mathewhe/aqua_rat huggingface dataset:
Question: If the sum of two numbers is 22 and the sum of their squares is 404, then the product of the numbers is
(A) 40
(B) 44
(C) 80
(D) 88
(E) 90
Rationale: Sol.
Let the numbers be x and y.
Then, (x+y) = 22 and x2 + y2 = 404.
Now, 2xy = (x+y)2 - (x2 + y2)
= (22)2 - 404 = 484 - 404 = 80
xy = 40.
Answer A
Answer: (A) 40
Question: Worker A takes 10 hours to do a job. Worker B takes 15 hours to do the same job. How long it take both A & B, working together but independently, to do the same job?
(A) 40 days
(B) 40/9 days
(C) 39/9 days
(D) 6 days
(E) 60/9 days
Rationale: A's one hour work = 1/10.
B's one hour work = 1/15.
(A+B)'s one hour work = 1/10+1/15 = 5/30 = 1/6.
Both A & B can finish the work in 6 days
D
Answer: (D) 6 days
Question: Each child has 5 crayons and 14 apples. If there are 10 children, how many crayons are there in total?
(A) 22
(B) 65
(C) 12
(D) 36
(E) 50
Rationale: 5*10=50.Answer is E.
Answer: (E) 50
Question: A person can swim in still water at 4 km/h. If the speed of water 2 km/h, how many hours will the man take to swim back against the current for 6km?
(A) 3
(B) 6
(C) 8
(D) 7
(E) 9
Rationale: M = 4
S = 2
US = 4 - 2 = 2
D = 6
T = 6/2 = 3
Answer: A
Answer: (A) 3
Question: Find the invalid no.from the following series 15, 16, 34, 105, 425, 2124, 12756
(A) 16
(B) 34
(C) 105
(D) 425
(E) 12755
Rationale: 2nd term = (1st term) * 1 + 1 = 15 *1 + 1 = 16.
3rd term = (2nd term) * 2 + 2 = 16 * 2 + 2 = 34
4th term = (3th term) *3 + 3 = 34 * 3 + 3 = 105
5th term = (4th term) * 4 + 4 = 105 * 4 + 4 = 424
6th term = (5th term) * 5 + 5 = 424 * 5 + 5 = 2125
5th term should 424 instead of 425.
D
Answer: (D) 425
Question: which number replaces the question mark and completes the puzzle ?
2 + 2 = 4
3 + 3 = 18
4 + 4 = 48
6 + 6= ?
(A) 135
(B) 150
(C) 185
(D) 180
(E) 190
Rationale: D
180
2 + 2 = 4 {2 * 2 * 1}
3 + 3 = 18 {3 * 3 * 2}
4 + 4 = 48 {4 * 4 * 3}
6 + 6 = 180 {6 * 6 * 5}
Answer: (D) 180
Question: What is the are of an equilateral triangle of side 16 cm?
(A) 64√8 cm2
(B) 64√2 cm2
(C) 62√3 cm2
(D) 64√3 cm2
(E) 44√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) 64√3 cm2
Question: A man deposited Rs 50000 in bank at 8% simple interest in 5 years ago. Now he decided to divide total amount among his 7 sons. How much money will get each son?
(A) 15000
(B) 8000
(C) 12000
(D) 16000
(E) 10000
Rationale: i = (50000*5*8)/100
i = 20000
Each son will get = (50000+20000)/7 = 10000
Answer: E
Answer: (E) 10000
Question: If m/63 is an integer, then each of the following must be an integer EXCEPT
(A) 4
(B) 3
(C) 5
(D) 11/2
(E) 2
Rationale: Now plug m =63 into the answer choices:
A. (63- 28)/7 =5. This is an integer
B. (63+ 21)/7 = 12. This is an integer
C. 14(63)/98 = 9. This is an integer
D. (63^2 - 49)/49 =80. This is an integer
E. (63+ 14)/14 = 11/2. This is NOT an integer
Answer: D
Answer: (D) 11/2
Question: A company charges a fixed rental of Rs. 350 per month. It allows 200 calls free per month. Each call is charge at Rs. 1.4 when the number of calls exceed 200 per month and it charges Rs. 1.6 when the number of calls exceeds 400 per month and so on. A customer made 150 calls in February and 250 calls in march. By how much percent each call is cheaper in March than each call in February.
