mathewhe/aqua_rat huggingface dataset:
Question: A = {0, 1, -3, 6, -8}
B = {-1, 2, -4, 7}
If a is a number that is randomly selected from Set A, and b is a number that is randomly selected from Set B, what is the probability that ab > 0?
(A) 1/4
(B) 1/3
(C) 2/5
(D) 4/9
(E) 1/2
Rationale: For the product of 2 numbers to be positive either both of them must be positive or both of them must be negative:
P(positive, positive) = 2/5*2/4 = 4/20;
P(negative, negative) = 2/5*2/4 = 4/20.
P = 4/20 + 4/20 = 8/20 = 2/5.
Answer: C.
Answer: (C) 2/5
Question: If (1 / 3.718) = 0.2689, Then find the value of (1 / 0.0003718).
(A) 2689
(B) 2869
(C) 2968
(D) 2986
(E) None of them
Rationale: (1 / 0.0003718 ) = ( 10000 / 3.718 ) = 10000 * (1 / 3.718) = 10000 * 0.2689 = 2689.
Answer is A.
Answer: (A) 2689
Question: A picnic attracts 240 persons. There are 60 more men than women, and 60 more adults than children. How many men are at this picnic?
(A) 240
(B) 75
(C) 110
(D) 130
(E) 85
Rationale: Adult + Children = 240
Let, Children = y
then, Adult = y+60
i.e. y+(y+60) = 240
i.e. y = 90
i.e. Adult = 90+20 = 110
Adults include only Men and Women
i.e. Men + Women = 110
Let women, W = x
then Men, M = x+60
i.e. x+(x+60) = 2x+60 = 110
i.e. x = 25
i.e. Men, M = 25+60 = 85
Answer: Option E
Answer: (E) 85
Question: A certain debt will be paid in 52 installments from January 1 to December 31 of a certain year. Each of the first 22 payments is to be $410; each of the remaining payments is to be $65 more than each of the first 22 payments. What is the average (arithmetic mean) payment that will be made on the debt for the year?
(A) 447.5
(B) 450
(C) 465
(D) 468
(E) 475
Rationale: Total number of installments = 52
Payment per installment for the first 22 installments = 410
Payment per installment for the remaining 30 installments = 410+65=475
Average = (22*410 + 30*475)/52 = 447.50
Answer A
Answer: (A) 447.5
Question: The length of a rectangle is reduced by 20%. By what % would the width have to be increased to maintainthe original area?
(A) 10%
(B) 21%
(C) 25%
(D) 40%
(E) 45%
Rationale: Sol. Required change = (20*100)/(100-20)=25%
C
Answer: (C) 25%
Question: A bag contains 5 red, 6 blue and 2 green balls. If 2 ballsare picked at random, what is the probability that both are red?
(A) 1/13
(B) 2/23
(C) 5/39
(D) 4/27
(E) 3/23
Rationale: P(Both are red),
5C213C2=6C213C2
=10/78=5/39
C
Answer: (C) 5/39
Question: The batting average of a particular batsman is 59 runs in 46 innings. If the difference in his highest and lowest score is 150 runs and his average excluding these two innings is 58 runs, find his highest score.
(A) 156
(B) 208
(C) 210
(D) 223
(E) 229
Rationale: Explanation:
Total runs scored by the batsman = 59*46 = 2714 runs
Now excluding the two innings the runs scored = 58*44 = 2552 runs
Hence the runs scored in the two innings = 2714 – 2552 = 162 runs.
Let the highest score be x, hence the lowest score = x – 150
x + (x - 150) = 162
2x = 312
x = 156 runs
ANSWER A
Answer: (A) 156
Question: How many two digit numbers are there such that the product of their digits after reducing it to the smallest form is a prime number? for example if we take 98 then 9*8=72, 72=7*2=14, 14=1*4=4. Consider only 4 prime no.s (2,3,5,7)
(A) 16
(B) 17
(C) 18
(D) 19
(E) 20
Rationale: we know prime no. are 2 ,3 , 5, 7
mulply by 1 is prime no
2 = 21(2*1)=73(7*3)
2 = 21 (2*1)=37(3*7)
2= 12(1*2)=43(4*3)or34(3*4)
or26(2*6)or62(6*2)
.
.
.similarly for all prime no then u will got it....
