mathewhe/aqua_rat huggingface dataset:
Question: A goods train runs at the speed of 72 km/hr and crosses a 80 m long platform in 26 sec. What is the length of the goods train?
(A) 382
(B) 440
(C) 278
(D) 270
(E) 881
Rationale: Speed = 72 * 5/18 = 20 m/sec.
Time = 26 sec.
Let the length of the train be x meters.
Then, (x + 80)/26 = 20
x = 440m.
Answer: B
Answer: (B) 440
Question: The profit earned by selling an article for $ 832 is equal to the loss incurred when the same article is sold for $ 448. What should be the sale price for making 35% profit?
(A) $480
(B) $450
(C) $960
(D) $864
(E) $660
Rationale: Let C.P. = $ x.
Then, 832 - x = x - 448
2x = 1280 => x = 640
Required S.P. = 135% of $ 640 = $ 864
D
Answer: (D) $864
Question: Half percent, written as a decimal, is
(A) 0.2
(B) 0.02
(C) 0.005
(D) 0.05
(E) None
Rationale: Solution: As we know, 1% = 1/100
Hence, 1/2% = (1/2 * 1/100) = 1/200 = 0.005.
Answer: Option C
Answer: (C) 0.005
Question: Enrollment in City College in 1980 was 37 percent of enrollment in 1990. What was the percent increase in the college’s enrollment from 1980 to 1990?
(A) 100%
(B) 170.27 %
(C) 200%
(D) 250%
(E) 183 1/3%
Rationale: Assume 100 enrollments present in 1990
37 % of 1990 = enrollments on 1980
enrollments on 1980 = 37
% change = (enrollment in 1990 - enrollment in 1980)*100/(enrollment in 1980)
=(100 - 37) *100 / 37
= 6300 / 37
= 170.27 %
Ans - B
Answer: (B) 170.27 %
Question: How many prime numbers are between 26/3 and 85/6?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: 26/3 = 8.xxx
85/6 = 14.xxx
So we need to find Prime numbers between 8 (Exclusive) - 13 (Inclusive)
There are 2 Prime numbers 1113
Hence answer will be (B) 2
B
Answer: (B) 2
Question: If 1400*x=1050. The, x=?
(A) 1.4
(B) 3/5
(C) 2/3
(D) 3/4
(E) None of these
Rationale: 1400*x=1050; x=1050/1400; x =3/4
Correct Option: D
Answer: (D) 3/4
Question: Create a number using only the digits 4,4,3,3,2,2,1 and 1. So i can only be eight digits. You have to make sure the ones are separated by one digit, the twos are separated by two digits the threes are separated with three digits and the fours are separated by four digits
(A) 61312432
(B) 41312432
(C) 51312432
(D) 31312432
(E) 21312432
Rationale: B
41312432
Answer: (B) 41312432
Question: Devon had $56.90 to spend at the toy store. She bought 4 toy cars that cost $2.50 each and a race track that cost $19.10. How much money does Devon have left to buy more toys?
(A) $70
(B) $55
(C) $33
(D) $27.80
(E) $14.20
Rationale: Step 1: Find the cost of the toy cars.
4 × $2.50 = $10.00
Step 2: Find the total cost of the toys.
$10.00 + $19.10 = $29.10
Step 3: Find the amount of money left.
$56.90 – $29.10 = $27.80
Devon has $27.80 left.
Answer is D.
Answer: (D) $27.80
Question: A can finish a work in 60days, B in 9days and C in 2days, B and C start the work but are forced to leave after 3 days. The remaining work was done by A in?
(A) 10days
(B) 25days
(C) 6days
(D) 7days
(E) 8days
Rationale: B+C 1day work = 1/9 + 1/12 = 7/36
work done by B and C in 3days = 7/36 * 3 = 7/12
Remaining work = 1 - 7/12 = 5/12
1/60 work is done by A in 1day
5/12 work is done by A in 60*5/12 = 25days
Answer is B
Answer: (B) 25days
Question: If 25x = 125^y, which of the following expresses x in terms of y?
