mathewhe/aqua_rat huggingface dataset:
Question: Eighty percent of the lights at Hotel California are on at 8 p.m. a certain evening. However, forty percent of the lights that are supposed to be off are actually on and ten percent of the lights that are supposed to be on are actually off. What percent K of the lights that are on are supposed to be off?
(A) 22(2/9)%
(B) 16(2/3)%
(C) 11(1/9)%
(D) 10%
(E) 5%
Rationale: Is the Answer D.
let me try..
Let the light which are supposed to be OFF = SO
Let the light which are supposed to be ON = SN
Let the light which are ACTUALLY OFF = AO
Let the light which are ACTUALLY ON = AN
Let the total no. of lights be 100,
So ACTUALLY ON lights = 80
And ACTUALLY OFF lights = 20
Also given >> forty percent of the lights that are supposed to off are actually on >>> (40/100)*SO are ACTUALLY ON
it means >>> (60/100)*SO are ACTUALLY OFF
Also given >> ten percent of the lights that are supposed to be on are actually off >>> (10/100)*SN are ACTUALLY OFF
it means >>> (90/100)*SN are ACTUALLY ON
So, Total ACTUALLY ON lights = (40/100)*SO + (90/100)*SN = 80
and Total ACTUALLY OFF lights = (60/100)*SO + (10/100)*SN = 80
From here we get SO = 20
we need to find: What percent of the lights that are on are supposed to be off >>> So light ACTUALLY ON are 80 and light which are ACTUALLY ON, which are supposed to be OFF = (40/100)*SO = 8.
So (8/80)*100 K= 10%.D
Answer: (D) 10%
Question: The number N is 5,2H7, where H represents the ten's digit. If N is divisible by 3, what is the value of H?
(A) 3
(B) 8
(C) 5
(D) 6
(E) 4
Rationale: If the number is divisible by 3, the sum of the digits must also be divisible by 3. Only 4 yields such a number.
Answer: E
Answer: (E) 4
Question: The jogging track in a sports complex is 640 m in circumference. Lata and Geeta start from the same point and walk in opposite directions at 4.2 km/hr and 3.8 km/hr respectively. They will meet for the first time in?
(A) 2.9 min
(B) 3.9 min
(C) 4.2 min
(D) 4.8 min
(E) 5.6 min
Rationale: Clearly, the two will meet when they are 640 m apart.
To be (4.2 + 3.8) = 8.0 km apart, they take 1 hour.That is 60 min.
To be 640 m apart, they take
(640/8000 * 60) min
= 4.8 min.
Answer: D
Answer: (D) 4.8 min
Question: A man can row downstream at the rate of 12 Km/hr and upstream at 8 Km/hr. Find man's rate in still water and the rate of current?
(A) 9,6
(B) 6,3
(C) 9,3
(D) 10,2
(E) None of these
Rationale: Explanation:
Rate of still water = 1/2 (12 + 8) = 10 Km/hr
Rate of current = 1/2 (12-8) = 2 Km/hr
Answer: Option D
Answer: (D) 10,2
Question: Which of the following CANNOT be a product of two distinct positive integers x and y?
(A) x
(B) y
(C) 3y + 2x
(D) y - x
(E) yx
Rationale: In these questions it is best to take an example as if something is true for all positive integers than it as to be true for the smallest and the easiest integers to work with
take x = 1 and y = 2 and work with the options
xy = 2
A) x take x =2, y = 1
B) y take x = 1 y = 2
C) 3y + 2x Seems tricky, lets see other options and then come back to it.
D) y - x take y = 1 and x = 2 --> y - x = -1 .. How the hell can product of two positive integers be negative ?? or less than each of them?
E) yx Always true
You don't even have to worry what C is !
ans D
Answer: (D) y - x
Question: How much greater is the combined area in square inches of the front and back of a rectangular sheet of paper measuring 11 inches by 15 inches than that of a rectangular sheet of paper measuring 7.5 inches by 11 inches?
(A) 50%
(B) 87%
(C) 100%
(D) 187%
(E) 200%
Rationale: Let's just look at the dimensions (no calculation needed).