12,13,15,17,21,26,31,34,35,37,43,51,53,57,62,71,73,75
ans is 18
ANSWER:C
Answer: (C) 18
Question: When positive integer N is divided by positive integer J, the remainder is 12. If N/J = 134.08, what is value of J?
(A) 22
(B) 56
(C) 78
(D) 112
(E) 150
Rationale: 1) We know that
decimal part of decimal quotient ={remainder/divisor}
So 0.08, the decimal part of the decimal quotient, must equal the remainder, 12, divided by the divisor J.
0.08 = 12/J
0.08*J = 12
J = 12/0.08 = 1200/8 = 300/2 = 150
So J = 150, answer = E.
Answer: (E) 150
Question: A man has Rs.10350 in the form of Rs.50 notes and Rs.500 notes. The total number of notes are 90.Find the number of notes of Rs.50 denomination.
(A) 15
(B) 21
(C) 17
(D) 57
(E) 77
Rationale: Total Money = Rs. 10350.
Let 50 rupees note was X.
Then 500 rupees note = 90 - X
Now,
50*X + 500 * (90 - X) = 10350
50X + 45000 - 500X = 10350
- 450X = - 34650
X = 77.
No. of 50 rupees note = 77.
Answer: Option E
Answer: (E) 77
Question: What is the difference between the C.I. on Rs. 5000 for 1 1/2 years at 4% per annum compounded yearly and half-yearly?
(A) Rs.2.04
(B) Rs.2.08
(C) Rs.2.02
(D) Rs.2.83
(E) Rs.2.42
Rationale: C.I. when interest is compounded yearly
= [5000 * (1 + 4/100) * (1 + (1/2 * 4)/100]
= 5000 * 26/25 * 51/50 = Rs. 5304
C.I. when interest is compounded half-yearly
= [5000 * (1 + 2/100)2]
= (5000 * 51/50 * 51/50 * 51/50)
= Rs. 5306.04 Difference
= (5306.04 - 5304)
= Rs.2.04.
Answer: A
Answer: (A) Rs.2.04
Question: A certain NYC taxi driver has decided to start charging a rate of r cents per person per mile. How much, in dollars, would it cost 3 people to travel x miles if he decides to give them a 50% discount?
(A) 3xr/2
(B) 3x/200r
(C) 3r/200x
(D) 3xr/200
(E) xr/600
Rationale: r/100 dollars per person per mile
one person going x miles will be charged rx/100
50% discount = rx/200
3 such people = 3rx/200 ;
ANSWER:D
Answer: (D) 3xr/200
Question: How many of the following numbers are divisible by 132?
396, 462, 792, 965, 2178, 5184, 6336
(A) 3
(B) 5
(C) 6
(D) 7
(E) 8
Rationale: Explanation:
A number is divisible by 132, if it is divisible by each one of 11, 3 and 4.
Clearly, 965 is not divisible by 3. None of 462 and 2178 is divisible by 4.
Also, 5184 is not divisible by 11.
Each one of remaining 3 is divisible by each one of 11, 3 and 4 and therefore, by 132.
Answer: A
Answer: (A) 3
Question: In the coordinate plane, one of the vertices of a square is the point (-5, -4). If the diagonals of that square intersect at point (3, 2), what is the area of that square?
(A) 100
(B) 225
(C) 169
(D) 256
(E) 324
Rationale: One point (-5-4), Intersection (3,2) so the distance from the first point -5-3=-8 is the midpoint of the square --> whole side 16, 16*16=256
D
Answer: (D) 256
Question: A train 125 m long passes a man, running at 8 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is:
(A) 35 km/hr
(B) 53 km/hr
(C) 45 km/hr
(D) 65 km/hr
(E) 87 km/hr
Rationale: Speed of the train relative to man
= (125/10) m/sec = (25/2) m/sec. [(25/2) * (18/5)] km/hr
= 45 km/hr. Let the speed of the train be x km/hr. Then, relative speed
= (x - 8) km/hr. x - 8 = 45 ==> x = 53 km/hr.
Answer: B
Answer: (B) 53 km/hr
Question: Right triangle ABC is to be drawn in the xy-plane so that the right angle is at A and AB is parallel to the y-axis. If the x- and y-coordinates of A, B, and C are to be integers that are consistent with the inequalities -3 ≤ x ≤ 2 and 4 ≤ y ≤ 9 , then how many different triangles can be drawn that will meet these conditions?
