mathewhe/aqua_rat huggingface dataset:
Question: A small company employs 3 men and 5 women. If a team of 4 employees is to be randomly selected to organize the company retreat, what is the probability Q that the team will have exactly 2 women?
(A) 1/14
(B) 1/7
(C) 2/7
(D) 3/7
(E) 1/2
Rationale: 5C2 * 3C2 -> it gives combination of exactly 2 women and 2 men.
8C4 -> gives total possibilities of 4 people from 5 women and 3 men.
Probability = 5C2*3C2 / 8C4 = 3/7
SECOND METHOD:
Probability of two women -> 5/8 * 4/7.
probability of two men -> 3/6 * 2/5.
Probability: (5/8 * 4/7) * (3/6 * 2/5) = 1/14.
Answer: (D) 3/7
Question: 10 books are placed at random in a shelf. The probability that a pair of books will always be together is ?
(A) 1/8
(B) 1/1
(C) 1/5
(D) 1/4
(E) 1/0
Rationale: Explanation:
10 books can be rearranged in 10! ways consider the two books taken as a pair then number of favourable ways of getting these two books together is 9! 2!
Required probability = 1/5
Answer:C
Answer: (C) 1/5
Question: Is a given rectangular block, a cube?
I. At least 2 faces of the rectangular block are squares.
II. The volume of the block is 64.
(A) I alone sufficient while II alone not sufficient to answer
(B) II alone sufficient while I alone not sufficient to answer
(C) Either I or II alone sufficient to answer
(D) Both I and II are not sufficient to answer
(E) Both I and II are necessary to answer
Rationale: EXPLANATION
I gives, any two of l, b, h are equal.
II gives, lbh = 64.
From I and II, the values of l, b, h may be (1 ,1 , 64), (2 ,2 ,16), (4, 4, 4).
Thus, the block may be a cube or cuboid.
Correct answer is (D).
Answer: (D) Both I and II are not sufficient to answer
Question: If s is the sum of consecutive even integers w, x, y, and z, where w < x < y < z, all of the following must be true EXCEPT
(A) z - w = 3(y - x)
(B) s is divisible by 8
(C) The average of w, x, y, and z is odd
(D) s is divisible by 4
(E) w + x + 8 = y + z
Rationale: Just assume that the numbers are 2a, 2a+2, 2a+4 and 2a+6.
s = 2a + 2a+2 + 2a+4 + 2a+6 = 8a + 12
Focus on the easiest options first. You see that s is not divisible by 8. Answer (B)
Answer: (B) s is divisible by 8
Question: A vendor bought toffees at 6 for a rupee. How many for a rupee must he sell to gain 80%?
(A) 10.8
(B) 20.8
(C) 28.8
(D) 18.8
(E) 17.8
Rationale: C.P. of 6 toffees = Re. 1
S.P. of 6 toffees = 480% of Re. 1 = Rs.24/5
For Rs. 24/5 , toffees sold = 6.
For Re. 1, toffees sold = 6 x 24/5 =28.8.
Answer C
Answer: (C) 28.8
Question: 5. Find the value for log58 + 5(1/1000)
(A) 3
(B) -3
(C) 4
(D) -4
(E) 5
Rationale: Solution:
log58 + 5(1/1000) = loglog5(8 x 1/1000)
= log5(1/125)
= log5(1/5)3
= log5(5)-3
= -3log5(5)
= -3 x 1
= -3
ANSWER IS B
Answer: (B) -3
Question: If the President and Vice President must sit next to each other in a row with 2 other members of the Board, how many different seating arrangements are possible?
(A) 120
(B) 240
(C) 12
(D) 360
(E) 720
Rationale: We need to take President and VP as one unit. Therefore we have 3 people to arrange=3! ways
Also, we both President and VP can be arranged in 2 ! ways.
Reqd no of ways=3!*2!=12 ways
Answer C
Answer: (C) 12
Question: here are 5 Rock songs, 6 karnatic songs and 3 Indi pop songs. How many different albums can be formed using the above albums should contain at least 1 Rock song and 1 karnatic song?