(A) 5^y
(B) 5^(3y-2)
(C) 5^(3y-1)
(D) 5^(2y-1)
(E) 5^(y-3)
Rationale: By exponential simplification. 25 = 5^2 and 125=5^3 therefore (5^2)x=(5^3)^y gives x=(5^3y)/(5^2) further simplified to x=(5^3y)(5^-2) which gives x=5^(3y-2) (because exponential is additive in multiplication. i.e. a^b*a^c=a^(b+c). Answer: B
Answer: (B) 5^(3y-2)
Question: The decimal 0.1 is how many times greater than the decimal (0.01)^5?
(A) 10^6
(B) 10^7
(C) 10^8
(D) 10^9
(E) 10^10
Rationale: 0.1 = 10^-1
(0.01)^5 = (10^-2)^5 = 10^-10
10^9 * 10^-10 = 10^-1
The answer is D.
Answer: (D) 10^9
Question: 3.20 can be expressed in terms of percentage as
(A) 3.20%
(B) 30.2%
(C) 320.00%
(D) 0.320%
(E) None of these
Rationale: Explanation:
While calculation in terms of percentage we need to multiply by 100, so
3.20 * 100 = 320
Answer: Option C
Answer: (C) 320.00%
Question: A dishonest dealer uses a scale of 97 cm instead of a metre scale and claims to sell at cost price. His profit is
(A) 9%
(B) 10%
(C) 12%
(D) 3.1%
(E) Cannot be determined
Rationale: Solution
Gain%	= (3 / 97 x 100)%
= 3.1%
Answer D
Answer: (D) 3.1%
Question: If (5^11)(9^6)=3(15^x), what is the value of x?
(A)  7
(B)  9
(C)  11
(D)  13
(E)  15
Rationale: (5^11)(9^6)=3(15^x)
=> 5^11 * 3^12 = 3 * 3^x * 5^x
=> 5^11 * 3^12 = 3^(x+1) * 5^x
Value of x = 11
Answer C
Answer: (C)  11
Question: A merchant has 1000 kg of sugar, part of which he sells at 8% profit and the rest at 18% profit. He gains 14% on the whole. The quantity sold at 18% profit is:
(A) 400 kg
(B) 560 kg
(C) 600 kg
(D) 640 kg
(E) 680 kg
Rationale: Profit on 1st part 8%
Profit on 2nd part 18%
Mean Profit 14%
Ration of 1st and 2nd parts = 4 : 6 = 2 : 3
Quantity of 2nd kind = (3/5 x 1000)kg = 600 kg.
Answer:C
Answer: (C) 600 kg
Question: There are 8 magazines lying on a table; 4 are fashion magazines and the other 4 are sports magazines. If 2 magazines are to be selected at random from the 8 magazines, what is the probability that at least one of the fashion magazines will be selected?
(A) 1/2
(B) 2/3
(C) 32/35
(D) 11/12
(E) 11/14
Rationale: answer is E
Total probability=8C2=28
4C2 +4C1*4C1=6+16=22
therefore the probability that at least one of the fashion magazines will be selected= 22/28=11/14
E
Answer: (E) 11/14
Question: Browny owns b video game cartridges. If Browny’s total is one-third the total owned by James and two times the total owned by Charlie, how many video game cartridges do the three of them own altogether, in terms of b?
(A) (16/3)b
(B) (17/4)b
(C) (13/4)b
(D) (9/2)b
(E) (7/12)b
Rationale: b = Browny’s total
3b = James’s total
(1/2)b = Charlie’s total
Add each total
b + 3b+ (1/2)b = 4b + (1/2)b = = (9/2)b
Answer : D
Answer: (D) (9/2)b
Question: How many pounds of salt at 50 cents/lb must be mixed with 40 lbs of salt that costs 35 cents/lb so that a merchant will get 20% profit by selling the mixture at 48 cents/lb?
(A) 20
(B) 15
(C) 40
(D) 50
(E) 25
Rationale: Selling price is 48 cents/lb
For a 20% profit, cost price should be 40 cents/lb (CP*6/5 = 48)
Basically, you need to mix 35 cents/lb (Salt 1) with 50 cents/lb (Salt 2) to get a mixture costing 40 cents/lb (Salt Avg)
weight of Salt 1/weight of Salt2 = (Salt2 - Salt Avg)/(Salt Avg - Salt 1) = (50 - 40)/(40 - 35) = 2/1
We know that weight of salt 1 is 40 lbs. Weight of salt 2 must be 20 lbs.
Answer (A)
Answer: (A) 20
Question: Harkamal purchased 10 kg of grapes at the rate of 70 per kg and 9 kg of mangoes at the rate of 55 per kg. How much amount did he pay to the shopkeeper?