(A) 28%
(B) 25%
(C) 18.5%
(D) 16%
(E) None of these
Rationale: Solution: Charge per call in February = 350/150 = 7/3 = 2.33
Charge per call in March = [350+(50*1.4)]/250 = 420/250 = 42/25 = 1.68
% Cheaper call rate in March = [(2.33-1.68)/2.33]*100 = 28%.
Answer: Option A
Answer: (A) 28%
Question: 456.62+7.523+59.6=?
(A) 163.45
(B) 523.743
(C) 385.69
(D) 4896.35
(E) 782.96
Rationale: 456.62
7.523
59.6
----------
523.743
Answer is B
Answer: (B) 523.743
Question: A jogger running at 9 km/hr along side a railway track is 240 m ahead of the engine of a 140 m long train running at 45 km/hr in the same direction. In how much time will the train pass the jogger?
(A) 19 sec
(B) 38 sec
(C) 36 sec
(D) 16 sec
(E) 11 sec
Rationale: Speed of train relative to jogger = 45 - 9 = 36 km/hr.
= 36 * 5/18 = 10 m/sec.
Distance to be covered = 240 + 140 = 360 m.
Time taken = 380/10 = 38 sec.
Answer: B
Answer: (B) 38 sec
Question: A person starting with Rs.64 and making 6 bets, wins three times and loses 3times, the wins and loses occurring in random order. The chance for a win is equal to the chance for a loss. If each wager is for half the money remaining at the time of the bet, then the final result is?
(A) Rs.37
(B) Rs.56
(C) Rs.65
(D) Rs.76
(E) Rs.81
Rationale: As the win leads to multiplying the amount by 1.5 and loss leads to multiplying the amount by 0.5, we will multiply initial amount by 1.5 thrice and by 0.5 thrice (in any order).
The overall resultant will remain same.
So final amount with the person will be (in all cases):
=64(1.5)(1.5)(1.5)(0.5)(0.5)(0.5)==64(1.5)(1.5)(1.5)(0.5)(0.5)(0.5)= Rs 2727
Hence the final result is:
64−27=3764−27=37:
A loss of Rs.37
A
Answer: (A) Rs.37
Question: If the sides of a triangle are 21 cm, 19 cm and 5 cm, what is its area?
(A) 42.25 cm2
(B) 57.5 cm2
(C) 42.5 cm2
(D) 47.5 cm2
(E) 52.5 cm2
Rationale: The triangle with sides 21 cm, 19 cm and 5 cm is right angled, where the hypotenuse is 21 cm.
Area of the triangle
= 1/2 * 19 * 5
= 47.5 cm2
Answer: D
Answer: (D) 47.5 cm2
Question: The maximum number of students among them 1345 pens and 775 pencils can be distributed in such a way that each student gets the same number of pens and same number of pencils is:
(A) 91
(B) 10
(C) 6
(D) 5
(E) None of these
Rationale: Explanation:
Required number of students = H.C.F of 1345 and 775 = 5. Answer: D
Answer: (D) 5
Question: 3 people, Amy, Beth, and Cassie, have speeds of 3 mph, 4 mph and 6 mph respectively. They run a race in which Beth gives Amy a head start of 2 hrs. If both Beth and Cassie overtake Amy at the same time, what head start did Cassie give Amy?
(A) 3 hours
(B) 4 hours
(C) 5 hours
(D) 9 miles
(E) 10 miles
Rationale: Question clearly states that A started first. B started after 2 hours and we need to determine When did C start.
As per the question, we know that All three meet at the same point.
So, we can determine when did A and B meet. The point they will meet would be the same at which C will be present at that time.
So,
A and B will meet after t = 6/(4-3) = 6 hours.
In these 6 hours, B would have covered 4*6=24 miles.
=> C would also have covered 24 miles and that would be in 24/6=4 hours.
Thus, C started 2 hours after B or 4 hours after A. hence, answer is B.