(A) 36254
(B) 45124
(C) 15624
(D) 45654
(E) 36254
Rationale: There are 2n ways of choosing ‘n’ objects. For e.g. if n = 3, then the three objects can be chosen in the following 23 ways - 3C0 ways of choosing none of the three, 3C1 ways of choosing one out of the three, 3C2 ways of choosing two out of the three and 3C3 ways of choosing all three.
In the given problem, there are 5 Rock songs. We can choose them in 25 ways. However, as the problem states that the case where you do not choose a Rock song does not exist (at least one rock song has to be selected), it can be done in 25 - 1 = 32 - 1 = 31 ways.
Similarly, the 6 Carnatic songs, choosing at least one, can be selected in 26 - 1 = 64 - 1 = 63 ways.
And the 3 Indi pop can be selected in 23 = 8 ways. Here the option of not selecting even one Indi Pop is allowed.
Therefore, the total number of combinations = 31 * 63 * 8 = 15624
Ans: C
Answer: (C) 15624
Question: 3 people are sitting in a 4 seat row watching a football game. At halftime they all get up. When they return, they each randomly sit down on one of the 4 chairs. What is the likelihood that none of the 4 end up sitting in the same chair that they sat in during the first half?
(A) 1/2
(B) 9/24
(C) 15/24
(D) 18/24
(E) 21/24
Rationale: Originally seated A B C D
now when after they get up and when they sit back again .
1st- A has option to sit on 3 seats ( apart from his previous seat . thus he now sits on B's seat.)
2nd- Similarly B has option to sit on 3 seats ( because A has already occupied B's previous seat, thus B sits on a's seat.)
3rd- Now C has only 1 option to sit on D's seat . and similarly D also has one option to sit on C's seat.)
hence total favourable outcomes 3*1*1=3
and total possible outcomes =3!=6
probability of the favourable outcome=1/2. A
Answer: (A) 1/2
Question: Average of six numbers comes out to be 3.95. Average of two of the numbers is 3.4 while the average of other two is 3.85. Determine the average of the two numbers left.
(A) 4.7
(B) 4.8
(C) 4.3
(D) 4.6
(E) 4.9
Rationale: Explanation:
In the given question we have taken average of 6 numbers taken 2 at a time which makes 3 numbers.
=> 3.95 (Average of 1st and 2nd number)
=> 3.85 (Average of 3rd and 4th number)
=> 3.4 (Average of 5th and 6th number)
3.95 = (3.4 + 3.85 + x)/3
x = 4.6
ANSWER D
Answer: (D) 4.6
Question: The rate of a certain chemical reaction is directly proportional to the square of the concentration of chemical A present and inversely proportional to the concentration of chemical E present. If the concentration of chemical E is increased by 100 percent, which of the following is closest to the percent change in the concentration of chemical A required to keep the reaction rate unchanged?
(A) 100% decrease
(B) 50% decrease
(C) 40% decrease
(D) 40% increase
(E) 50% increase
Rationale: Let A and E be the concentratrations of the individual chemicals.
Rate of chemical reaction = A^2/E
Since new E is increased by 100%
Rate = A^2/(2E)
For the rate to be constant, new value of A should be square root(2)
So new value of A = 1.414A
That means A is increased by 41.4%
Nearest solution is D
Answer: (D) 40% increase
Question: Peter read R books last year, and Nikki read N books last year. If Peter read 35 more books than Nikki last year, which of the following reflects this relationship?
(A) R > 35N
(B) R < N − 35
(C) R > N + 35
(D) R = N − 35
(E) R = N + 35
Rationale: Peter read R books last year, and Nikki read N books last year. If Peter read 35 more books than Nikki last year, which of the following reflects this relationship?
A. R > 35N
B. R < N − 35
C. R > N + 35
D. R = N − 35
E. R = N + 35
Since Peter read more books than Nikki we have R>N. Moreover since Peter reads 35 more books than Nikki easily we can have R=N+35.
So the answer is (E).