With dimension 11 the same, the other dimension 15 is twice 7.5
Then the area will be double which means 100% greater.
The answer is C.
Answer: (C) 100%
Question: For which of the following values of n is (300+n)/n NOT an integer?
(A)  1
(B)  2
(C)  3
(D)  4
(E)  7
Rationale: Solution:
This problem is easiest solved by plugging in each answer choice.
A) (300 + 1)/1 = 301/1 = 301
Answer choice A yields an integer.
B) (300 + 2)/2 = 302/2 = 151
Answer choice B yields an integer.
C) (300 + 3)/3 = 303/3 = 101
Answer choice C yields an integer.
D) (300 + 4)/4 = 304/4 = 76
Answer choice D yields an integer.
E) (300 + 7)/7 = 307/7 = 43, remainder 6
Answer choice E DOES NOT yield an integer.
Thus, the correct answer is answer choice E.
Answer: (E)  7
Question: 4 dice are thrown simultaneously on the board. Find the probability show the same face?
(A) 2/113
(B) 1/215
(C) 1/216
(D) 3/113
(E) 4/113
Rationale: The total number of elementary events associated to the random experiments of throwing four dice simultaneously is:
=6×6×6×6=64=6×6×6×6=64
n(S)=64n(S)=64
Let XX be the event that all dice show the same face.
X={(1,1,1,1,),(2,2,2,2),(3,3,3,3),(4,4,4,4),(5,5,5,5),(6,6,6,6)}X={(1,1,1,1,),(2,2,2,2),(3,3,3,3),(4,4,4,4),(5,5,5,5),(6,6,6,6)}
n(X)=6n(X)=6
Hence required probability,
=n(X)n(S)=664=n(X)n(S)=664
=1/216
C
Answer: (C) 1/216
Question: Two trains 190 m and 160 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions on parallel tracks. The time which they take to cross each other is?
(A) 10.7
(B) 10.9
(C) 10.6
(D) 12.6
(E) 18.8
Rationale: Relative speed = 60 + 40 = 100 km/hr.
= 100 * 5/18 = 250/9 m/sec.
Distance covered in crossing each other = 190 + 160 = 350 m.
Required time = 350 * 9/250
= 12.6 sec.
Answer:D
Answer: (D) 12.6
Question: A dishonest dealer professes to sell goods at the cost price but uses a weight of 900 grams per kg, what is his percent?
(A) 11.11%
(B) 25%
(C) 22%
(D) 29%
(E) 45%
Rationale: 900 --- 100
100 --- ? => 11.11%
Answer:A
Answer: (A) 11.11%
Question: After running a series of television advertisements, a leading beverage producer saw its sales increase by 50% to $1 million dollars per month. Prior to the advertising campaign, about how many dollars in sales did the company average per day?
(A) $1.25 million
(B) $22,000
(C) $750,000
(D) $27,000
(E) $10,000
Rationale: Let sales in previous month = X
1.5 X=1,000,000
3/2 X= 1,000,000 ..........> X=666,666
sales per day= 666,666/30= less than 25,000 so closest number is 22,000
Answer: B
Answer: (B) $22,000
Question: In school there are some bicycles and 4 wheeler wagons.one Tuesday there are 190 wheels in the campus.How many bicycles are there?
(A) 35
(B) 36
(C) 37
(D) 38
(E) 39
Rationale: Let no. of bicycles be x
& no. of wagons be y
so, 2x+4y=190
by solving, we get
no. of bicycles=39 (wheels=>2*39=78)
no. of wagons=28 (wheels=>4*28=112)
ANSWER:E
Answer: (E) 39
Question: A university cafeteria offers 4 flavors of pizza - 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) 16
(E) 32
Rationale: There are 4 flavors of pizza and each can be:
1. Without cheese and mushrooms;
2. With cheese;
3. With mushrooms;
4. With cheese and mushrooms.
So, the total number of pizza varieties is 4*4 = 16.
Answer: D.