(A) A)1190
(B) B)1065
(C) C)1070
(D) D)1075
(E) E)1080
Rationale: Cost of 10 kg grapes = 70 × 10 = 700.
Cost of 9 kg of mangoes = 55 × 9 = 490.
Total cost he has to pay = 700 + 490 = 1190
A
Answer: (A) A)1190
Question: If the given two numbers are respectively 5% and 25% of a third number, then what percentage is the first of the second ?
(A) 20%
(B) 25%
(C) 18%
(D) 30%
(E) none of these
Rationale: Here, l = 5 and m = 25
Therefore, first number = l/m x 100% of second number = 5/25 x 100% of second number = 20% of second number
ANSWER:A
Answer: (A) 20%
Question: The length of a rectangle is two - fifths of the radius of a circle. The radius of the circle is equal to the side of the square, whose area is 4225 sq.units. What is the area (in sq.units) of the rectangle if the rectangle if the breadth is 10 units?
(A) 140 sq.units
(B) 260 sq.units
(C) 167sq.units
(D) 178sq.units
(E) 176sq.units
Rationale: Given that the area of the square = 4225 sq.units
=> Side of square = √4225 = 65 units
The radius of the circle = side of the square = 65 units Length of the rectangle = 2/5 * 65 = 26 units
Given that breadth = 10 units
Area of the rectangle = lb = 26 * 10 = 260 sq.units
Answer:B
Answer: (B) 260 sq.units
Question: A person distributed 15% of his income to his 3 children each. He deposited 30% of his income to his wife's account. He donated 5% of remaining amount to an orphan house.Finally he has $40000. Find his total income?
(A) A)452000
(B) B)200000
(C) C)800000
(D) D)500000
(E) E)652000
Rationale: 3 children got = 3*15% = 45%
wife got = 30%
orphan house = 5%
total = 45+30+5 = 80%
remaining = 100-80 = 20%
20% = 40000
100% = 40000*100/20 = $200000
Answer is B
Answer: (B) B)200000
Question: A fruit seller had some oranges. He sells 20% oranges and still has 400 oranges. How many oranges he had originally?
(A) 420
(B) 700
(C) 220
(D) 500
(E) None of these
Rationale: Explanation :
He sells 20% of oranges and still there are 400 oranges remaining
=> 80% of oranges = 400
⇒ (80 × Total Oranges)/100 = 400
⇒ Total Oranges/100 = 5
⇒ Total Oranges = 5 × 100 = 500
Answer : Option D
Answer: (D) 500
Question: The sum of two numbers is 35 and their product is 1050. What will be the sum of their reciprocals?
(A) (1/30)
(B) (11/210)
(C) (35/4)
(D) (75/8)
(E) None
Rationale: Solution
x+y=35 xy=1050 1/x+1/y=x+y/xy 35/1050 = (1/30).
Answer A
Answer: (A) (1/30)
Question: The cost price of a radio is Rs.1500 and it was sold for Rs.1230, find the loss %?
(A) 18%
(B) 71%
(C) 28%
(D) 12%
(E) 72%
Rationale: 1500 ---- 270
100 ---- ? => 18%
Answer: A
Answer: (A) 18%
Question: Which one of the following numbers is exactly divisible by 11?
(A) 235641
(B) 245642
(C) 315624
(D) 415624
(E) Done
Rationale: (4 + 5 + 2) - (1 + 6 + 3) = 1, not divisible by 11.
(2 + 6 + 4) - (4 + 5 + 2) = 1, not divisible by 11.
(4 + 6 + 1) - (2 + 5 + 3) = 1, not divisible by 11.
(4 + 6 + 1) - (2 + 5 + 4) = 0, So, 415624 is divisible by 11.
D)
Answer: (D) 415624
Question: If x is divisible by 3 and 7, which of the following must divide evenly into x? I. 60 II. 30 III. 21
(A) II only
(B) III only
(C) I only
(D) I,II only
(E) I,III only
Rationale: If x is divisible by 3,7 means it will be = or > 21, 42,84 etc...
That are not divisible by 60, 30.
So, the answer is B
Answer: (B) III only
Question: The sum of three consecutive odd natural numbers, each divisible by 3 is 84. What is the largest among them?