Answer: (B) 4 hours
Question: Set #1 = {A, B, C}
Set #2 = {K, L, M, N, O, P}
There are these two sets of letters, and you are going to pick exactly one letter from each set. What is the probability of picking at least one vowel?
(A) 1/6
(B) 1/3
(C) 4/9
(D) 2/3
(E) 5/6
Rationale: So Not a vowel in Set-1 : 2/3
And not a vowel in Ser-2:5/6
Now,
2/3∗5/6=5/9
This is for not a vowel.
Then for at least one vowel will be = 1−5/9=4/9
Answer will be C.
Answer: (C) 4/9
Question: P is a set of four numbers 1, 2, 3 and 1. In every step, one is added to any two numbers in the set P. In how many such steps is it possible to make all the four numbers in the set P equal?
(A) 4
(B) 5
(C) 6
(D) 1
(E) 2
Rationale: If all the four numbers are equal, then their sum in the end of the process must be multiple of 4.
Now the sum of the given numbers is equal to 7. Each time we are adding 1 to two of any two numbers, so the sum increases by 2 each time. So the sum never becomes a multiple of 4 as odd + even = always odd.
Answer:A
Answer: (A) 4
Question: If a is a positive integer, and if the units digit of a^2 is 4 and the units digit of (a+1)^2 is 9, what is the units digit of (a+2)^2?
(A) 0
(B) 2
(C) 4
(D) 6
(E) 8
Rationale: If the units digit of a^2 is 4, then the units digit of a is either 2 or 8.
If the units digit of (a+1)^2 is 9, then the units digit of a+1 is either 3 or 7.
To satisfy both conditions, the units digit of a must be 2.
Then a+2 has the units digit of 4, thus the units digit of (a+2)^2 will be 6.
The answer is D.
Answer: (D) 6
Question: A, B and C are entered into a partnership. A invested Rs.6500 for 6 months, B invested Rs.8400 for 5 months and C invested for Rs.10000 for 3 months. A is a working partner and gets 5% of the total profit for the same. Find the share of C in a total profit of Rs.7400.
(A) 1278
(B) 1900
(C) 2888
(D) 2771
(E) 2322
Rationale: 65 * 6 : 84 * 5 : 100 * 3
26:28:20
C share = 74000 * 95/100 = 7030 * 20/74 => 1900
Answer: B
Answer: (B) 1900
Question: You have 5 sticks of lengths 20, 30, 40, 50, and 60 centimeters. The number of non-congruent triangles that can be formed by choosing three of the sticks to make the sides is
(A) 3
(B) 6
(C) 7
(D) 10
(E) 12
Rationale: The length of any side of a triangle must be larger than the positive difference of the other two sides, but smaller than the sum of the other two sides.
Based on this there can be only 7 triangles formed: (20, 30, 40), (20, 40, 50), (20, 50, 60), (30, 40, 50), (30, 40, 60), (30, 50, 60), (40, 50, 60).
Answer; C
Answer: (C) 7
Question: The product of two numbers is 120 and the sum of their squares is 289. The sum of the number is
(A) 20
(B) 23
(C) 27
(D) 150
(E) 255
Rationale: Explanation:
We know
(x+y)2=x2+y2+2xy
=>(x+y)2=289+2(120)
=>(x+y)=529−−−√=23
Option B
Answer: (B) 23
Question: A car mechanic purchased four old cars for Rs. 1 lakh. He spent total 2 lakh in the maintenance and repairing of these four cars. what is the average sale price of the rest three cars to get 80% total profit if he has already sold one of the four cars at Rs. 1.2 lakh?
(A) 1.8 lakh
(B) 1.4 lakh
(C) 1.9 lakh
(D) 8.1 lakh
(E) 6.1 lakh
Rationale: Explanation:
Total cost of 4 cars = 1+2 = 3 lakh
Total SP of 4 cars = 3 x 1.8 = 5.4 lakh
SP of 1 car = 1.2 lakh
SP of rest 3 cars = 5.4 - 1.2 = 4.2 lakh
Average SP of all the 3 cars = 1.4 lakh
Answer: B)
Answer: (B) 1.4 lakh
Question: The Reserve Bank of India will transfer its surplus profit of 65,896 crore rupees to the Centre. This amount is ___ percent higher than previous year.