Answer: (D) 16
Question: A feed shop sells two varieties of birdseed: Product A, which is 40% millet and 60% sunflower, and Product B, which is 65% millet and 35% safflower. If a customer purchases a mix of the both types of birdseed that is 50% millet, what percent of the mix is Product A?
(A) 50%
(B) 55%
(C) 60%
(D) 40%
(E) 45 %
Rationale: Yes there is a simple method :
Consider the following method
Product A : 40% millet and 60% sunflower
Product B : 65% millet and 35% safflower
Mix : 50% millet
Here the weighted average is 50%,
Now Product A has 40% millet, which is 10% less than the weighted average of mix = - 0.10 A --------------- I
Similarly, Product B has 65 % millet, which is 15 % more than the weighted average of mix = + 0.15 B ------------ II
Now, both Product A and Product B are combined to give a 50% mix containing millet, so equate I and II
implies, 0.10 A = 0.15 B
Therefore A/B = 0.15/0.10 = 3/2
A : B : (A + B) = 3 : 2 : (3+2) = 3 : 2 : 5
We have to find, percent of the mix is Product A i.e. A : (A + B) = 3 : 5 = (3 / 5) * 100 = 60 %
Here is a pictorial representation :
Product A= 40%------------------------10% or 0.10 below average, A times-----------------Total below = - 0.10 A
----------------------------------------------------------------------------------------Average = 50% or 0.50
Product B = 65 %--------------------------15% or 0.15 above average, B times-----------------Total above = + 0.15 B
Since the amount below the average has to equal the average above the average; therefore,
0.10 A = 0.15 B
A/B = 3/2
A:B: Total = 3:2:5
A/Total = 3:5 = 60 %
Answer: C
Answer: (C) 60%
Question: Ramesh completes a piece of work in 4 days, Ranjith completes the same work in 20 days. If both of them work together, then the number of days required to complete the work is?
(A) 6 days
(B) 8 days
(C) 10 days
(D) 12 days
(E) 3.33 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 =4 × 20/24 = 3.33 days
Answer : E
Answer: (E) 3.33 days
Question: If x = 3y, where y is a prime number greater than 2, how many different positive even divisors does x have, including x?
(A) 0
(B) 1
(C) 2
(D) 3
(E) It cannot be determined from the information given
Rationale: For x to have even divisors, xx has to be an even number.
We know that x=3y, where yy is a prime number greater than 2. As 2 is the only even prime number, y has to be an odd prime number.
This means that x must also be an odd number, since odd x odd = odd.
As x is odd, it cannot have any even divisors.
Therefore, A is the correct answer.
Answer: (A) 0
Question: 21 friends went to a hotel and decided to pay the bill amount equally. But 20 of them could pay Rs. 30 each as a result 21st has to pay Rs. 200 extra than his share. Find the amount paid by him.
(A) 120
(B) 250
(C) 110
(D) 220
(E) None
Rationale: Explanation:
Average amount paid by 20 persons = Rs. 30
Increase in average due to Rs. 200 paid extra by the 21st men = Rs. 200/20= Rs. 10
Therefore, Average expenditure of 21 friends = Rs. 30 + Rs. 10 = Rs. 40
Therefore, Amount paid by the 21st men = Rs. 40 + Rs. 200 = Rs. 240
Correct Option: E
Answer: (E) None
Question: A train 360 m long runs with a speed of 45 km/hr. What time will it take to pass a platform of 340 m long?
(A) 38 sec
(B) 35 sec
(C) 44 sec
(D) 40 sec
(E) 56
Rationale: Speed = 45 km/hr = 45 Ã— (5/18) m/s
= 150/12 = 50/4 = 25/2 m/s
Total distance = length of the train + length of the platform
= 360 + 340 = 700 meter
Time taken to cross the platform = 700/(25/2) = 700 Ã— 2/25 = 56 seconds
ANSWER:E
Answer: (E) 56
Question: Bani has only pennies, dimes, and nickels in a jar. The jar has at least 1 but no more than 4 pennies. If the jar has at least 1 nickel and 1 dime, which of the following could NOT be the total amount of money in the jar?
