mathewhe/aqua_rat huggingface dataset:
Question: A sum of Rs. 2678 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) 1629
(B) 1648
(C) 2677
(D) 2986
(E) 2679
Rationale: (x*8*3)/100 = ((2678 - x)*3*5)/100
24x/100 = 40170/100 - 15x/100
39x = 40170 => x = 1030
Second sum = 2678 â€“ 1030 = 1648
Answer:B
Answer: (B) 1648
Question: Each of three investments has a 20% of becoming worthless within a year of purchase, independently of what happens to the other two investments. If Simone invests an equal sum in each of these three investments on January 1, the approximate chance that by the end of the year, she loses no more than 1/3 of her original investment is
(A) 90%
(B) 80%
(C) 70%
(D) 60%
(E) 40%
Rationale: Since amount invested is same for all 3 , and probability of investment turning worthless is 20%, the required probability is
80%×80%×80% + 20%×80%×80×\frac{3!}{2!}
=89.6%
Answer A
Answer: (A) 90%
Question: If xy not equal 0 and x^2*y^2 -xy = 20, which of the following could be y in terms of x?
I. 1/2x
II. -5/x
III. 4/x
(A) II
(B) II and III
(C) I &II
(D) III
(E) IV
Rationale: x2y2 - xy = 20
x2y2-xy-20 = 0
(xy-4)(xy+5)=0
xy = 4 or xy=-5
y = 4/x or y = -5/x
II and III only
B
Answer: (B) II and III
Question: The price of the jewel, passing through three hands, rises on the whole by 74%. If the first and the second sellers 20% and 25% profit respectively find the percentage profit earned by the third seller.
(A) 20
(B) 10
(C) 16
(D) 25
(E) 30
Rationale: Let the original price of the jewel be $ p and let the profit earned by the third seller be x% Then, (100+x)% of 125% of 120% of P =174% Of P ((100+X)/100*125/100*120/100*P)=(174/100*P)
==> (100+X)=(174*100*100)/(125*120)=116=>X=16%
Answer C
Answer: (C) 16
Question: Write 230,000,000,000 in scientific notation.
(A) 2.3 x 10*11*eleventh
(B) 2.03 x 10*11*eleventh
(C) 23 x 10*11*eleventh
(D) 23.0 x 10*11*eleventh
(E) 230 x 10*11*eleventh
Rationale: a × 10 n , where a is a real number such that 1 ≤ |a| < 10 and n is an integer.
230,000,000,000 = 2.3 × 100,000,000,000 = 2.3 × 10 *11*
correct answer A)2.3 x 10*11*eleventh
Answer: (A) 2.3 x 10*11*eleventh
Question: A man bought 40 shares of Rs. 60 at 7 discount, the rate of dividend being 1212%The rate of interest obtained is
(A) 13.64%
(B) 15.5%
(C) 14%
(D) 14.15%
(E) 14.95%
Rationale: Explanation :
Face Value of a share = Rs.60
He bought each share at Rs.60 - Rs.7 = Rs.53
Number of shares = 40
Dividend = 12 1/2%=25/2%
Dividend per share = 60×25/2×100=Rs.7.5
Total dividend = (40 × 7.5)
ie, He got a dividend of (40 × 7.5) for an investment of Rs.(40 × 53)
Interest obtained = 40×7.5×100/40×53=14.15%
Answer : Option D
Answer: (D) 14.15%
Question: In a chocolate company, 30 men completed two-fifth of a piece of work in 28 days. How many more men should be employed to finish the rest of the work in 35 more days?
(A) 32
(B) 36
(C) 6
(D) 8
(E) 7
Rationale: Explanation :
Solution: Let the total number of men be x. work done = 2/5, remaining work = (1-2/5) = 3/5.
More work, more men (DP)
More days, less men (IP)
work 2/5 : 3/5
} : : 30 : x
days 35 : 28
.'. (2/5 * 35 * x) = 3/5 * 28 * 30
=> x = 36.