Answer: (E) R = N + 35
Question: Simplify
25âˆ’[2âˆ’(6+2(7âˆ’8âˆ’5Â¯Â¯Â¯Â¯Â¯Â¯Â¯Â¯Â¯Â¯Â¯))]
(A) 37
(B) 25
(C) 28
(D) 30
(E) 32
Rationale: Explanation:
=25âˆ’[2âˆ’(6+2(7âˆ’8+5))]
(Please check due to overline, sign has been changed)
=25âˆ’[2âˆ’(6+2Ã—4))]
=25âˆ’[âˆ’12]=25+12=37
Option A
Answer: (A) 37
Question: A man performs 1/2 of the total journey by rail, 1/3 by bus and the remaining 6km on foot. His total journey is
(A) 16km
(B) 10km
(C) 12km
(D) 24km
(E) 36km
Rationale: Explanation:
Let the journey be x km
Then, 1x/2 + 1x/3 +6 =x
5x +36 =6x
X = 36km
Answer: Option E
Answer: (E) 36km
Question: To fill a tank, 25 buckets of water is required. How many buckets of water will be required to fill the same tank if the capacity of the bucket is reduced to two-fifth of its present ?
(A) 10
(B) 35
(C) 25
(D) 45
(E) 15
Rationale: 2/5 of 25 = 10
ANSWER:A
Answer: (A) 10
Question: The average expenditure of a labourer for 6 months was 95 and he fell into debt. In the next 4 months by reducing his monthly expenses to 60 he not only cleared off his debt but also saved 30. His monthly income i
(A) 70
(B) 72
(C) 75
(D) 78
(E) 84
Rationale: Income of 6 months = (6 × 95) – debt
= 570 – debt
Income of the man for next 4 months
= 4 × 60 + debt + 30
= 270 + debt
∴ Income of 10 months = 840
Average monthly income = 840 ÷ 10 = 84
Answer E
Answer: (E) 84
Question: A four-character password consists of one letter of the alphabet and three different digits between 0 and 7, inclusive. The letter must appear as the second or third character of the password. How many different passwords are possible?
(A) 5,040
(B) 18,720
(C) 17,472
(D) 37,440
(E) 52,000
Rationale: 4 character password: DLDD
First digit can be chosen in 8 ways.
The letter can be chosen in 26 ways.
Next digit can be chosen in 7 ways.
Next digit can be chosen in 6 ways.
This gives us 8*26*7*6ways
Now, the letter can also be DDLD so there will be another 8*26*7*6 ways
Total = 8*26*7*6*2 = 17,472 ways C
Answer: (C) 17,472
Question: A single discount equivalent to the discount series of 20%, 10% and 5% is?
(A) 20
(B) 99
(C) 7878
(D) 656
(E) 27
Rationale: SP2 = 2/3 SP1
CP = 100
SP2 = 80
2/3 SP1 = 80
SP1 = 120
100 --- 20 => 20% Answer: A
Answer: (A) 20
Question: If p/8 = r/2 and r = 0.75s, what is the ratio of p to r to s?
(A) 2 : 3 : 4
(B) 8 : 12 : 9
(C) 24 : 6 : 8
(D) 6 : 4 : 3
(E) 12 : 8 : 3
Rationale: p/8=r/2, r=0.75s, what is p:r:s?
we get p/r=8/2 and r/s=3/4, so
8/3*3/2 and 2/2*3/4
24/6 and 6/8
C
Answer: (C) 24 : 6 : 8
Question: A car gets 40 kilometers per gallon of gasoline. How many gallons of gasoline would the car need to travel 190 kilometers?
(A) 3.5 gallons
(B) 2.7 gallons
(C) 5.7 gallons
(D) 4.75 gallons
(E) 7.5 gallons
Rationale: Each 40 kilometers, 1 gallon is needed. We need to know how many 40 kilometers are there in 190 kilometers?
190 Ã· 40 = 4.75 Ã— 1 gallon = 4.75 gallons
correct answer is D) 4.75 gallons
Answer: (D) 4.75 gallons
Question: In a cricket team, the average of eleven players is 28 years. Out of these, the average ages of three groups of three players each are 25 years, 28 years and 34 years respectively. If in these groups, the captain and the youngest player are not included, and the captain is eleven years older than the youngest player, what is the age of the captain ?
(A) 33 years
(B) 34 years
(C) 35 years
(D) 36 years
(E) 29 years
Rationale: Explanation :
Let the age of youngest player be x.
Then, age of the captain = (x + 11).