(A) 71
(B) 72
(C) 73
(D) 74
(E) 75
Rationale: Let there be a pennies , b nickels and c dimes
so total amount can be 1+5b+10c cents to 4+5b+10c
as you can see the equation of total whenever divided by 5 would leave a remainder from 1 to 4 ( as pennies can only be from 1 to 4 and hence a is limited to values from 1 to 4)
So the total can never be divisible by 5 and hence only 75 that is c is the option which is divisible by 5.
so answer is E
Answer: (E) 75
Question: A shopkeeper loses 15%,if an article is sold for Rs. 102. What should be the selling price of the article to gain 20%?
(A) 333
(B) 144
(C) 188
(D) 199
(E) 121
Rationale: Given that SP = Rs. 102 and loss = 15%
CP = [100(SP)]/(100 - l%) = (100 * 102)/85 = 20 * 6 = Rs. 120.
To get 20% profit, New SP = [(100 + p%)CP]/100 = (120 * 120)/100 = Rs. 144.Answer: B
Answer: (B) 144
Question: A bus from city M is traveling to city N at a constant speed while another bus is making the same journey in the opposite direction at the same constant speed. They meet in point P after driving for 2 hours. The following day the buses do the return trip at the same constant speed. One bus is delayed 24 minutes and the other leaves 36 minutes earlier. If they meet 24 miles from point P, what is the distance R between the two cities?
(A) 48
(B) 72
(C) 96
(D) 120
(E) 192
Rationale: Hmmm I did this question a while ago and got it wrong so trying again
Rate x time = distance.
For the initial trip lets the distance R to the midpoint be represented by P.
EQN1: R x 2 = P
For the second trip we know one bus left late and one left early. Together this is just a tricky way of saying one bus left an hour after the other. We know the total trip takes 4 hours (since getting to P is 2 hours). The second trip can be represented by:
Since the trip takes 4 hours if a bus leaves one hour early, the reminaining 3 hours are split between the two buses, ie. 1 + 3/2 = 2.5
EQN2: R x 2.5 = P + 24
EQN2-EQN1 : 0.5R=24
R=48
So the distance is rate x time = 48 x 4 = 192.
ANS = E
Answer: (E) 192
Question: If 9 is a factor of 2y, then which of the following may not be an integer?
(A) 6y/54 + 2y/3
(B) (4y-18)/9
(C) (2y+27)/9
(D) (81-4y^2)/81
(E) (2y-3)/3
Rationale: I got the right answer A after plugging in 18 for y.
While going through Kaplan's explanation, I couldn't understand the part about choice A.
"6y/54 + 2y/3 = 3/6 * 2y/9 + 2y/3.
Since 9 is a factor of 2y, 3 is also factor of 2y. So 2y/3 is an integer, as is 2y/9. But 3/6 = 1/2, so if 2y/9 is not even, the expression 3/6 * 2y/9 will not be even."
But, isn't 2y/9 always even? 9 is a factor of 2y, which means that we could have 2(9), 2(2)(9), 2(3)(9), and so forth. The 9 in the denominator cancels out the 9 in the numerator. So we are left with 2 * something. So 2y/9 is even.A
Answer: (A) 6y/54 + 2y/3
Question: 3 buffaloes eat as much as 4 cows or 2 oxen. At a farm there are 15 buffaloes, 8 oxen and 24 cows. The fodder for these cattle is available for 24days. If 8 more cows & 9 more buffaloes are brought in, how long will the fodder last?
(A) 10
(B) 12
(C) 13
(D) 18
(E) 21
Rationale: Sol. 2 oxen = 3 buffaloes = 4 cows 8 oxen = 16 cows and 15 buffaloes = 20 cows 16 cows + 20 cows + 24 cows = 60 cows Since fodder is available for 60 cows for 24 days
So fodder will be available for (60 + 8 + 12) = 80 cows c 24x60 .0 .
for-^—=18 days.