(A) 54
(B) 432
(C) 2,160
(D) 2,916
(E) 148,824
Rationale: We have the rectangle with dimensions 9*3 (9 horizontal dots and 3 vertical). AB is parallel to y-axis and AC is parallel to x-axis.
Choose the (x,y) coordinates for vertex A: 9C1*3C1;
Choose the x coordinate for vertex C (as y coordinate is fixed by A): 8C1, (9-1=8 as 1 horizontal dot is already occupied by A);
Choose the y coordinate for vertex B (as x coordinate is fixed by A): 2C1, (3-1=2 as 1 vertical dot is already occupied by A).
9C1*3C1*8C1*2C1=432.
Answer: B.
Answer: (B) 432
Question: What is the % change in the area of a rectangle when its length increases by 10% and its width decreases by 10%?
(A) 0%
(B) 20% increase
(C) 20% decrease
(D) 1% decrease
(E) Insufficient data
Rationale: Explanatory Answer
Whenever you encounter problems like this, use a numerical example and then proceed.
For ease of computation, it is safe in most cases, to assume the length to be 100 units and the width to be 100 units.
(Remember, a square is a rectangle too and the problem works the same way when you assume different values for length and width. Computation becomes a bit tedious with different values for length and width)
Area of a rectangle = length * width = 100 * 100 = 10,000 sq units.
When the length increases by 10%, the new length becomes 110 units.
And as the width decreases by 10%, new width becomes 90 units.
Therefore, New area = 110 * 90 = 9900 sq units.
New area is 100 sq units lesser than the original area.
% change in area = ((change in area)/(original area)) * 100
= (100/10,000)*100 = 1% decrease in area
The correct choice is (D)
Answer: (D) 1% decrease
Question: How many digits will be there to the right of the decimal point in the product of 95.75 and .02554?
(A) 5
(B) 6
(C) 7
(D) 8
(E) 9
Rationale: Solution
Som of decimal places	= 7.
Since the last digit to the extreme right will be zero ( ∴ 5 x 4 = 20), so there will be 6 significant digits to the right of the decimal point.
Answer B
Answer: (B) 6
Question: The product of the prime integers between 53 and 60, inclusive, is:
(A) 50! – 40!
(B) 178,239
(C) 2,303
(D) 2,021
(E) 2,000
Rationale: only prime number bet ween 53 and 60 inclusive are 53, 57, 59
thus 53*57 * 59= 178,239
Ans: B
Answer: (B) 178,239
Question: If (4 - x)/(4 + x) = x, what is the value of x^2 + 5x - 4?
(A) 0
(B) 2
(C) 4
(D) 6
(E) 8
Rationale: (4-x) = x*(4+x)
(4-x) = 4x+x^2
0 = x^2+5x-4
The answer is A.
Answer: (A) 0
Question: Rohan spends 40% of his salary on food, 20% on house rent, 10% on entertainment and 10% on conveyance. If his savings at the end of a month are Rs. 3000. then his monthly salary is
(A) Rs. 15000
(B) Rs. 12000
(C) Rs. 9000
(D) Rs. 6000
(E) Rs. 3000
Rationale: Sol.
Saving = [100 - (40 + 20 + 10 + 10]% = 20%.
Let the monthly salary be Rs. x.
Then, 20% of x = 3000
â‡” 20 / 100x = 3000
â‡” x = 3000 Ã— 5 = 15000.
Answer A
Answer: (A) Rs. 15000
Question: In a two digit number, if it is known that its units digit exceeds its ten's digit by 2 and that the product of the given number and the sum of its digits is equal to 144, then the number is
(A) 42
(B) 46
(C) 22
(D) 24
(E) None
Rationale: Sol.
Let the ten's digit be x.
Then, units digit = x + 2.
Number = 10x + (x+2) = 11x + 2;
Sum of digits = x + (x+2) = 2x +2.
∴ (11x +2)(2x+2) = 144
⇔ 22x2 + 26x - 140 = 0
⇔ 11x2 + 13x - 70 = 0
⇔ (x - 2)(11x+35) = 0 ⇔ x =2.
Hence, required number = 11x + 2 = 24.
Answer D
Answer: (D) 24
Question: Suresh can complete a job in 15 hours. Ashutosh alone can complete the same job in 35 hours. Suresh works for 9 hours and then the remaining job is completed by Ashutosh. How many hours will it take Ashutosh to complete the remaining job alone?