Answer : C
Answer: (C) 6
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: EXPLANATION
Sum of decimal places = 7.
Since the last digit to the extreme right will be zero (since 5 x 4 = 20), so there will be 6 significant digits to the right of the decimal point.
Answer B
Answer: (B) 6
Question: A retailer bought a shirt at wholesale and marked it up 80% to its initial price of $45. By how many more dollars does he need to increase the price to achieve a 100% markup?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: x is the buy price. x+80%x = 1,8x is the sale price = 45 so x, the buy price becomes 45/1,8=25
%100 mark up means x+100%x=2x so 50. 50-45=5
ANSWER:E
Answer: (E) 5
Question: In a group of 80 children and 10 youngsters, each child got sweets that are 15% of the total number of children and each youngster got sweets that are 25% of the total number of children. How many sweets were there?
(A) 1160
(B) 1100
(C) 1080
(D) 1210
(E) None of these
Rationale: Number of sweets each child got = 15% of 80 = 15/100 * 80 = 12.
Number of sweets 80 children got = 80 * 12 = 960.
Number of sweets each youngster got = 25% of 80 = 25/100 * 80 = 20.
Number of sweets 10 youngsters got = 10 * 20 = 200.
Total number of sweets = 960 + 200 = 1160.
ANSWER:A
Answer: (A) 1160
Question: If Teena is driving at 55 miles per hour and is currently 7.5 miles behind Yoe, who is driving at 40 miles per hour in the same direction then in how many minutes will Teena be 15 miles ahead of Yoe?
(A) 15
(B) 60
(C) 75
(D) 90
(E) 105
Rationale: This type of questions should be solved without any complex calculations as these questions become imperative in gaining that extra 30-40 seconds for a difficult one.
Teena covers 55 miles in 60 mins.
Yoe covers 40 miles in 60 mins
So teena gains 15 miles every 60 mins
Teena need to cover 7.5 +15 miles.
Teena can cover 7.5 miles in 30 mins
Teena will cover 15 miles in 60 mins
So answer 30+60= 90 mins.D
Answer: (D) 90
Question: How many 2x2x2 cubes could fit in a box of 7x9x4?
(A) 31
(B) 32
(C) 30
(D) 33
(E) 29
Rationale: The answer is A) 31. A 2x2x2 cube has an area of 8. A 7x9x4 box has an area of 252. If you divide 252 by 8, you get 31.5. Since that means you can only fit 31 entire cubes in the box, the answer is 31.
Answer: (A) 31
Question: A and B’s salaries together amount to Rs. 4,000. A spends 95% of his salary and B spends 85% of his. If now their savings are the same, what is B’s salary?
(A) 2777
(B) 1000
(C) 2789
(D) 2776
(E) 2881
Rationale: (5/100) A = (15/100) B
A = 3B
A + B = 1000
4B = 1000 => B = 1000
Answer B
Answer: (B) 1000
Question: If population of certain city increases at the rate of 2%. If population in 1981 was 138915, then population in 1978 was?
(A) 12,0000
(B) 130000
(C) 261000
(D) 130903
(E) 12690
Rationale: Explanation:
X * (102/100) * (102/100) * (102/100) = 138915
X = 138915/1.061208
X = 130902.70=130903
Answer: Option D
Answer: (D) 130903
Question: Which of the following fractions is greater than 8/10 and less than 9/10?
1. 8/10 2. 9/10 3. 1/2 4.8/9 5. 1/3 6. 19/10
(A) 8/9
(B) 8/10
(C) 9/10
(D) 1/2
(E) 19/10
Rationale: 8/10 = 0.8, 9/10 = 0.9, 1/2= 0.5, 8/9= 0.88, 1/3= 0.33, 19/10= 1.9.
Clearly, 0.88 lies between 0.80 and 0.90.
Therefore, 8/9 lies between 8/10 and 9/10.
Answer is A.
Answer: (A) 8/9
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: 7, 8, 8, 7, 9, 9, 6, 6, 8 and 7. By what percent did she fall short of her goal?