D
Answer: (D) 18
Question: A container contains a mixture of two liquids P and Q in the ratio 7 : 5. When 9 litres of mixture are
drawn off and the container is filled with Q, the ratio of P and Q becomes 7 : 9. How many litres of liquid
P was contained in the container initially?
(A) 23
(B) 21
(C) 19
(D) 17
(E) 18
Rationale: Explanation :
Let's initial quantity of P in the container be 7x and initial quantity of Q in the container be 5xNow 9
litres of mixture are drawn off from the containerQuantity of P in 9 litres of the mixtures drawn off =
9×712=6312=214Quantity of Q in 9 litres of the mixtures drawn off = 9×512=4512=154HenceQuantity of
P remains in the mixtures after 9 litres is drawn off =7x−214Quantity of Q remains in the mixtures after 9
litres is drawn off =5x−154Since the container is filled with Q after 9 litres of mixture is drawn
off,Quantity of Q in the mixtures=5x−154+9=5x+214Given that the ratio of P and Q becomes 7 :
9⇒(7x−214):(5x+214)=7:9⇒(7x−214)(5x+214)=7963x−(9×214)=35x+(7×214)28x=(16×214)x=(16×214×28)
litres of P contained in the container initially = 7x=(7×16×214×28)=16×214×4=21
Answer : Option B
Answer: (B) 21
Question: A certain university will select 2 of 3 candidates eligible to fill a position in the mathematics department and 4 of 5 candidates eligible to fill 2 identical positions in the computer science department. If none of the candidates is eligible for a position in both departments, how many different sets of 3 candidates are there to fill the 3 positions?
(A) 42
(B) 10
(C) 40
(D) 65
(E) 15
Rationale: 3C2*5C4 = 3*5 = 15
the answer is (E)
Answer: (E) 15
Question: How many even integers n, such that 20<=n<=180 are of the form 3k+4, where k is any natural number?
(A) 24
(B) 27
(C) 30
(D) 33
(E) 36
Rationale: The first number is 22 = 16+6(1).
We can continue adding 6 to make a list: 22, 28, 34,...
The last number is 278 = 16+6(27)
There are 27 numbers in the list.
The answer is B.
Answer: (B) 27
Question: There are 12 dozen mangoes in a box. If there are 43
such boxes, how many mangoes are there in all the
boxes together?
(A) 516
(B) 3096
(C) 6192
(D) 628
(E) None
Rationale: Number of mangoes = 12 dozens
= 12 × 12 = 144
∴ Number of mangoes in 43 boxes
= 43 × 144 = 6192
Answer C
Answer: (C) 6192
Question: 3 candidates in an election and received 1136, 7636 and 11628 votes respectively. What % of the total votes did the winningcandidate got in that election?
(A) 34%
(B) 56%
(C) 57%
(D) 67%
(E) 78%
Rationale: Total number of votes polled = (1136 + 7636 + 11628) = 20400
So, Required percentage = 11628/20400 * 100 = 57%
C
Answer: (C) 57%
Question: If 28a+30b+31c=395.
then a+b+c=?.a,b,c are natural numbers
(A) 5
(B) 8
(C) 12
(D) 13
(E) 42
Rationale: have a look on your calender
since,we all know a year consist of 365 days
february is d only month which has 28 days
4 months in a year has 30 days
and,rest 7 months has 31 days..
so,following d given eq. we can write 28*1 + 30*5+ 31*7..
hence values of a,b and c are 1, 5 and 7 respectively..
a+b+c=13
ANSWER:D
Answer: (D) 13
Question: K is a 3 digit number such that the the ratio of the number to the sum of its digits is least.What is the difference between the hundreds and tens digit?
(A) 9
(B) 8
(C) 7
(D) 6
(E) 5
Rationale: Explanation :
This is only possible only when the hundreds digit has the least value and tens and units has the highest value.so we could get the highest possible sum but possible lowest number.so by this logic this number could only be 199.so the difference is 8.
note:remember a number given as abc i.e abc=aX100+bX10+c.
so 123=1X100+2X10+3.