(A) 21
(B) 24
(C) 27
(D) 31
(E) 45
Rationale: Let the 3 consecutive odd numbers each divisible by 3 be X, X+3, X+6
Given, X + X+3 + X+6 = 84
3X = 75
X = 25
The numbers are 25, 28, 31
Therefore the largest number is 31
Answer D.
Answer: (D) 31
Question: A goes 8 km East, then 3 km South, 4km West. How far is he from starting point and in which direction?
(A) 5 km south west
(B) 5 km south east
(C) 8 km south
(D) 9 km south
(E) Don,t remember
Rationale: 8E, 3S,4W
Subtract opposite direction 8E-4W,3S=> 4E, 3S
Square root of(4^2+ 3^2)= 5 Km South East.
ANSWER:B
Answer: (B) 5 km south east
Question: In how many ways can the letters of the word SPECULATION be arranged such that all the vowels always appear together?
(A) 6!*5!
(B) 7!*5!
(C) 11!
(D) 11!*6!
(E) 11!*5!
Rationale: The 11 letters can be grouped into 6 consonants and one set of 5 vowels.
The number of ways to arrange 7 units is 7!
Then, for each arrangement, the 5 vowels can be arranged in 5! ways.
The total number of arrangements is 7!*5!
The answer is B.
Answer: (B) 7!*5!
Question: If BASKET is coded as 116,then COLOUR is coded as,
(A) 158
(B) 168
(C) 179
(D) 188
(E) 198
Rationale: NUMBER THE ALPHABETS
B=2, A=1, S=19, K=11, E=5, T=20
BASKET = 116
2(B+A+S+K+E+T) ==>2(2+1+19+11+5+20) = 2(58) = 116
Similarly C=3, O=15, L=12, O=15, U=21, R=18
2(C+O+L+O+U+R) = 2(3+15+12+15+21+18) = 2(84) = 168
ANSWER:B
Answer: (B) 168
Question: The ratio of two numbers is 3 : 6 and their H.C.F. is 7. Their L.C.M. is
(A) 48
(B) 42
(C) 56
(D) 27
(E) 67
Rationale: Explanation:
Let the numbers be 3x and 6x. Then, their H.C.F. = x. So, x = 7.
So, the numbers 21 and 42.
L.C.M. of 21 and 42 = 42.
Option B
Answer: (B) 42
Question: If one positive integer is greater than another positive integer by 3, and the difference of their cubes is 189, what is their sum?
(A) 6
(B) 7
(C) 8
(D) 9
(E) 10
Rationale: 1^3 = 1
2^3 = 8
3^3 = 27
4^3 = 64
5^3 = 125
6^3 = 216
The two numbers are 3 and 6.
The answer is D.
Answer: (D) 9
Question: Which of the following functions does not intersect with R = 3x^2 + 2x + 1
(A) R = 3x^2 + 3x + 1
(B) R = 2x^2 + 3x + 1
(C) R = 3x^2 + 2x + 3
(D) R = 4x^2 + 2x - 3
(E) R = x^2 + 2x + 3
Rationale: Let’s find the actual intersecting point of given function and each choice R
A. 3x^2 + 2x + 1 = 3x^2 + 3x + 1 --> x=0
B. 3x^2 + 2x + 1 = 2x^2 + 3x + 1 --> x^2 – x =0 --> x=0 or 1
C. 3x^2 + 2x + 1 = 3x^2 + 2x + 3 --> 1=3(X) --> they don’t have any intersect.
D. 3x^2 + 2x + 1 = 4x^2 + 2x - 3 --> x^2 –4=0 --> x= 2 or -2
E. 3x^2 + 2x + 1 = x^2 + 2x + 3 --> 2x^2 –2 =0 --> x= 1 or –1.
So only choice (C) has no intersecting point. The answer is (C).
Answer: (C) R = 3x^2 + 2x + 3
Question: The owner of a furniture shop charges his customer 30% more than the cost price. If a customer paid Rs. 8450 for a computer table, then what was the cost price of the computer table?
(A) Rs. 5725
(B) Rs. 5275
(C) Rs. 6275
(D) Rs. 6500
(E) None of these
Rationale: CP = SP * (100/(100 + profit%))
= 8450(100/130) = Rs. 6500.
ANSWER:D
Answer: (D) Rs. 6500
Question: Twenty times a positive integer is less than its square by 96. What is the integer?