(A)  4%
(B)  5%
(C)  8%
(D)  3.75%
(E)  12%
Rationale: Expected minimum rating = 8
Deviation from the expected minimum rating = (-1 + 0 + 0 - 1 + 1 + 1 - 2 - 2 + 0 - 1)/10 = -3/10 = -0.3
Current rating is 0.3 less than 8.
Percentage = (0.3/8)*100 = 3.75%
Answer: D
Answer: (D)  3.75%
Question: What is the length of a bridge (in meters), which a train 140 meters long and travelling at 45 km/h can cross in 30 seconds?
(A) 205
(B) 220
(C) 235
(D) 250
(E) 265
Rationale: speed = 45 km/h = 45000 m / 3600 s = 25/2 m/s
In 30 seconds, the train can travel 25/2 * 30 = 375 meters
375 = length of train + length of bridge
length of bridge = 375 - 140 = 235 meters
The answer is C.
Answer: (C) 235
Question: Gwen drove an average speed of 15 miles per hour for the first 40 miles of a tripthen at a average speed of 30 miles/hr for the remaining 40 miles of the trip if she made no stops during the trip what was Gwen's avg speed in miles/hr for the entire trip
(A) 35
(B) 20
(C) 45
(D) 50
(E) 55
Rationale: Avg. speed = total distance / total time
Total distance = 80 miles
Total time = 40 / 15 + 40/30 = 4
Avg. speed = 20.
Answer - B
Answer: (B) 20
Question: Mary drove at an average speed of 40 mph for some time and then at an average speed of 60 mph for the rest of the journey. If she made no stops during the trip and her average speed for the entire journey was 50 mph, for what fraction of the total time did she drive at 40 mph?
(A)  1/5
(B)  1/3
(C)  1/2
(D)  2/3
(E)  3/5
Rationale: We don't need to get into calculations for solving this question. We can use the concept of weighted averages.
One thing for sure we know that if the average speed for the entire journey is 50 mph, means she drove at 40 mph and 60 mph for an equal duration of time.
10 10
40-----50----60
This shows that you can divide the entire journey into 2 equal parts. Thus, 1/2 parts she drove at 40 mph and 1/2 part she drove at 60 mph.
Answer: C
Answer: (C)  1/2
Question: If Rs. 782 is divided into three parts, proportional to
1/2:2/3:3/4 find the first part.
(A) 190
(B) 204
(C) 220
(D) 230
(E) None of these
Rationale: Explanation:
1/2:2/3:3/4=6:8:9First part =782∗6/23=204
Option B
Answer: (B) 204
Question: Find the average of first 4 multiples of 5?
(A) 10
(B) 12.5
(C) 22.5
(D) 31.3
(E) 40.8
Rationale: average = (5+10+15+20)/4 = 12.5
Answer is B
Answer: (B) 12.5
Question: How many five-digit numbers are there, if the two leftmost digits are even, the other digits are odd and the digit 4 cannot appear more than once in the number.
(A) 1875
(B) 2000
(C) 2375
(D) 2500
(E) 3875
Rationale: Number of combo with 4 as first digit + Number of combos with 4 as second digit = 1*4*5*5*5 + 3*5*5*5 = 2375
ANSWER:C
Answer: (C) 2375
Question: How many different words beginning with O and ending with E can be formed with the letters of the word ORDINATE, so that the words are beginning with O and ending with E?
(A) 8!
(B) 6!
(C) 7!
(D) 7!/2!
(E) None
Rationale: Solution
6! ways, O fixed 1st and E fixed in last.
Answer B
Answer: (B) 6!
Question: (3192 + 6160) / 28
(A) 380
(B) 350
(C) 334
(D) 310
(E) None of these
Rationale: Explanation:
As per BODMAS rule, first we will solve the equation in bracket then we will go for division
= (9352)/28 = 334
Option C
Answer: (C) 334
Question: Of the 250 employees at company X, 80 are full-time, and 100 have worked at company X for at least a year. There are 20 employees at company X who aren’t full-time and haven’t worked at company X for at least a year. How many full-time employees of company X have worked at the company for at least a year?