=> 3*25 + 3*28 + 3*34 + x + x + 11 = 11*28.
=> 75+84+102+2x+11=308
so 2x = 36
so x = 18.
Age of the captain = (x+11)
= 29 years.
Answer : E
Answer: (E) 29 years
Question: What sum of money put at C.I amounts in 2 years to Rs.8820 and in 3 years to Rs.9261?
(A) 8000
(B) 8077
(C) 2776
(D) 2976
(E) 2971
Rationale: 8820 ---- 441
100 ---- ? => 5%
x *105/100 * 105/100 = 8820
x*1.1025=8820
x=8820/1.1025 => 8000.Answer: A
Answer: (A) 8000
Question: How many kg of sugar costing Rs. 9/kg must be mixed with 27kg of sugar costing Rs. 7/ kg so that there may be a gain of 10% the mixture at Rs. 9.24 per kg?
(A) 51
(B) 56
(C) 58
(D) 62
(E) 63
Rationale: Selling Price(SP) of 1 kg mixture= Rs. 9.24
Profit = 10%
Cost Price(CP) of 1 kg mixture =100(100+Profit%)×SP
=100(100+10)×9.24=100110×9.24=92.411= Rs.8.4
By rule of alligation,
CP of 1 kg sugar of 1st kind	CP of 1 kg sugar of 2nd kind
Rs. 9	Rs. 7
Mean Price
Rs.8.4
8.4 - 7 = 1.4	9 - 8.4 = 0.6
i.e., to get a cost price of 8.4, the sugars of kind1 and kind2 should be mixed in the ratio 1.4 : 0.6 = 14 : 6 = 7 : 3
Suppose x
kg of kind1 sugar is mixed with 27 kg of kind2 sugar.
then x : 27 = 7 : 3
⇒3x=27×7⇒x=9×7=63
E
Answer: (E) 63
Question: By how much does the larger root of the equation 2q^2+5q = 12 exceed the smaller root?
(A)  5/2
(B)  10/3
(C)  7/2
(D)  14/3
(E)  11/2
Rationale: For 2q^2+5q = 12 Roots are [-5 + sqrt(25 + 96)]/4 OR [-5 - sqrt(25 + 96)]/4
= 1.5 OR -4
Hence larger root 1.5 is 1.5 - (-4) = 5.5 = 11/2 greater than smaller root (-4).
Hence option (E).
Answer: (E)  11/2
Question: A basketball player succeeds with 80% of her free throws. If she has a set of three free throws, what is the probability that she succeeds at least once?
(A) 0.972
(B) 0.978
(C) 0.984
(D) 0.992
(E) 0.998
Rationale: P(missing all 3 free throws) = 0.2^3 = 0.008
P(succeeding at least once) = 1 - 0.008 = 0.992
The answer is D.
Answer: (D) 0.992
Question: What is x if x + 2y = 10 and y = 4?
(A) A)10
(B) B)8
(C) C)6
(D) D)4
(E) E)2
Rationale: x = 10 - 2y
x = 10 - 8.
x = 2
Answer : E
Answer: (E) E)2
Question: A batsman scored 150runs which included 5 boundaries and 5 sixes. What percent of his total score did he make by running between the wickets.
(A) 40%
(B) 50%
(C) 60%
(D) 66.66%
(E) 70%
Rationale: Explanation:
Number of runs made by running = 150 - (5 x 4 + 5 x 6)
= 150 - (50)
= 100
Now, we need to calculate 100 is what percent of 150.
=> 100/150 * 100 = 66.66 %
Option D
Answer: (D) 66.66%
Question: If shares of two persons in profits are Rs.400 and Rs.600 then ratio of their capitals is
(A) 3:4
(B) 2:3
(C) 4:3
(D) 1:3
(E) 1:2
Rationale: profit=time*capital
so 400:600=2:3
ANSWER:B
Answer: (B) 2:3
Question: If the cost of x metres of wire is d rupees, then what is the cost of y metres of wire at the same rate?
(A) Rs.(yd/U)
(B) Rs.(yI/x)
(C) Rs.(Od/x)
(D) Rs.(yd/x)
(E) Rs.(yd/D)
Rationale: Cost of x metres = Rs. d.