(A) 4
(B) 5
(C) 14
(D) 12
(E) None of these
Rationale: The part of job that Suresh completes in 9 hours
= 9â„15 = 3â„5
Remaining job = 1 - 3â„5 = 2â„5
Remaining job can be done by Ashutosh in 2â„5 Ã— 35 = 14 hours
Answer C
Answer: (C) 14
Question: In how many ways can 7 boys be seated in a circular order?
(A) 110
(B) 230
(C) 720
(D) 420
(E) 680
Rationale: Number of arrangements possible
=(7−1)!=6!=6x5x4x3x2x1=720
Answer: C
Answer: (C) 720
Question: If y is 70 percent greater than x, then x is what percent less than y?
(A) 41%
(B) 47%
(C) 55%
(D) 63%
(E) 70%
Rationale: y = 1.7x
x = y/1.7 = 10y/17 = y - (7/17)*y
7/17 is about 41%.
The answer is A.
Answer: (A) 41%
Question: Find k if 56 / k = 4.
(A) 16
(B) 17
(C) 18
(D) 14
(E) 13
Rationale: Since 56 /k = 4 and 56/ 14 = 4, then
k = 14 correct answer D
Answer: (D) 14
Question: The circumferences of two circles are 264 meters and 352 meters. Find the difference between the areas of the larger and the smaller circles?
(A) 4329
(B) 2799
(C) 4312
(D) 2799
(E) 2712
Rationale: Let the radii of the smaller and the larger circles be s m and l m respectively.
2∏s = 264 and 2∏l = 352
s = 264/2∏ and l = 352/2∏
Difference between the areas = ∏l2 - ∏s2
= ∏{1762/∏2 - 1322/∏2}
= 1762/∏ - 1322/∏
= (176 - 132)(176 + 132)/∏
= (44)(308)/(22/7) = (2)(308)(7) = 4312 sq m
Answer: C
Answer: (C) 4312
Question: A certain sum of money at simple interest amounted Rs.840 in 10 years at 3% per annum, find the sum?
(A) 277
(B) 262
(C) 298
(D) 646
(E) 267
Rationale: 840 = P [1 + (10*3)/100]
P = 646
Answer: D
Answer: (D) 646
Question: Find the least number must be subtracted from 62575 so that remaining number is divisible by 99.
(A) 93
(B) 7
(C) 54
(D) 9
(E) 6
Rationale: On dividing 62571 by 99 we get the remainder 7, so 7 should be subtracted. Answer is
B
Answer: (B) 7
Question: A train passes a station platform in 36 sec and a man standing on the platform in 20 sec. If the speed of the train is 18 km/hr. What is the length of the platform?
(A) 80
(B) 240
(C) 288
(D) 277
(E) 221
Rationale: Speed = 18 * 5/18 = 5 m/sec.
Length of the train =5 * 20 = 100 m.
Let the length of the platform be x m . Then,
(x + 100)/36 = 5 => x = 80 m.
Answer: A
Answer: (A) 80
Question: How many ways are there to split a group of 6 girls into two groups of 3 girls each? (The order of the groups does not matter)
(A) 35
(B) 10
(C) 40
(D) 20
(E) 25
Rationale: the combination is 6C3 /2
= 6!/3!*3!*2 = 20/2 =10
B
Answer: (B) 10
Question: A certain sum amounts to Rs.1725 in 3 years and Rs.1875 in 5 years. Find the rate % per annum?
(A) 9%
(B) 5%
(C) 3%
(D) 1%
(E) 8%
Rationale: 3 --- 1725
5 --- 1875
--------------
2 --- 150
N = 1 I = 75 R = ?
P = 1725 - 225 = 1500
75 = (1500*1*R)/100
R = 5%
Answer: B
Answer: (B) 5%
Question: In how many different ways can the letters of the word 'MATHEMATICS' be arranged so that the vowels always come together?
(A) 120028 ways
(B) 120860 ways
(C) 120960 ways
(D) 120920 ways
(E) 120930 ways
Rationale: In the word 'MATHEMATICS', we treat the vowels AEAI as one letter.
Thus, we have MTHMTCS (AEAI).
Now, we have to arrange 8 letters, out of which M occurs twice, T occurs twice and the rest are different.
Number of ways of arranging these letters =	8!/(2!)(2!)	= 10080.
Now, AEAI has 4 letters in which A occurs 2 times and the rest are different.