(A) 20
(B) 30
(C) 50
(D) 80
(E) 100
Rationale: Full time employee who have NOT worked for at least one year = a
Full time employee who have worked for at least one year = b
NON Full time employee who have worked for at least one year = c
NON Full time employee who have NOT worked for at least one year = d
a+b+c+d = 150
a+b = 80
i.e. c+d = 70
b+c = 100
i.e. a+d = 50
d = 20
i.e. c = 70-20 = 50
i.e. b = 100-50 = 50
i.e. a = 80-50 = 30
b = 100
Answer: Option E
Answer: (E) 100
Question: The radius of a wheel is 22.4 cm. What is the distance covered by the wheel in making 125 resolutions?
(A) 794 m
(B) 704 m
(C) 454 m
(D) 186 m
(E) 176 m
Rationale: In one resolution, the distance covered by the wheel is its own circumference. Distance covered in 125 resolutions.
= 125 * 2 * 22/7 * 22.4
= 17600 cm
= 176 m
Answer: E
Answer: (E) 176 m
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) 287 km
(B) 960 km
(C) 187 km
(D) 173 km
(E) 266 km
Rationale: 60(x + 1) = 64x
X = 15
60 * 16 = 960 km
Answer: B
Answer: (B) 960 km
Question: How many multiples of 5 are there between 5 to 75?
(A) 9
(B) 18
(C) 17
(D) 13
(E) Cannot be determined
Rationale: Explanation :
As you know, multiples of 5 are integers having 0 or 5 in the digit to the extreme right (i.e. the units place).
So the numbers are 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70.
Answer : D
Answer: (D) 13
Question: What is the value of x in the equation below?
4 + √(1-3x) = 12
(A) 21
(B) 12
(C) -21
(D) -12
(E) 4
Rationale: 4 + √(1-3x) = 12
(4-4) + √(1-3x) = 12 - 4 = √(1-3x) = 8
(√(1-3x))^2 = (8)^2 = 1-3x = 64
(1 -1) - 3X = 64 - 1 = -3x = 63
(-3x) / -3 = 63 / -3 = x = -21
Correct option: C) -21
Answer: (C) -21
Question: On a Saturday night, each of the rooms at a certain motel was rented for either $40 or $60. If 10 of the rooms that were rented for $60 had instead been rented for $40, then the total rent the motel charged for that night would have been reduced by 20 percent. What was the total rent the motel actually charged for that night ?
(A)  $600
(B)  $800
(C)  $1,000
(D)  $1,600
(E)  $2,400
Rationale: Let total rent the motel charge for all rooms =x
If 10 rooms that were rented for 60 $ had instead been rented for 40 $,
then total difference in prices = 20 $ * 10 = 200 $
Total rent the motel charged would have been reduced by 20 %
.2x = 200
=> x= 1000
Answer C
Answer: (C)  $1,000
Question: A man can row 6 kmph in still water. When the river is running at 1.2 kmph, it takes him 1 hour to row to a place and black. How far is the place?
(A) 2.87
(B) 2.88
(C) 2.78
(D) 2.29
(E) 2.27
Rationale: M = 6
S = 1.2
DS = 6 + 1.2 = 7.2
US = 6 - 1.2 = 4.8
x/7.2 + x/4.8 = 1
x = 2.88
Answer: B
Answer: (B) 2.88
Question: If x and y are positive integers such that (3x + 7y) is a multiple of 11, then which of the following will be divisible by 11 ?
(A) 4x - 9y
(B) 9x + 4y
(C) x + y + 4
(D) x + y + 5
(E) 4x + 6y
Rationale: By hit and trial, we put x = 5 and y = 1 so that (3x + 7y) = (3 x 5 + 7 x 1) = 22, which is divisible by 11.