Answer : B
Answer: (B) 8
Question: An inlet pipe can fill the tank in 30 minutes. B an outlet pipe can empty the tank in 45 minutes. In what time the tank be filled if both pipes work simultaneously?
(A) 90 minutes
(B) 80 minutes
(C) 70 minutes
(D) 60 minutes
(E) 50 minutes
Rationale: Time taken to fill the tank= LCM = 90
= Ratio= 30:45=2:3
= 90/(3 - 2) = 90/1 = 90 minutes
ANSWER:A
Answer: (A) 90 minutes
Question: The average age of a class of 22 students is 21 years. The average increased by 1 when the teacher's age also included. What is the age of the teacher?
(A) 44
(B) 48
(C) 45
(D) 43
(E) 50
Rationale: Total age = 22 * 21
tot age of all stu + age of the teacher = 23*22
age of the teacher = 23*22-22*21 = 44
ANSWER A
Answer: (A) 44
Question: Rs.1170 is divided so that 4 times the first share, thrice the 2nd share and twice the third share amount to the same. What is the value of the third share?
(A) Rs.530
(B) Rs.540
(C) Rs.550
(D) Rs.560
(E) Rs.570
Rationale: A+B+C = 1170
4A = 3B = 2C = x
A:B:C = 1/4:1/3:1/2 = 3:4:6
6/13 * 1170 = Rs.540
B
Answer: (B) Rs.540
Question: Camel and carriage for Rs. 5000. He SP the camel at a gain of 20% and the carriage at a loss of 10%. If he gains 3% on the whole, then find the CP of the camel?
(A) Rs.2166.67
(B) Rs.2234
(C) Rs.2345.13
(D) Rs.2456.34
(E) Rs.2550.34
Rationale: Now, in this numerical, there is no common loss and gain %.
Hence, solve it making equations.
Let cost price of camel be x.
As cost of camel and carriage = Rs 5000
Cost of carriage = Rs. (5000 – x)
After selling camel he gains 20% and on carriage a loss of 10%. But on the whole he gains 3%.
Therefore,
20% of x – 10 % of (5000 – x) = 3 % of 5000
20 × x – 10 × (5000 – x) = 3 × 5000
100 100 100
x – (5000 – x) = 150
5 10
10x – (5000 – x) × 10 = 150 × 10
5 10
2x-5000+x=1500
3x=1500+5000
x=2166.67
The cost of camel = Rs.2166.67
Option (A) is the correct answer
Answer: (A) Rs.2166.67
Question: If two students are made to sit in a row, then 6 don't have seats. If 6 students are made to sit in a row, then three rows are empty. How many students have to sit a row such that each row has equal number of students and all students are seated?
(A) 0
(B) 3
(C) 4
(D) 5
(E) 9
Rationale: Let there be a rows.
Then 2a + 6 = 6(a-3) [equating the number of students]
=> a= 6
and total number of students = 18
Therefore 3 students much sit in each row such that each row has an equal number of students and all students are seated.
Option (B)
Answer: (B) 3
Question: Find the value of k for which there are infinite solutions for the given set of equations.
5x + 2y = k and 10x + 4y = 3
(A) 3/0
(B) 3/2
(C) 3/1
(D) 3/8
(E) 3/4
Rationale: For the two sets of equation to have infinite solutions, we have 510=24=k3510=24=k3. Hence, k = 3/2
Answer:	B
Answer: (B) 3/2
Question: If n is an integer greater than 8, which of the following must be divisible by 3?
(A) 1. n (n+1) (n-4)
(B) 2. n (n+2) (n-1)
(C) 3. n (n+3) (n-5)
(D) 4. n (n+4) (n-2)
(E) 5. n (n+5) (n-6)
Rationale: We need to find out the number which is divisible by three,
In every 3 consecutive integers, there must contain 1 multiple of 3.