Cost of 1 metre = Rs. d
x
Cost of y metres = Rs. d	. y = Rs. yd	.
x	x
View Answer Discuss in Forum
Answer:D
Answer: (D) Rs.(yd/x)
Question: An investor receives a total combined return of 7% on his two different investments. On his $10,000 investment he receives a return of 6%. What is the return on his $20,000 investment?
(A) 7.25%
(B) 7.5%
(C) 8%
(D) 8.5%
(E) 9%
Rationale: Total investment = $30000
on which he receives 7% = 2100
now,
on his $10000 he receives 6% = $600
remaining $1500
which is (1500/20000)*100 = 7.5
ANSWER:B
Answer: (B) 7.5%
Question: A train 320 m in length crosses a telegraph post in 16 seconds. The speed of the train is?
(A) 22 kmph
(B) 77 kmph
(C) 54 kmph
(D) 72 kmph
(E) 88 kmph
Rationale: S = 320/16 * 18/5 = 72 kmph
Answer:D
Answer: (D) 72 kmph
Question: P is able to do a piece of work in 5 days and Q can do the same work in 10 days. If they can work together for 3 days, what is the fraction of work completed?
(A) 13/10
(B) 4/5
(C) 11/10
(D) 7/10
(E) 9/10
Rationale: Explanation :
Amount of work P can do in 1 day = 1/5
Amount of work Q can do in 1 day = 1/10
Amount of work P and Q can do in 1 day = 1/5 + 1/10 = 3/10
Amount of work P and Q can together do in 3 days = 3 × (3/10) = 9/10
Answer : Option E
Answer: (E) 9/10
Question: If 50 percent of X is 25 percent of Y, then what is the relation between X and Y?
(A) X=Y
(B) 2X=Y
(C) X=2Y
(D) 1
(E) NONE OF ABOVE
Rationale: 50/100(X) = 25/100(Y)
2X=Y..
Option B.
Answer: (B) 2X=Y
Question: In a game of billiards, A can give B 20 points in 60 and he can give C 30 points in 60. How many points can B give C in a game of 100?
(A) 22
(B) 28
(C) 025
(D) 20
(E) 11
Rationale: A scores 60 while B score 40 and C scores 30.
The number of points that C scores when B scores 100 = (100 * 30)/40 = 25 * 3 = 75.
In a game of 100 points, B gives (100 - 75) = 25 points to C.
Answer: C
Answer: (C) 025
Question: A dozen bananas and 10 pounds of oranges are currently at the same price. If the price of a dozen bananas rises by 20 percent and the price of oranges rises by 4 %. How much more will it cost to buy a dozen bananas and 10 pounds of oranges.
(A) 24%
(B) 22%
(C) 23%
(D) 25%
(E) 29%
Rationale: Say currently both a dozen bananas and 10 pounds of oranges cost $100 (they are at the same price). So, to buy a dozen bananas and 10 pounds of oranges we need $200.
After the increase, the price of a dozen bananas will be $120 and the price of 10 pounds of oranges will be $104. So after the increase, to buy a dozen bananas and 10 pounds of oranges we'll need $224.
Increase = 24%.
Answer: A.
Answer: (A) 24%
Question: What is the rate percent when the simple interest on Rs.4000 amount to Rs.640 in 2 Years?
(A) 8.2%
(B) 8%
(C) 8.5%
(D) 9%
(E) 9.5%
Rationale: Interest for 1 year = 640/2 = 320
Interest on Rs 4000 p/a = 320
interest rate = 320/4000*100 = 8%
Answer : B
Answer: (B) 8%
Question: If x is divisible by 20, 14, and 70, which of the following must be the least multiple of x?
(A) 70
(B) 140
(C) 210
(D) 350
(E) 700
Rationale: We are looking for the LCM (which is not 0) of 20 = 2^2*5, 70 = 2*7*5, 14 = 2*7:
2^2 * 5 * 7 = 140
The answer is B.
Answer: (B) 140
Question: The longest side of a triangle is 3 times the shortest side and the third side is 2 cm shorter than the longest side. If the perimeter of the triangle is at least 61 cm,What is the minimum length of the shortest side?