(4x + 6y) = ( 4 x 5 + 6 x 1) = 26, which is not divisible by 11;
(x + y + 4 ) = (5 + 1 + 4) = 10, which is not divisible by 11;
(9x + 4y) = (9 x 5 + 4 x 1) = 49, which is not divisible by 11;
(4x - 9y) = (4 x 5 - 9 x 1) = 11, which is divisible by 11.
Answer is A
Answer: (A) 4x - 9y
Question: If b/x = 7/4 and b/y =7/ 5, then (y -x) =
(A) b/2
(B) b/7
(C) 2b
(D) 3b/7
(E) b
Rationale: Ratio 1:
4b = 7x
Ratio 2:
5b = 7y
y -x = b/7
Answer is B
Answer: (B) b/7
Question: A train 880 m long is running at a speed of 78 km/hr. If it crosses a tunnel in 1 min, then the length of the tunnel is?
(A) 510
(B) 540
(C) 500
(D) 420
(E) 589
Rationale: Speed = 78 * 5/18 = 65/3 m/sec.
Time = 1 min = 60 sec.
Let the length of the train be x meters.
Then, (880 + x)/60 = 65/3
x = 420 m.
Answer: Option D
Answer: (D) 420
Question: A and B can do a piece of work in 12 days and 16 days respectively. Both work for 3 days and then A goes away. Find how long will B take to complete the remaining work?
(A) 7 days
(B) 8 days
(C) 5 days
(D) 9 days
(E) 3 days
Rationale: 3/12 + (3 + x)/16 = 1
x = 9 days
Answer: D
Answer: (D) 9 days
Question: Find the next term
8,8,6,2,..?
(A) -2
(B) -4
(C) -6
(D) -8
(E) -9
Rationale: 8 , 8, 6, 2, x
i guess each differ in d range of 2
8 - 8 = 0
8 - 6 = 2
6 - 2 = 4
2 - x should be "6"
2 - x = 6
x = -4
ANSWER:B
Answer: (B) -4
Question: If a: b = 7: 5, b: c = 9: 11, find a: b: c?
(A) 63: 45: 58
(B) 63: 45: 55
(C) 63: 45: 56
(D) 63: 45: 50
(E) 63: 45: 51
Rationale: a: b = 7: 5
b: c = 9: 11
a: b: c = 63: 45: 55
Answer: B
Answer: (B) 63: 45: 55
Question: A boy has seven trousers and 8 shirts. In how many different ways can he select a trouser and a shirt?
(A) 56 ways
(B) 57 ways
(C) 58 ways
(D) 108 ways
(E) 59 ways
Rationale: The boy can select one trouser in seven ways.
The boy can select one shirt in 8 ways.
The number of ways in which he can select one trouser and one shirt is 7 * 8 = 56 ways.
Answer:A
Answer: (A) 56 ways
Question: The cost of registration at a professional association meeting was $50 per person; a lunch for registrants only was available for an additional $22 per person. If the number of registrants who paid for lunch was 10 more than the number who did not, and if receipts for registration and lunch totaled $61720, how many people paid just for registration at the meeting?
(A) 700
(B) 800
(C) 1,300
(D) 500
(E) 1,800
Rationale: Hope this might be useful to you.
Let the number of people who have opted only to register = x
Now since the registration cost is 50$ per person, the total amount sums to = 50x $
As per the information given in the question, the number of registrants who paid for lunch was 10 more than the number who did not. That means, total number of people who registered and paid for lunch = 10 + x.
For the people who registered for lunch the cost is 50 $ (for the event registration) + 22 $ (for lunch) = 72 $.
Total amount in this case sums to = 72(10 + x) = 720 + 72x
Now, total amount received was 61,720.
Thus, from the above data,
50x + 720 + 72x = 61720
122x = 61720 - 720
122x = 61000
x = 500.
Hence the correct Ans is D
Answer: (D) 500
Question: A bowl of nuts is prepared for a party. Brand P mixed nuts are 20% almonds and Brand Q's Deluxe nuts are 25% almonds. If a bowl contains a total of 68 ounces of nuts, representing a mixture of both brands, and 15 ounces of the mixture are almonds, how many ounces of Brand Q's Deluxe mixed nuts are used?
