16 years
ANSWER: A
Answer: (A) 16
Question: A and B invests Rs.3000 and Rs.4000 respectively in a business. If A doubles his capital after 6 months. In what ratio should A and B divide that year's profit?
(A) 9:6
(B) 9:8
(C) 9:1
(D) 9:9
(E) 9:5
Rationale: (3*6 + 6*6): (4*12)
54:48 => 9:8.Answer:B
Answer: (B) 9:8
Question: If x-y=10, which of the following must be true?
I. Both x and y are positive
II. If x is negative, y must be negative
III.If x is positive, y must be positive
(A) I only
(B) II only
(C) III only
(D) I and II
(E) II and III
Rationale: The best way to approach such questions is to plug in values for x and y
Given: x-y=10
I. Both x and y are positive:
Let x=12 and y=2
x-y=10
But,
Let x=6 and y=-4
x-y=8
Therefore, NOT TRUE
III. If x is positive, y must be positive
Let x=12 and y=2
x-y=10
But,
Let x = 6 and y=-4
x-y=10
Therefore, NOT TRUE
II. If x is negative, y must be negative
If x is negative, for the expression x-y=8 to be true, y must be a -ve number. Otherwise, the sum of two negative numbers will yield another negative number!
Therefore, TRUE
Ans: 'B'
Answer: (B) II only
Question: If each side of a square is increased by 25%, find the percentage change in its area?
(A) 65.25
(B) 56.25
(C) 65
(D) 56
(E) 25
Rationale: let each side of the square be a , then area = a x a
New side = 125a / 100 = 5a / 4
New area =(5a x 5a) / (4 x 4) = (25a²/16)
increased area== (25a²/16) - a²
Increase %= [(9a²/16 ) x (1/a² ) x 100]% = 56.25%
Answer: B
Answer: (B) 56.25
Question: If the sum and difference of two numbers are 20 and 8 respectively, then the difference of their square is:
(A) 12
(B) 28
(C) 160
(D) 180
(E) 18
Rationale: Let the numbers be x and y.
Then, x + y = 20 and x - y = 8
x2 - y2 = (x + y)(x - y) = 20 * 8 = 160.
ANSWER:C
Answer: (C) 160
Question: If $500 is deposited into a savings account at an annual interest rate of 5% that compounds monthly, what is the value of the investment after 10 years?
(A) $750.00
(B) $823.50
(C) $973.25
(D) $1000.25
(E) $1100.00
Rationale: ROI = 5% per annum compounded Monthly
Tenure, n = 10 years = 120 month
Principal = $500
5% per annum compounded monthly will be a little more than 5% at end of an year compounded anually = 6% per annum (approx)
in 10 years the among simple rate will increase by 60% but at coumpound rate the amount wil increase more by 60%
This question can only be solved by approximation
60% of $500 = $300
i.e. amount after 10 years will be a little more than 500+300 = $800
i.e. B option seems the closest possible answer
Answer: option B
Answer: (B) $823.50
Question: Two jars contain milk and water in the ratio 5: 4 and 2: 1 regpectively. What volume should be taken out from the first jar if volumes have to be taken out from both jars so as to fill up a third 30 l jar with milk to water in the ratio 1: 1 ?
(A) 7.5 l
(B) 15 l
(C) 22.5 l
(D) It is impossible
(E) none of these
Rationale: In both jars concentration of milk is more than 50%.
Therefore, in jar three concentration of milk cannot be 50%.
Hence, we cannot decide the volumes
ANSWER:D
Answer: (D) It is impossible
Question: A clock shows the time as 9 a.m. If the minute hand gains 5 minutes every hour, how many minutes will the clock gain by 5 p.m.?
(A) 30 min
(B) 35 min
(C) 45 min
(D) 40 min
(E) 55 min
Rationale: there are 8 hours in between 9 a.m. to 5 p.m.
8*5=40 minutes.
ANSWER:D
Answer: (D) 40 min