Number of ways of arranging these letters =	4!/2!	= 12.
Required number of words = (10080 x 12) = 120960.
Answer:C
Answer: (C) 120960 ways
Question: The probability that A speaks truth is 3/5 and that of B speaking truth is 4/7. What is the probability that they agree in stating the same fact?
(A) 18/35
(B) 18/37
(C) 18/39
(D) 18/33
(E) 18/31
Rationale: If both agree stating the same fact, either both of them speak truth of both speak false.
Probability = 3/5 * 4/7 + 2/5 * 3/7
= 12/35 + 6/35
= 18/35
Answer:A
Answer: (A) 18/35
Question: The L.C.M of two numbers is 2310 and their H.C.F is 30. If one number is 330 the Other is
(A) 330
(B) 300
(C) 210
(D) 250
(E) 350
Rationale: The other number
= L.C.M * H.C.F/given number
= 2310*30/330 = 210
Answer is C.
Answer: (C) 210
Question: A certain car uses one gallon of gasoline every 36 miles when it travels on highway, and one gallon of gasoline every 20 miles when it travels in the city. When a car travels 4 miles on highway and 4 additional miles in the city, it uses what percent more gasoline than if it travels 8 miles on the highway?
(A) 15%
(B) 20%
(C) 22.5%
(D) 25%
(E) 40%
Rationale: 4 miles on the highway = 4/36 gallons;
4 miles in the city = 4/20 gallons;
Total = 4/36 + 4/20 = 14/45 gallons.
8 miles on the highway = 8/30 gallons .
The % change = (14/45 - 8/36)/(8/36) = 0.40.
Answer: E.
Answer: (E) 40%
Question: If the selling price of 50 articles is equal to the cost price of 40 articles, then the loss or gain percent is:
(A) 20% loss
(B) 20% gain
(C) 25% loss
(D) 25% gain
(E) 35% gain
Rationale: Let C.P. of each article be Re. 1.
Then, C.P. of 50 articles = Rs. 50;
S.P. of 50 articles = Rs. 40.
Loss % = 10/50 * 100 = 20%
ANSWER:A
Answer: (A) 20% loss
Question: The set X consists of the following terms: {4,44,444,4444,.....}, where the nth term has n 4's in it for example 10th term is 4444444444. What is the hundreds digit of the sum of the first 35 terms of set X?
(A) 1
(B) 3
(C) 5
(D) 7
(E) 9
Rationale: 35*4 + 34*40 + 33*400 = 140 + 1360 + 13200 = 14700
The hundreds digit is 7.
The answer is D.
Answer: (D) 7
Question: If log10 5 + log10 (5x + 1) = log10 (x + 5) + 1, then x is equal to:
(A) 15
(B) 8
(C) 9
(D) 3
(E) 10
Rationale: Explanation:
log10 5 + log10 (5x + 1) = log10 (x + 5) + 1
log10 5 + log10 (5x + 1) = log10 (x + 5) + log10 10
log10 [5 (5x + 1)] = log10 [10(x + 5)]
5(5x + 1) = 10(x + 5)
5x + 1 = 2x + 10
3x = 9
x = 3.
answer D
Answer: (D) 3
Question: One water pump can fill half of a certain empty tank in 6 hours. Another pump can fill half of the same tank in 6.5 hours. Working together, how long will it take these two pumps to fill the entire tank?
(A) 6 7/13
(B) 1 5/8
(C) 3 1/4
(D) 6 6/25
(E) 3 1/2
Rationale: One pump can fill a tank in 6 hours and another in 6.5 hours
so the rate at which both can half fill the tank is (1/6+1/6.5) => 25/78
Thus half of the tank can be filled in 78/25
so for filling the complete tank => 78/25*2 = 156/25 = 6 6/25
ANSWER:D
Answer: (D) 6 6/25
Question: Annika hikes at a constant rate of 10 minutes per kilometer. She has hiked 2.5 kilometers east from the start of a hiking trail when she realizes that she has to be back at the start of the trail in 35 minutes. If Annika continues east, then turns around and retraces her path to reach the start of the trail in exactly 35 minutes, for how many kilometers total did she hike east?
(A) 3.625
(B) 3.5
(C) 3
(D) 4
(E) 4.5
Rationale: Set up two R x T =D cases.
1. 1/10 km/ min x T = 2.5
from which T= 25 mins.