(A)  16
(B)  28
(C)  32
(D)  44
(E)  48
Rationale: lets say x ounces of P is mixed with Q.
=> 68-x ounces of Q is present in the mixture (as the total = 68 ounces)
given total almond weight = 15 ounces
(20x/100)+(25/100)(68-x) = 15
=> x = 40
=> 68-40 = 28 ounces of Q is present in the mixture.
Answer is B.
Answer: (B)  28
Question: Bill has d animals, 12 of which were sold at a profit of 10% each while the rest were sold at a loss of 20% each. Overall, Bill made neither a profit nor a loss. Which of the following is equal to d?
(A) 6
(B) 12
(C) 18
(D) 24
(E) 36
Rationale: Total d animals, suppose each has price of x - total price = dx
now 12 were sold at profit of 10%, making equation - - 12*1.1x
now d-12 were sold at loss of 20%, making eqn --- (d-12)*0.8x
Now he made no profit or loss so,
dx = 12*1.1x + (d-12)*0.8x
solving for d, we get d=18
Ans C
Answer: (C) 18
Question: Jill, who lives in City C, plans to visit 2 different cities L, and S. She plans to visit each city exactly once and return to City C after the 2 visits. She can visit the cities in any order. In how many different orders can she visit the 2 cities?
(A)  3
(B)  2
(C)  8
(D)  9
(E)  12
Rationale: 2! = 2=B
Answer: (B)  2
Question: The overall ages of Kumar, Hathim and Rahul is 93 years. 1 decade ago, the ratio of their ages was 2 : 3 : 4. What is the current age of Rahul?
(A) 38
(B) 37
(C) 34
(D) 35
(E) 33
Rationale: A
38
If the ages of Kumar, Hathim and Rahul 1 decade ago be 2A, 3A and 4A years correspondingly
Then, (2A + 10) + (3A + 10) + (4A + 10) = 93
9A = 93-30
9A = 63
A = 7
Rahul’s current age = (4A + 10)
= 38 years.
Answer: (A) 38
Question: A bus started its journey from Mumbai and reached Pune in 44min with its average speed of 50 km/hr. If the average speed of the bus is increased by 5km/hr, how much time will it take to cover the same distance?
(A) 30 min
(B) 35 min
(C) 37 min
(D) 40 min
(E) 50 min
Rationale: Sol. Distance between Ramgarh and Devgarh =(50*44)/60=110/3
Average speed of the bus is increased by 5 km/hr then the
speed of the bus = 55 km/hr
Required time = 110/3*60/55 = 40 min
D
Answer: (D) 40 min
Question: There are 12 pieces of radioactive metal V that look identical. 11 of the pieces give the same radiation count when measured, the 12th piece is a counterfeit and gives a different radiation level, which may be more or less than the other 11. We are given a radiation scale, which can take 2 sets of samples and compare their added up radiation levels to tell us if the sums are the same or if different, which set has the higher level of radiation. What is the minimum number of comparisons we need on this scale to identify the counterfeit sample and to also determine whether it has more or less radiation than the other samples ?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
Rationale: First of all if you are down to just 3 pieces and you know that if the offending piece is less or more active, then it takes exactly 1 measurement to find out the offending piece. So you know you have to reduce the problem to three.
Now when you are down to either A or B after measurement 1, you need the next measurement to (a) reduce the problem set to 3 and (b) to know whether anser is more or less. Now you cannot compare a group of 4 to 4, as in the best case it will only reduce the problem to 4 elements which is not good enough.