(A) 25%
(B) 29%
(C) 35%
(D) 28%
(E) 65%
Rationale: ANSWER: A
Answer: (A) 25%
Question: S1 = 2
S2 = 5
...
Sn = 3n + 4
For the sequence above, in which any term n is defined as 3n + 4, what is the value of n for the first term in the sequence to exceed 50?
(A) 13
(B) 12
(C) 14
(D) 11
(E) 16
Rationale: term 16 = 3*16+4 = 52
Answer : E
Answer: (E) 16
Question: If w>0, which of the following must be true?
(A) 1 < w
(B) 0 <w < 2
(C) -1 < w < 1
(D) -10 < w
(E) 1/100 < w
Rationale: All we know is that w is some positive number. Right away we can see that D must be true: if w is positive then it MUST be true that it's greater than -10. Still let's check each option.
A. 1 < w. We don't know whether the number is greater than 1, it could be a positive number less than or equal to 1. Discard.
B. 0 < w < 2. The same here: we don't know whether the number is less than 2, it could be more than or equal to 2. Discard.
C. -1 < w < 1. The same as A. Discard.
E. 1/100 < w. We don't know whether the number is greater than 1/100, it could be a positive number less than or equal to 1/100. Discard.
Answer: D.
Answer: (D) -10 < w
Question: A and B go around a circular track of length 300 m on a cycle at speeds of 18 kmph and 54 kmph. After how much time will they meet for the first time at the starting point?
(A) 120 sec
(B) 198 sec
(C) 60 sec
(D) 665 sec
(E) 276 sec
Rationale: Time taken to meet for the first time at the starting point
= LCM { length of the track / speed of A , length of the track / speed of B}
= LCM { 300/ (90 * 5/18) , 300/ (54 * 5 /18) }
= LCM (12, 20) = 60 sec.
Answer:C
Answer: (C) 60 sec
Question: How is 1% expressed as a decimal fraction?
(A) 0.1
(B) 0.001
(C) 0.01
(D) 0.0001
(E) 1
Rationale: 1/100= 0.01
ANSWER:C
Answer: (C) 0.01
Question: The average age of three boys is 40 years and their ages are in proportion 6:10:8. What is the age in years of the youngest boy?
(A) 8
(B) 10
(C) 7
(D) 6
(E) 5
Rationale: 6x + 10x + 8x = 40
x =1.6
6x = 10
Answer:B
Answer: (B) 10
Question: In a company, 48 percent of the employees are men. If 60 percent of the employees are unionized and 70 percent of these are men, what percent of the non-union employees are women?
(A) 85%
(B) 80%
(C) 75%
(D) 70%
(E) 65%
Rationale: The percent of employees who are unionized and men is 0.7*0.6 = 42%
The percent of employees who are unionized and women is 60 - 42 = 18%
52% of all employees are women, so non-union women are 52%-18% = 34%
40% of all employees are non-union.
The percent of non-union employees who are women is 34%/40% = 85%
The answer is A.
Answer: (A) 85%
Question: A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 sec. The speed of the train is?
(A) 17 km/hr
(B) 50 km/hr
(C) 76 km/hr
(D) 55 km/hr
(E) 51 km/hr
Rationale: Speed of the train relative to man = 125/10 = 25/2 m/sec.
= 25/2 * 18/5 = 45 km/hr
Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr.
x - 5 = 45 => x
= 50 km/hr.
Answer: B
Answer: (B) 50 km/hr
Question: 4/15 of 5/7 of a number is greater than 4/9 of 2/5 of the same number by 8.
What is half of that number?
(A) 315
(B) 310
(C) 314
(D) 318
(E) 319
Rationale: Let the number be x. then 4/15 of 5/7 of x-4/9 of 2/5 of x=8<=>4/21x-8/45x=8
<=>(4/21-8/45)x=8<=>(60-56)/315x=8<=>4/315x=8
x=(8*315)/4=630<=>1/2x=315
Answer is A.
Answer: (A) 315
Question: A man's regular pay is $3 per hour up to 40 hours. Overtime is twice the payment for regular time. If he was paid $168, how many hours overtime did he work?