(A) 20
(B) 24
(C) 30
(D) 34
(E) 38
Rationale: Let the integer be x. Then,
x2 - 20x = 96
(x + 4)(x - 24) = 0
x = 24
ANSWER:B
Answer: (B) 24
Question: A bag contains 50p,Rs.1/- and Rs2/- coins in the ratio of 4:2:1 respectively. If the total money in the bag is Rs.60/-. Find the number of 50p coins in that bag?
(A) 20 coins
(B) 40 coins
(C) 60 coins
(D) 70 coins
(E) None
Rationale: 50paisa : Rs.1/- : Rs.2/- = 4 : 2 : 1 ---> coins ratio
= 2 : 2 : 2 ----> money ratio
Rs.2/- * 10 coins = Rs.20/-
Rs.1/- * 20 coins = Rs.20/-
50 Paisa * 40 coins = Rs.20/-
Then 50 paisa coins in that bag = 40 coins
B)
Answer: (B) 40 coins
Question: In order to obtain an income of Rs. 650 from 10% stock at Rs. 96, one must make an investment of:
(A) 3488
(B) 6240
(C) 2776
(D) 2889
(E) 7721
Rationale: Explanation:
To obtain Rs. 10, investment = Rs. 96.
To obtain Rs. 650, investment = = Rs. 6240
Answer: B) 6240
Answer: (B) 6240
Question: A box contains 5 black, 10 white and 8 yellow marbles. 4 marbles are drawn from the box at random. What is the probability that all three marbles are of the same color?
(A) 224/8855
(B) 225/8855
(C) 245/8855
(D) 285/8855
(E) 244/8855
Rationale: Explanation:
Total marbles in a box = 5 black +10 white + 8 yellow marbles = 23 marbles
4 marbles are drawn from 23 marbles at random. Therefore,
n(S) = 23C4 = 8855 ways
Let A be the event that 4 marbles drawn at random are of the same color. Number of cases favorable to the event A is
n(A) = 5C4 + 10C4 + 8C4 = 5 +210 + 70= 285
Therefore, by definition of probability of event A,
P(A) = n(A)/n(S) =285/8855
ANSWER:D
Answer: (D) 285/8855
Question: Two men and 7 children complete a certain piece of work in 4 days while 4 men and 4 children complete the same work in only 3 days. The number of days required by 1 man to complete the work is
(A) 60 days
(B) 15 days
(C) 6 days
(D) 51 days
(E) 50 days
Rationale: Two men and 7 children complete a certain piece of work in 4 days
or 8 men and 28 children complete a certain piece of work in 1 days
4 men and 4 children complete the same work in only 3 days.
or 12 men and 12 children complete the same work in only 3 days.
so 8 men +28 children = 12 men +12 children
1Man = 4 children
4 men and 4 children complete the same work in only 3 days
or 4 men and 1 man ( in place of 4 children ) complete the same work in only 3 days
or 5 men complete the same work in 3 days
or 1 man will complete the same work in 5* 3 =15 days
ANSWER:B
Answer: (B) 15 days
Question: When p is divided by 9, the remainder is 4. All of the following are possible values of p, except for which of the following?
(A) 13
(B) 31
(C) 49
(D) 56
(E) 67
Rationale: If a number is divisible by 9, the sum of its digits must be divisible by 9. --> If a number leaves a remainder 4 when divided by 9 the sum of its digits must be 4.
56
Answer: D
Answer: (D) 56
Question: Of the 80 people in a room, 2/5 are women. If 1/2 of the people are married, what is the maximum number of women in the room who could be unmarried?
(A) 20
(B) 22
(C) 26
(D) 30
(E) 32
Rationale: women = 2/5 * 80 = 32
married = 1/2 * 80 = 40
unmarried = 40
max(un-married women) = 32
E
Answer: (E) 32
Question: Johnny travels a total of one hour to and from school. On the way there he jogs at 5 miles per hour and on the return trip he gets picked up by the bus and returns home at 30 miles per hour. How far is it to the school?
(A) 2 miles
(B) 4 miles
(C) 4.8 miles
(D) 8 miles
(E) 6.9 miles
Rationale: Answer: E) 6.9 miles.