If you have to choose a set of 3 to compare, you cannot pick any 3 on the same side from the same set (A or B) because if you do this, a quick check will show you that in every choice there is a case where you can only get down to 4 elements. Eg. If you weighed {1,2,3} v/s {5,9,10} and they were equal you're problem would only reduce to {4,6,7,8}
The easiest way to solve this then is to compare 3 to 3, and make sure each side has elements from both AB such that whatever the measurement outcome in the worst case the problem reduces to 3 elements only. Which is why the sets {1,5,9} and {2,6,7} OR {A,B,C}{A,B,B}. The extra element from C is just taken to make the problem symmetric so to say, we have 8 elements and we make it 9, to compose 3 sets of 3 each.=B
Answer: (B) 3
Question: On dividing a number by 48, we get 29 as remainder. On dividing the same number by 8, what will be the remainder ?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
Rationale: Number=48x+29 (∵ since the number gives 29 as remainder on dividing by 48)
=(6×8×x)+(3×8)+5
Hence, if the number is divided by 8, we will get 5 as remainder.
ANSWER:D
Answer: (D) 5
Question: The difference of 2 digit number & the number obtained by interchanging the digits is 36. What is the difference the sum and the number if the ratio between the digits of the number is 1:2 ?
(A) 6
(B) 8
(C) 12
(D) 14
(E) 16
Rationale: Let the number be xy.
Given xy – yx = 36.
This means the number is greater is than the number got on reversing the digits.
This shows that the ten’s digit x > unit digit y.
Also given ratio between digits is 1 : 2 => x = 2y
(10x + y) – (10y +x) = 36 => x – y = 4 => 2y – y =4.
Hence, (x + y) – (x – y) = 3y – y = 2y = 8
B
Answer: (B) 8
Question: If a solid sphere of radius 10 cms is moulded into 8 spherical solid balls of equal radius, then surface area of each ball (in cm2) is?
(A) 100
(B) 728
(C) 278
(D) 168
(E) 268
Rationale: 4/3 π * 10 * 10 * 10
= 8 * 4/3 πr3
r = 5
4π * 5 * 5
= 100π
Answer: A
Answer: (A) 100
Question: A person crosses a 1800 m long street in 12 minutes. What is his speed in km per hour?
(A) 4.1
(B) 4.5
(C) 4.8
(D) 5.4
(E) 9
Rationale: Speed = 1800/(12x60) m/sec
= 2.5 m/sec.
Converting m/sec to km/hr =2.5 x(18/5) km/hr
= 9 km/hr.
ANSWER :E
Answer: (E) 9
Question: what is the value of (5)^-5?
(A) 1/3125
(B) 1/3000
(C) 1/658
(D) 1/500
(E) 1/75
Rationale: 5^-5= 1/(5)^5= 1/3125
ANSWER:A
Answer: (A) 1/3125
Question: How many four letter words are formed using the letters of the word POLICE?
(A) 280
(B) 321
(C) 330
(D) 360
(E) 370
Rationale: The number of letters in the given word is four.
The number of three letter words that can be formed using these four letters is 6P4
= 6 * 5 * 4 * 3 = 360.
Answer: D
Answer: (D) 360
Question: We bought a total of 80 books at the store. Math books cost $4 and history books cost $5. The total price was $390. How many math books did we buy?
(A) 10
(B) 20
(C) 30
(D) 40
(E) 50
Rationale: M + H = 80
H = 80 - M
4M + 5H = 390
4M + 5*(80 - M) = 390
M = 10
The answer is A.
Answer: (A) 10
Question: The cost price of a radio is Rs.1500 and it was sold for Rs.1230, find the loss %?
(A) 18%
(B) 17%
(C) 78%
(D) 14%
(E) 38%
Rationale: 1500 ---- 270
100 ---- ? => 18%
Answer: A
Answer: (A) 18%
Question: A certain sum becomes Rs. 20720 in four years and 24080 in six years at simple interest. Find sum and rate of interest?
(A) 11
(B) 12
(C) 44
(D) 66
(E) 81
Rationale: :
Let the interest for one year be x.
As amount = Principal + Interest, we have
P + 4x = 20720 --- (1) ; P + 6x = 24080 --- (2)
Solving the equations (1) and (2), we can get
P = Rs. 14000 and x = Rs. 1680
Interest for one year on Rs. 14000 is Rs. 1680
So, R = (100 * 1680)/(14000 * 1) = 12% p.a.Answer: B
Answer: (B) 12