(A) 8
(B) 5
(C) 9
(D) 6
(E) 10
Rationale: Ans is A
At $3 per hour up to 40 hours, regular pay = $3 x 40 = $120 If total pay = $168, overtime pay = $168 - $120 = $48 Overtime rate (twice regular) = 2 x $3 = $6 per hour => number of overtime hours = $48/$6 = 8
Answer: (A) 8
Question: A pump can fill a tank with water in 2 hours. Because of a leak, it took 7 hours to fill the tank. The leak can drain all the water in ?
(A) 15hr 10min
(B) 16hr 20min
(C) 2hr 48min
(D) 15hr
(E) 14hr 25min
Rationale: Work done by the leak in 1 hour = 1/2 - 1/7 = 5/14
Leak will empty the tank in 14/5 hrs = 2hr 48min
Answer is C
Answer: (C) 2hr 48min
Question: A salesmanâ€™s terms were changed from a flat commission of 5% on all his sales to a fixed salary of Rs.1000 plus 2.5% commission on all sales exceeding Rs. 4,000. If his remuneration as per new scheme was Rs. 500 more than that by the previous schema, his sales were worth?
(A) s. 14,000
(B) s. 12,000
(C) s.16,000
(D) s. 40,000
(E) s. 50,000
Rationale: [1000 + (X-4000) * (2.5/100)] - X * (5/100) = 600
X = 16000
ANSWER:C
Answer: (C) s.16,000
Question: A ring x of diameter 16 inches is placed inside another ring y of diameter of 18 inches. How much fraction of the ring x surface is not covered by the ring y?
(A) 13/15
(B) 12/4
(C) 16/17
(D) 22/16
(E) 17/81
Rationale: The questions asks us to find the surface which is not covered by the ring x i.e., area of the surface not covered.
Where as circumference is the length along the edge of the circle,
2*pi*r implies the length of the curve
pi*r^2 implies area enclosed by that curve..hence Area of the circle is considered for this problem
Area of the ring x=pi* r^2, where r=8
=>pi*64
Area of the ring y=pi*81
Surface not covered by the ring x=pi*81-pi*64=Pi*17
fraction of ring y's surface is not covered by a ring x= Pi*17/total area of the ring y
=>Pi*17/Pi*81
17/81
Answer E
Answer: (E) 17/81
Question: On dividing 21 by a number, the quotient is 10 and the remainder is 1. Find the divisor.
(A) 1
(B) 2
(C) 4
(D) 6
(E) 7
Rationale: d = (D-R)/Q
= (21 - 1)/10
= 20/10 = 2
B
Answer: (B) 2
Question: Soniya deposited Rs.8000 which amounted to Rs.9200 after 3 years at simple interest. Had the interest been 2% more. She would get how much?
(A) 9680
(B) 9850
(C) 9745
(D) 9623
(E) 9324
Rationale: (8000*3*2)/100 = 480
9200
--------
9680
ANSWER A
Answer: (A) 9680
Question: A watch was sold at a loss of 10%. If it was sold for Rs.140 more, there would have been a gain of 4%. What is the cost price?
(A) Rs.1000
(B) Rs.1029
(C) Rs.1028
(D) Rs.1007
(E) Rs.1297
Rationale: 90%
104%
--------
14% ---- 140
100% ---- ? => Rs.1000
Answer: A
Answer: (A) Rs.1000
Question: 6 college friends go on vacation together during spring break. Their rental house costs $1250. If each friend pays the same amount and no one has bills smaller than $1, how much money do they pay for the rental?
(A) $1250
(B) $1251
(C) $1252
(D) $1253
(E) $1254
Rationale: In order to divide the sum in 6 parts, the amount must be divisible by 6.
Divisibility rule of 6: A number is divisible by 6 if it is divisible by both 2 and 3
Divisibility rule of 3: A number is divisible by 3 if the sum of the digits is divisible by 3
We need to make this number even in order for it to be divisible by 2.
Sum of digits of 1250 = 8 and 12 is divisible by both 3 and yields an even number.
Hence, we need to add 4 to this number for it to be divisible by 6
Correct Option: E
Answer: (E) $1254
Question: 30% of all fishermen in Piscataquis County are also hunters while only 20% of all hunters are fishermen. If there are 1500 hunters in Piscataquis County then how many fishermen are there?