(A) 8cm
(B) 9cm
(C) 10cm
(D) 11cm
(E) 12cm
Rationale: let the shortest measurement be x cm
then the largest side will be 3x cm
and the third side will be (3x-2)cm
now according to the problem
x+3x+3x-2 >=61
7x-2 >= 61
7x >= 63
therefore x>=9cm
ANSWER:B
Answer: (B) 9cm
Question: Let the function T(n) represent the product of the first n prime numbers, where n > 0. If x = T(n) + 1, which of the following must be true?
(i) x is always odd
(ii) x is always prime
(iii) x is never the square of an integer
(A) ii only
(B) iii only
(C) i and ii only
(D) i and iii only
(E) ii and iii only
Rationale: T(n) is always even, because the first prime is 2 and no matter what n is, 2 always will be a divisor of T(n). Thus, T(n) + 1 = even + 1 = odd. So, (i) is always true.
Now, use logic:
If (ii) is true (so if x is always prime), then (iii) must automatically be true: no prime is the square of an integer. So, the correct answer must be i only; i, ii, and iii only; or i and iii only. since onlyi and iii onlyis among the options, then it must be true.
Or, since (i) is always true, then from options the answer must be either C or D. C cannot be correct because if (ii) is true, then so must be (iii). Thus only D remains.
Answer: D.
Answer: (D) i and iii only
Question: A rower can row upstream at 15 kph and downstream at 35 kph. What is the speed of the rower in still water?
(A) 22
(B) 23
(C) 24
(D) 25
(E) 26
Rationale: Let V be the rower's speed in still water.
Let S be the speed of the current in the stream
V-S = 15
V+S = 35
When we add the two equations, we get: 2V = 50
Then V = 25 kph.
The answer is D.
Answer: (D) 25
Question: A university cafeteria offers 5 flavors of pizza - pork,pepperoni, chicken, Hawaiian and vegetarian. If a customer has an option (but not the obligation) to add extra cheese, mushrooms or both to any kind of pizza, how many different pizza varieties are available ?
(A) 4
(B) 8
(C) 12
(D) 25
(E) 32
Rationale: 5 flavours * 5 choices = 5C1*5C1 = 5*5=25=D
Answer: (D) 25
Question: A man goes from A to B at a speed of 20 kmph and comes back to A at a speed of 30 kmph. Find his average speed for the entire journey?
(A) 24 kmph
(B) 22 kmph
(C) 23 kmph
(D) 21 kmph
(E) 25 kmph
Rationale: A
24 kmph
Distance from A and B be 'd'
Average Speed = total distance/total time
Average Speed = (2d)/[(d/20) + (d/30)]
= (2d)/[5d/60) => 24 kmph.
Answer: (A) 24 kmph
Question: A certain car can travel 40 kilometers on a liter of fuel. If the fuel tank’s contents decrease by 3.9 gallons over a period of 5.7 hours as the car moves at a constant speed, how fast is the car moving, in miles per hour? (1 gallon = 3.8 liters; 1 mile = 1.6 kilometers)
(A) 52
(B) 65
(C) 78
(D) 91
(E) 104
Rationale: Fuel used 3.9 gallons ;convert to liters--> 3.9 x 3.8 liters
Time = 5.7 hours
1 mile = 1.6 kilometers ;convert to miles--> 1km = 1/1.6 mile
Speed (km/hour)= D/T = 40 (km*) x 3.9 x 3.8 / 5.7
replace (km*) to miles ; multiply by 1/1.6 mile
Speed (miles/hour)= 40 x 3.9 x 3.8 / 5.7 x 1.6 = 78 miles/hour
Ans :C
PS :i felt the factors were easy to cancel out ,so didn't require much rounding off
= 40 x 3.9 x 3.8 / 5.7 x 1.6
= 65
B
Answer: (B) 65
Question: An area of a circularplace is 17 hectares. Find the cost of fencing it at the rate of Rs. 3 permeter approximately.
(A) Rs. 4000
(B) Rs. 4450
(C) Rs. 4457
(D) Rs. 4560
(E) Rs. 5457
Rationale: Area = (17.56 x 10000) m2= 175600 m2.
ΠR2 = 175600 ⇔ (R)2 = (175600 x (7/22)) ⇔ R = 236.37 m.