Average speed for round trip = 2*a*b/(a+b), where a,b are speeds
so, average speed was = 2*5*30/(5+30) = 6.9 m/hr
the distance between schoolhome should be half of that. ie. 6.9 miles
Answer E
Answer: (E) 6.9 miles
Question: Mangala completes a piece of work in 12 days, Raju completes the same work in 18 days. If both of them work together, then the number of days required to complete the work is?
(A) 5.2 days
(B) 6.2 days
(C) 7.2 days
(D) 8.2 days
(E) 9.2 days
Rationale: If A can complete a work in x days and B can complete the same work in y days, then, both
of them together can complete the work in x y/ x+ y days.
That is, the required No. of days = 12 Ã— 18/30 = 7.2 days.
C)
Answer: (C) 7.2 days
Question: If 35*s is a perfect square then s can be which of the following numbers?
(A) 21
(B) 35
(C) 54
(D) 105
(E) 150
Rationale: My solution:
For a number to be a perfect square all the prime factors must be in pairs. So,
Prime factors of 35 are 5 * 7
1) 21 = 3 * 7
2) 35 = 5 * 7
3) 54 = 2 * 3 * 3 * 3
4) 105 = 3 * 5 * 7
5) 150 = 2 * 3 * 5 * 5
So only answer choice B completes the pairing of 5 and 7. It adds a3, a5, and a7to the prime factors of 35 (5*7) and makes it a perfect square. B
Answer: (B) 35
Question: A committee that includes 12 members is about to be divided into 3 subcommittees with 4 members each. On what percent of the possible subcommittees that Michael is a member of is Annie also a member?
(A) 39%
(B) 35%
(C) 31%
(D) 27%
(E) 23%
Rationale: Michael is a member of one of the subcommittees.
P(Annie is on the same subcommittee) = 3/11 which is about 27%.
The answer is D.
Answer: (D) 27%
Question: An empty fuel tank with a capacity of 214 gallons was filled partially with fuel A and then to capacity with fuel B. Fuel A contains 12% ethanol by volume and fuel B contains 16% ethanol by volume. If the full fuel tank contains 30 gallons of ethanol, how many gallons of fuel A were added?
(A) 160
(B) 150
(C) 100
(D) 80
(E) 106
Rationale: Say there are A gallons of fuel A in the tank, then there would be 214-A gallons of fuel B.
The amount of ethanol in A gallons of fuel A is 0.12A;
The amount of ethanol in 214-A gallons of fuel B is 0.16(214-A);
Since the total amount of ethanol is 30 gallons then 0.12A+0.16(214-A)=30 --> A=106.
Answer: E.
Answer: (E) 106
Question: A dishonest dealer professes to sell his goods at Cost Price but still gets 30% profit by using a false weight. What weight does he substitute for a kilogram?
(A) 769 1/7 grams
(B) 769 3/13 grams
(C) 769 8/3 grams
(D) 769 1/3 grams
(E) 769 1/13 grams
Rationale: If the cost price is Rs.100, then to get a profit of 30%, the selling price should be Rs.130.
If 130kg are to be sold, and the dealer gives only 100kg, to get a profit of 30%.
How many grams he has to give instead of one kilogram(1000 gm).
130 gm ------ 100 gm
1000 gm ------ ?
(1000 * 100)/130 = 769 3/13 grams.
Answer:B
Answer: (B) 769 3/13 grams
Question: A motor cyclist participant of a race says "We drove with the speed of 10 miles an hour one way, but while returning because of less traffic we drove on the same route with 16 miles per hour." What was their average speed in the whole journey?
(A) 10 miles/hour
(B) 12.3 miles/hour
(C) 11 miles/hour
(D) 13 miles/hour
(E) 14 miles/hour
Rationale: 2xy/x+y=12.3 miles/hour
ANSWER:B
Answer: (B) 12.3 miles/hour
Question: If x > 0 and m is x percent of y, then, in terms of x, y is what percent of m?
(A) a) 100m
(B) b) 1/100m
(C) c) 1/m
(D) d) 10/m
(E) e) 10,000/x
Rationale: m= x/100 * y
So y= 100/x *m
So y= (10000/x)/100 * m
E
Answer: (E) e) 10,000/x
Question: An amount of money was invested at 10% a year. Five times that amount was invested at 15%. How much was invested at 15% if the total annual return was $1,615?
(A) 9500
(B) 1000
(C) 10500
(D) 11000
(E) 11500
Rationale: Let x and 5x be the amounts invested as 10% and 15% respectively.