(A) 800
(B) 1000
(C) 1200
(D) 1500
(E) 1800
Rationale: 800score Official Solution:
People who do both hunting and fishing make 30% of fishermen and 20% of hunters. There are 1500 hunters so 1500 × 20% = 300 pers. do both hunting and fishing. Same people make 30% of all fishermen.30% of fishermen = 300 pers.
Fishermen = (300 / 30) × 100 pers. = 1000 pers.
The correct answer is choice (B).
Answer: (B) 1000
Question: There are two concentric circles with radii 5 and 4. If the radius of the outer circle is increased by 20% and the radius of the inner circle decreased by 50%, by what percent does the area between the circles increase?
(A) 56
(B) 156
(C) 256
(D) 356
(E) 456
Rationale: The area of a circle is piR^2, where R is the radius.
The area of the big circle is 25pi.
The area of the small circle is 16pi.
The area A1 between the circles is 9pi.
When the big circle's radius increases, the new area is 36pi.
When the small circle's radius decreases, the new area is 4pi.
The area A2 between the circles is 32pi.
The ratio of A2/A1 is 32/9 = 3.56 which is an increase of 256%.
The answer is C.
Answer: (C) 256
Question: The function F is defined for all positive integers n by the following rule: f(n) is the number of position integer each of which is less than n, and has no position factor in common with n other than 1. If p is any prime number then f(p)
(A) p-1
(B) p-2
(C) (p+1)/2
(D) (p-1)/2
(E) 2
Rationale: The confusing moment in this question is its wording. Basically question is: how many positive integers are less than given prime number p which has no common factor with p except 1.
Well as p is a prime, all positive numbers less than p have no common factors with p (except common factor 1). So there would be p-1 such numbers (as we are looking number of integers less than p).
If we consider p=7 how many numbers are less than 7 having no common factors with 7: 1, 2, 3, 4, 5, 6 --> 7-2=5.
Answer: B.
Answer: (B) p-2
Question: 12, 38, 116, 350, 1052, ?
(A) 2158
(B) 3158
(C) 2178
(D) 4121
(E) 9186
Rationale: 12
12 × 3 + 2 = 38
38 × 3 + 2 = 116
116 × 3 + 2 = 350
350 × 3 + 2 = 1052
1052 × 3 + 2 = 3158
Answer is B
Answer: (B) 3158
Question: Indu gave Bindu Rs.1250 on compound interest for 2 years at 4% per annum. How much loss would Indu has suffered had she given it to Bindu for 2 years at 4% per annum simple interest?
(A) Rs.10
(B) Rs.2
(C) Rs.5
(D) Rs.3
(E) Rs.4
Rationale: 1250 = D(100/4)2
D = 2
ANSWER:B
Answer: (B) Rs.2
Question: John invests $x at the semi-annual constant compounded rate of 2 percent and also does $8,000 at the quarterly constant compounded rate of 4 percent. If the interests are the same after 1 year, what is the value of x??
(A) 10000
(B) 12000
(C) 16160.8
(D) 14000
(E) 15000
Rationale: A = P(1+r/n)^nt
A= total amount accrued
P = principal deposited
r = rate of interest in decimal form
n = number of times per year, interest compounded
t = time in number of years.
.
x(1+0.02/2)^2 - x = 8,000(1+0.04/4)^4 - 8,000 [ when the principal is subtracted from the total amount accrued , the resulting difference is the interest portion and question states interests are equal)
=> x[(1.01)^2 - 1] = 8,000[(1.01)^4 - 1]
=> x[(1.01)^2 - 1] = 8,000[(1.01)^2+1][(1.01)^2-1] --> Using a^2-b^2 = a+b X a-b formula and cancel common expression on both sides
=> x = 8,000(1.0201+1) =16160.8
Hence answer is C.
Answer: (C) 16160.8
Question: How many 6-digit even numbers can be formed from the digits 1, 2, 3, 4, 5, 6 and 7 so that the digits should not repeat and the second last digit is even?