Circumference = 2ΠR = (2 x (22/7) x 236.37) m =1485.78 m.
Cost of fencing = Rs. (1485.78 x 3) = Rs. 4457.
C
Answer: (C) Rs. 4457
Question: A 12 month project had a total budget of $18,000. After five months, the project had spent $6,400. At this point, how much was the project under budget?
(A) $1000
(B) $1100
(C) $1200
(D) $1300
(E) $1400
Rationale: Each month, the project should spend $18,000 / 12 = $1500.
In 5 months, the project should spend 5*$1500=$7500.
The project is under budget by $7500 - $6400 = $1100.
The answer is B.
Answer: (B) $1100
Question: Dana borrows 6500 pounds annually for her college education. If Dana gives her parents 3% of that amount back each month, how much will she still owe her parents after four years of college?
(A) 16240
(B) 16340
(C) 16440
(D) 16540
(E) 16640
Rationale: dana borrows 6500 and returns 3% per month.
so returns 195 per month. and 2340 per year.
so dana owes 6500-2340=4160 per year.
after 4 years she will owe 16640.
Ans (E)
Answer: (E) 16640
Question: A work could be completed in 100days by x workers. However, due to the absence of 10workers, it was completed in 110days. The original no.of workers was:
(A) 90
(B) 100
(C) 110
(D) 134
(E) 154
Rationale: sax Letlheo g alnumberofworkers hex
x workers can do the wor - 100 days
(x — 10) workers can do the work in 110 days
4 100x 1u1x— 10)
1100 Q x 110
C
Answer: (C) 110
Question: When m is divided by 9, the remainder is 4. When m is divided by 13, the remainder is 10. If 1 < m < 200, what is the greatest possible value of m?
(A) 47
(B) 65
(C) 103
(D) 117
(E) 166
Rationale: Looking at the choices, options BD can be eliminated as they are divisible by 13
Starting from the highest number 164;
166 = 162 + 4 (162 divisible by 9)
166 = 156 + 10 (156 divisible by 13)
it fits the result
Answer = E
Answer: (E) 166
Question: Tough and Tricky questions: Exponents.
If a and b are positive integers and x = 24^a and y = 9^b, which of the following is a possible units digit of xy?
(A) 1
(B) 6
(C) 5
(D) 7
(E) 8
Rationale: Only Units digit of X and Y contribute to the Units digit of XY.
Finding all values ofXfor positive values ofa
When,
a=1; X=24
a=2; X=576
a=3; X=13824........ Units digit repeat in a cycle of 4,6,4,6......
Similarly, Finding all values ofYfor positive values ofb
When,
b=1; Y=9
b=2; Y= 81
b=3; Y= 729....... Units digit repeat in cycle of 9,1,9,1....
So, possible value of Units digit of XY can be found by considering all possibilities of Units digit of X and Y
When X=4 and Y=9: Units digit of XY = 6
When X=4 and Y=1: Units digit of XY = 4
When X=6 and Y=9: Units digit of XY = 4
When X=6 and Y=1: Units digit of XY = 6
Only two possibilities for Units digit of XY i.e. 4 and 6.
Only 6 is given in answer choices, therefore answer is B
Answer: (B) 6
Question: Alex has $246,713 dollars in his savings account. What is the least amount of money (in whole number of dollars) that he must remove from his account if he wants to split this money evenly among his 6 children?
(A) $1
(B) $2
(C) $3
(D) $4
(E) $5
Rationale: In order to divide the sum into 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 246,713 = 23 and 21 is divisible by 3. Subtracting 2 does not yields an even number.
Sum of digits 246,713 = 23 and 18 is divisible by 3. Subtracting 5 yields an even number.
Hence, we need to subtract 5 from this number for it to be divisible by 6.
Correct Option: E
Answer: (E) $5
Question: An inspector rejects 0.008% of the meters as defective. How many will be examine to project ?
(A) 2000
(B) 230
(C) 2700
(D) 25000
(E) 250
Rationale: Let the number of meters to be examined be x.
Then, 0.008% of x =2
[(8/1000)*(1/100)*x] = 2
x = [(2*100*1000)/8] = 25000
Answer is D.
Answer: (D) 25000