We know total journey time now is 35 +25 = 60
The rate is the same ie 1/10km/min.
set up second R x T =D case.
1/10 km/min x 60 = 6 km
Now the total journey would be halved as distance would be same in each direction. 6/2 =3
C
Answer: (C) 3
Question: A and B invested in a business in the ratio 7 : 11, in the annual profit they donated 10% of the profit to a charity, and after donating, A received Rs.12600 as his share in the profit, then what amount is donated to the charity ?
(A) Rs.2500
(B) Rs.1800
(C) Rs.3600
(D) Rs.1260
(E) Rs.1860
Rationale: Ratio of investments of A and B = 7 : 11 = [18 units].
A received = Rs.12600.
Total profit = 12600 / 7 × 18 = Rs.324000.
Profit after donation = Rs.32400 which is [Profit – 10% = 90% of the actual profit].
Profit before donation = 32400 / 90 × 100 = Rs.36000.
Actual profit = Rs.360000 => Donation = Rs.36000 × 10 / 100 = Rs.3600
Option C
Answer: (C) Rs.3600
Question: In a group of 150 readers who read science fiction or literacy works or both, 120 read science fiction and 90 read literacy works. How many read both science fiction and literacy works?
(A) 70
(B) 60
(C) 90
(D) 100
(E) 110
Rationale: Consider total number of reader n(S U L) = 150
People who read science fiction n(S) = 120
People who read literacy works n(L) = 90
both science fiction and literacy n(S âˆ© L) = ?
n(S U L) = n(S)+ n(L) - n(S âˆ© L)
150 = 120 + 90- n(S âˆ© L)
n(S âˆ© L) = 210 -150
n(S âˆ© L) = 60
SO People read both science fiction and literacy works are 160
ANSWER:B
Answer: (B) 60
Question: 5 men are equal to as many women as are equal to 8 boys. All of them earn Rs.150 only. Menâ€™s wages are?
(A) 6Rs
(B) 2Rs
(C) 4Rs
(D) 9Rs
(E) 10Rs
Rationale: 5M = xW = 8B
5M + xW + 8B ----- 150 Rs.
5M + 5M + 5M ----- 150 Rs.
15M ------ 150 Rs. => 1M = 10Rs.
Answer: E
Answer: (E) 10Rs
Question: A wholesaler marks his wares 60% more than the real price and allows 25% discount. His profit is:
(A) 15%
(B) 20%
(C) 25%
(D) 30%
(E) None of these
Rationale: Let the CP = 100 Rs.
Mark Price = 160
Discount = 25%
Selling price 75/100 Ã— 160
Hence profit = 20%
Answer: B.
Answer: (B) 20%
Question: The principal that amounts to Rs. 5913 in 3 years at 6 1/4 % per annum C.I. compounded annually, is?
(A) s. 3096
(B) s. 4076
(C) s. 4085
(D) s. 4096
(E) s. 5096
Rationale: Principal = [4913 / (1 + 25/(4 * 100))3]
= 5913 * 16/17 * 16/17 * 16/17 = Rs. 5096.
ANSWER:E
Answer: (E) s. 5096
Question: Find the value of (75983*75983- 45983*45983/30000)
(A) 129166
(B) 121696
(C) 126196
(D) 121966
(E) None of them
Rationale: Given expression=(75983)2-(45983)2/(75983-45983)
=(a-b)2/(a-b)
=(a+b)(a-b)/(a-b)
=(a+b)
=75983+45983
=121966
Answer is D.
Answer: (D) 121966
Question: what is the radius of a circle that has a circumference of 3.14 meters?
(A) 0.5 mtr
(B) 1.5 mtr
(C) 2.3 mtr
(D) 0.2 mtr
(E) 1.2 mtr
Rationale: circumference of a cirlce = 2nr, given circumference= 3.14 mtr.
2nr= 3.14, 2 x 3.14 x r= 3.14, = 6.28 x r=3.14, r= 3.14/6.28, = 0.5mtr. correct answer: (A)
Answer: (A) 0.5 mtr
Question: A watch was sold at a loss of 5%. If it was sold for Rs.500 more, there would have been a gain of 5%. What is the cost price?
(A) 1000
(B) 2998
(C) 2778
(D) 2788
(E) 2991
Rationale: 95%
105%
--------
10% ---- 500
100% ---- ? => Rs.5000
Answer:D
Answer: (D) 2788
Question: Marketing executives for a certain chewing gum company projected a 20 percent increase in revenue this year over that of last year, but revenue this year actually decreased by 35%. What percent of the projected revenue was the actual revenue ?