(A) 320
(B) 720
(C) 6480
(D) 2160
(E) 520
Rationale: let last digit is 2
when second last digit is 4 remaining 4 digits can be filled in 120 ways,similarly is second last digit is 6 remaind 4 digits can be filled in 120 ways,
so for last digit=2,total numbers=240
last digit=4,tot no=240
and last =6,tot no=240
so total of 720 even numbers are possible
ANSWER:B
Answer: (B) 720
Question: If 8 is added to twice a number and this sum is multiplied by 4, the result is the same as if the number is multiplied by 4 and 8 is added to the product. What is the number?
(A) -6
(B) -8
(C) -9
(D) 10
(E) 11
Rationale: let the number be x;
4(8+2x)=4x+8;
x=-6
ANSWER:A
Answer: (A) -6
Question: A sum of money at simple interest amounts to Rs. 815 in 3 years and to Rs. 854 in 4 years. The sum is:
(A) Rs. 650
(B) Rs. 690
(C) Rs. 698
(D) Rs. 700
(E) Rs. 712
Rationale: S.I. for 1 year = Rs. (854 - 815) = Rs. 39.
S.I. for 3 years = Rs.(39 x 3) = Rs. 117.
Principal = Rs. (815 - 117) = Rs. 698.
Answer: Option C
Answer: (C) Rs. 698
Question: Irin, Ingrid and Nell bake chocolate chip cookies in the ratio of 9.18: 5.17: 2.05. If altogether they baked a batch of 148 cookies, what percent of the cookies did Irin bake?
(A) 0.125%
(B) 1.25%
(C) 55.4%
(D) 125%
(E) 0.152%
Rationale: 9.18x+5.17x+2.05x = 16.4x = 148 cookies
x= 148/16.4 = 9 (approx)
So, Irin baked 9*9.18 cookies or 82 cookies (approx)
% share = 82/148 = 55.4 approx
Hence, answer is C.
Answer: (C) 55.4%
Question: According to a survey, at least 48% of people like apples, at least 75% like bananas and at least 80% like cherries. What is the minimum percentage of people who like all three?
(A) 0%
(B) 3%
(C) 8%
(D) 15%
(E) 18%
Rationale: To minimize the percentage who like all three, let's maximize the percentage who like 2 out of 3.
80% like cherries and 20% don't like cherries.
Let's combine this with the people who like bananas.
20% don't like cherries but do like bananas.
55% like cherries and bananas.
25% like cherries but not bananas.
Now let's distribute the people who like apples.
20% like bananas and apples, but not cherries.
25% like cherries and apples, but not bananas.
3% like all three.
52% like cherries and bananas, but not apples.
The answer is B.
Answer: (B) 3%
Question: If x + 4y = 5 and 5x + 6y = 7, then 3x + 5y = ?
(A) 6
(B) 5
(C) 4
(D) 3
(E) 2
Rationale: Add the left terms and right terms of the two equation to obtain a new equation
x + 5x + 4y + 6y = 5 + 7
Group and simplify
6x + 10y = 12
Divide all terms of the above equation by 2 to obtain a new equation
3x + 5y = 6
correct answer A
Answer: (A) 6
Question: At what rate of interest is an amount doubled in two years, when compounded annually?
(A) 41.4%
(B) 43.4%
(C) 31.4%
(D) 30%
(E) 21.4%
Rationale: Let the rate of interest be r. The amount gets doubled in two years => P(1 + r/100)2 = 2p => 1 + r/100 = √2 => r/100 = √2 - 1 = 0.414 => r = 100(0.414) = 41.4%
ANSWER:A
Answer: (A) 41.4%
Question: Which of the following is greatest?
(A) 2/3
(B) 6/3
(C) 7/3
(D) 8/3
(E) 10/3
Rationale: simply we know that 10/3 is greater than all others.
Answer is : E
Answer: (E) 10/3
Question: There were two candidates in an election. Winner candidate received 62% of votes and won the election by 288 votes. Find the number of votes casted to the winning candidate?
(A) 776
(B) 744
(C) 299
(D) 257
(E) 125
Rationale: W = 62% L = 38%
62% - 38% = 24%
24% -------- 288
62% -------- ? => 744
Answer:B
Answer: (B) 744