So n+4 and n+1 are same if we need to find out the 3's multiple. replace all the numbers which are more than or equal to three
1. n (n+1) (n-4) = > n(n+1)(n-1) = > (n-1)n(n+1)
2. n (n+2) (n-1) = > n(n+2)(n-1) = > (n-1)n(n+1)
3. n (n+3) (n-5) = > n(n+0)(n-2) = > (n-2)n(n)
4. n (n+4) (n-2) = > n(n+1)(n-2) = > (n-2)n(n+1)
5. n (n+5) (n-6) = > n(n+2)(n-0) = > (n)n(n+2)
from the above onlyoption Ais product of consecutive three numbers.
C
Answer: (C) 3. n (n+3) (n-5)
Question: Due to 10% decrease in the price of sugar and John can buy 5kg more sugar in Rs100 , then find the CP of sugar?
(A) Rs. 1(2/9)
(B) Rs. 2(2/9)
(C) Rs. 2(1/9)
(D) Rs. 4(2/9)
(E) Rs. 3(1/9)
Rationale: Here r = 10 % ,x = 100 and A = 5 kg
Actual price of sugar = 10*100/((100-10 )*5) = Rs. 2(2/9)
B
Answer: (B) Rs. 2(2/9)
Question: A work which could be finished in 9 days was finished 3 days earlier after 10 more men joined. The number of men employed was?
(A) 8
(B) 9
(C) 10
(D) 20
(E) 30
Rationale: x ------- 6
(x + 10) ---- 3
x * 6 = (x + 10)3
x = 10
ANSWER:C
Answer: (C) 10
Question: 36 is divided in 2 parts such that 8 times the first part added to 3 times the second part makes 203. What is the first part?
(A) 19
(B) 88
(C) 267
(D) 26
(E) 28
Rationale: Explanation:
Let the first part be x.
8x + 3 (36 – x) = 203
8x + 108 – 3x = 203
5x + 108 = 203
5x = 95
x = 19
ANSWER: A
Answer: (A) 19
Question: In a nationwide poll, N people were interviewed. If 1/5 of them answered yes to question 1, and of those, 1/4 answered yes to question 2, which of the following expressions represents the number of people interviewed who did NOT answer yes to both questions?
(A) N/9
(B) 8N/9
(C) 19N/20
(D) 31N/40
(E) 37N/40
Rationale: The number of people who answered yes to both questions is (1/4)(1/5)N = N/20
The number of people who did not answer yes to both is 1 - N/20 = 19N/20
The answer is C.
Answer: (C) 19N/20
Question: The cost price of 60 articles is the same as the selling price of x articles. If the profit is 20%, what is x?
(A) 42
(B) 45
(C) 48
(D) 50
(E) 54
Rationale: Let the cost price = y
The cost price of 60 articles = 60y
The selling price of x articles = 1.20y*x
1.20y*x = 60y
x = 60 / 1.2 = 50
The answer is D.
Answer: (D) 50
Question: The grade point average of the entire class is 84. If the average of one fourth of the class is 96, what is the average of the rest of the class?
(A) 76
(B) 77
(C) 78
(D) 79
(E) 80
Rationale: Let x be the number of students in the class.
Let P be the average of the rest of the class.
84x = (1/4)96x + (3/4)(P)x
336 = 96 + 3P
3P = 240
P = 80.
The answer is E.
Answer: (E) 80
Question: 2 – [2 – {2 – 2 (2 + 2)}] = ?
(A) -4
(B) 4
(C) 6
(D) None of these
(E) Cannot be determined
Rationale: Solution
Given exp. = 2 - [2-{2-2×4}]
= 2 -[2-{2-8}]
= 2-[2-(-6)]
= 2-[2+6]
= 2-8
= -6
Answer D
Answer: (D) None of these
Question: How many D ways are there of placing 6 marbles in 4 bowls, if any number of them can be placed in each bowl?
(A) 6C4
(B) 6P4
(C) 4^6
(D) 6^4
(E) 6!
Rationale: Each marble has 4 options, so there are total of D=4*4*4*4*4*4=4^6 ways.
Answer: C.
The total number of ways of dividing n identical items among r persons, each one of whom, can receive 0,1,2 or more items is (n+r -1)C(r-1).
Answer: (C) 4^6