(A) 54.2%
(B) 58%
(C) 62.5%
(D) 64%
(E) 75%
Rationale: Last year revenue = 100 (assume);
This year revenue = 65;
Projected revenue = 120.
Actual/Projected*100=65/120*100 = 54.2%.
Answer: A.
Answer: (A) 54.2%
Question: A windmill is taking advantage of strong air currents in order to produce electrical energy. On a typical day the wind speed is around 20 mph and in that speed the windmill produces 400 kw/h (kilowatts per hour). On a stormy day a windmill produces 20% more energy. How much kw/h can three windmills produce in two hours on a stormy day?
(A) 2880.
(B) 4860.
(C) 5780.
(D) 5760.
(E) 6380.
Rationale: Efficiency per machine = 400 watt/hr
Efficiency due to increase in wind speed = 400*120% => 480 watt/hr
Production by each machine in 2 hours is 480*2 => 960 watt
Production by 3 machines => 960 watt * 3 = 2880 watt
Answer will be (A)
Answer: (A) 2880.
Question: There are k-2 members in a certain band, including Jim and Ellen. Two members are to be selected to attend the Grammy awards ceremony. If there are 3 possible combinations in which Jim and Ellen are not selected, what is the value of k?
(A) 6
(B) 7
(C) 8
(D) 9
(E) 10
Rationale: There are k-2 members in the band, and k-4 members without Jim and Ellen.
(k-4)C2 = 3
(k-4)(k-5)/2 = 3
(k-4)(k-5) = 6 = 3*2
k = 7
The answer is B.
Answer: (B) 7
Question: Two cars cover the same distance at the speed of 60 and 64 kmps respectively. Find the distance traveled by them if the slower car takes 1 hour more than the faster car.
(A) 398
(B) 88
(C) 960
(D) 781
(E) 2891
Rationale: 60(x + 1) = 64x
X = 15
60 * 16 = 960 km.Answer:C
Answer: (C) 960
Question: A sum of money at simple interest amounts to Rs. 805 in 3 years and to Rs. 854 in 4 years. The sum is:
(A) s. 650
(B) s. 690
(C) s. 688
(D) s. 700
(E) s. 718
Rationale: S.I. for 1 year = Rs. (854 - 815) = Rs. 39.
S.I. for 3 years = Rs.(39 x 3) = Rs. 117.
Principal = Rs. (805 - 117) = Rs. 688.
Answer: Option C
Answer: (C) s. 688
Question: Aaron will jog from home at 2 miles per hour and then walk back home by the same route at 4miles per hour. How many miles from home can Aaron jog so that he spends a total of 3 hours jogging and walking?
(A) 5
(B) 7
(C) 3
(D) 9
(E) 10
Rationale: xyt/(x+y)
x= 2, y=4 t= 3
2*4*3/2+4 = 18/6 = 3
Answer : C
Answer: (C) 3
Question: There are 7 points marked on the circumference of a circle. How many hexagons can be formed by connecting 6 points of the 7 points?
(A) 5
(B) 6
(C) 7
(D) 8
(E) 9
Rationale: 7C6=7
The answer is C.
Answer: (C) 7
Question: The numerator of a certain fraction is 8 less than the denominator. If 3 is added to the numerator and 3 is subtracted from the denominator, the fraction becomes 3/4. Find the original fraction?
(A) 2/5
(B) 7/9
(C) 3/11
(D) 8/5
(E) 9/5
Rationale: The denominator be P, the numerator will be (P - 8).
The fraction will be (P - 8)/P.
Adding 3 to the numerator and subtracting 3 from the denominator, (P - 8 + 3)/(P - 3) = 3/4.
(P - 5)/(P - 3) = 3/4
P = 20 - 9 => P = 11.
The fraction is: 3/11.
ANSWER:C
Answer: (C) 3/11
Question: A number whose fifth part increased by 5 is equal to its fourth part diminished by 5 is ?
(A) 160
(B) 180
(C) 200
(D) 220
(E) None
Rationale: Answer
Let the number be N.
Then, (N/5) + 5 = (N/4) - 5
⇒ (N/4) - (N/5) = 10
⇒ (5N - 4N)/20 = 10
∴ N = 200
Option: C
Answer: (C) 200