Annual return for x = .1x
Annual return for 5x = .75x
Total return = .85x = 1615
x = 1900
So amount invested for 15% = 9500.
ANSWER:A
Answer: (A) 9500
Question: There are 24 students in Chadâ€™s class. He brought 27 cookies to pass out
for his birthday. How many cookies will each student get? Will there be
any cookies left over?
(A) 1-9
(B) 1-7
(C) 2-8
(D) 1-3
(E) 3-10
Rationale: 27/24 = 1 R 3 Chad will give each student 1 cookie and there will be 3
cookies left over
correct answer D
Answer: (D) 1-3
Question: Mary can do a piece of work in 11 days. Rosy is 10% more efficient than Mary. The number of days taken by Rosy to do the same piece of work is?
(A) 10
(B) 15
(C) 20
(D) 25
(E) 30
Rationale: Ratio of times taken by Mary and Rosy = 110:100 =11:10
Suppose Rosy takes x days to do the work.
11:10 :: 11:x => x= 10 days.
Hence, Rosy takes 10 days to complete the work.
Answer: A
Answer: (A) 10
Question: If the average (arithmetic mean) of 2x, 4x, and 8x is 140, what is the value of x?
(A) 20
(B) 30
(C) 15
(D) 33
(E) 31
Rationale: AM of 2x, 4x and 8x = 2x + 4x + 8x / 3 = 14x/3
Given that 14x/3 = 140
x = 30
Answer is B
Answer: (B) 30
Question: If y is a positive integer, which of the following could NOT be the square of y?
(A) 4432
(B) 9426
(C) 4966
(D) 6415
(E) 3155
Rationale: A number ending in 2 cannot be a perfect square.
4432 ends in a number 2, making that the correct answer
(A) 4432
Answer: (A) 4432
Question: Find the odd man out. 24,36,52,72,96
(A) 72
(B) 52
(C) 36
(D) 24
(E) 96
Rationale: Explanation :
All except 52 are multiples of 6
Answer : Option B
Answer: (B) 52
Question: After a storm deposits 120 billion gallons of water into the city reservoir, the reservoir is 60% full. If the original contents of the reservoir totaled 240 billion gallons, the reservoir was approximately what percentage full before the storm?
(A) 40%
(B) 48%
(C) 54%
(D) 58%
(E) 65%
Rationale: When the storm deposited 120 billion gallons, volume of water in the reservoir = 240 + 120 = 360 billion gallons
If this is only 60% of the capacity of the reservoir, the total capacity of the reservoir = 360/0.6 = 600 billion gallons
Therefore percentage of reservoir that was full before the storm = (240/600)*100 = 40%
Option C
Answer: (C) 54%
Question: A prize of $800 is to be distributed among 20 winners, each of whom must be awarded at least $20. If 2/5 of the prize will be distributed to 3/5 of the winners, what is the greatest possible individual award?
(A) $200
(B) $220
(C) $280
(D) $300
(E) $340
Rationale: Total value of the prize =$800
Number of people = 20
2/5 of 800 (=$320) should be distributed among 3/5 of 20 (=12 people ) with each getting $20 each. Remaining money = 800-320 = $480. Now in order to 'maximize' 1 prize, we need to minimise the others and we have been given that each should get $20. Thus, minimising the remaining 7 people (=20-12-1. '-1' to exclude 1 that needs to be maximised) = 7*20=140.
Thus the maximum award can be = 480-140 = $340, hence E is the correct answer.
Answer: (E) $340
Question: A professional basketball player just signed a contract that has a 10% raise in base salary from last year to this year. The contract also has provisions for a performance bonus of up to $10,000. If he earns the maximum performance bonus, his new effective salary will be a 10.5% raise over last year's total salary, when he received no performance bonus. Assuming he earns the full performance bonus, what will be his new salary?
(A) 2,010,000
(B) 2,110,000
(C) 2,150,000
(D) 2,200,000
(E) 2,210,000
Rationale: let x=old salary
then (1+.10)*x+10,000 = (1+.105)*x
i.e. new base salary +10,000 = effective new salary
thus 1.1*x + 10,000 = 1.105*x
10,000 = .005*x
2,000,000 = x
thus the new effective salary is 1.105*2,000,000 = 2,210,000
E
Answer: (E) 2,210,000