mathewhe/aqua_rat huggingface dataset:
Question: A certain car dealership offers its newest model in ten exterior and six interior colors. If the ten interior colors are identical to the ten exterior colors, and the dealership sells every pair of colors except those that would result in a car with an identically colored interior and exterior, how many different color combinations are possible?
(A) 45
(B) 81
(C) 90
(D) 10!/2!
(E) 36
Rationale: I lined up the 10 different colours for Exterion and Interior like this:
E: A B C D E F G H I J
I: A B C D E F G H I J
I calculated the number of combinations: 10*10= 100 combinations.
But, from these 100 we need to delete sth: the same colours.
There are 10 possible pairs of coulours that will be the same. So, I deleted these 10 pairs from 100, resulting in 36.
Mind here, that the 10 do not result in 20 colours, because 1 pair is one unit that is not allowed. So, 10 units are not allowed (surprised that 80 wasn't among the answer options to confuse test takers...).
E
Answer: (E) 36
Question: The ratio of red boxes to blue boxes in a certain warehouse is 20 to 25. If the number of the red boxes were doubled and the number of blue boxes were increased by 150 the ratio would be halved. How many total boxes are in the warehouse?
(A) 37
(B) 74
(C) 111
(D) 90
(E) 244
Rationale: Ratio = R/B = 20/25 or R = 20/25 B -----------(1)
2R/B+150 = 20/25*1/2 = 2/5 or we can say that 10R=2B+300 -------------(2)
solving (1) and (2) we get
B=50 and R = 40
so total boxes is B + R = 50+40=90
Hence D. 90 is the correct answer
Answer: (D) 90
Question: It was Sunday on Jan 1, 2006. What was the day of the week Jan 1, 2010?
(A) Sunday
(B) Saturday
(C) Friday
(D) Wednesday
(E) Monday
Rationale: On 31st December, 2005 it was Saturday.
Number of odd days from the year 2006 to the year 2009 = (1 + 1 + 2 + 1) = 5 days.
On 31st December 2009, it was Thursday.
Thus, on 1st Jan, 2010 it is Friday.
Answeer:C
Answer: (C) Friday
Question: A gym offers 11 levels of fitness classes, and in an attempt to reward those who progress toward higher levels of fitness it charges $50 less per course for each level of fitness. Jessica completed all 11 levels by taking one course at each level, and her total cost was $4675. What is the cost Q for a course at the gym's highest level?
(A) $175
(B) $245
(C) $425
(D) $675
(E) $725
Rationale: Let the cost of a course in level 1 = x
=> Cost of level 2 = x-(50*1)... and so on
=> cost of level 11 = x-(50*10) = x-500
=> Total cost Q of 1 course in each of the 11 levels = x+(x-50)+(x-100)+.....+(x-500)
= 11x -50 (1+2+....+10)
= 11x - (50*55)
=> 11x-2750 = 4675
11x = 7425
x= 675
x-500=175
Answer A
Answer: (A) $175
Question: One fourth of one third of two fifth of a number is 25. What will be40% of that number
(A) 140
(B) 300
(C) 180
(D) 200
(E) 250
Rationale: Explanation:
(1/4) * (1/3) * (2/5) * x = 25 then x = 25 * 30 = 750
40% of 250 = 300
Answer: Option B
Answer: (B) 300
Question: The banker’s gain on a certain sum due 1½ years hence is 3/25 of the banker’s discount. The rate percent is :
(A) 3 1/3 %
(B) 6 1/6 %
(C) 9 1/9 %
(D) 9 1/6 %
(E) None
Rationale: Sol.
Let B.D. = Re 1. Then, B.G. = Re 3/25.
∴ T.D. = (B.D. - B.G.) = Re[1 - 3/25] = Re 22/25.
Sum = [1 * 22/25 / 1 - 22/25] = Rs. 22/3.
S.I. on Rs. 22/3 for 1 ½ years is Re 1.
∴ Rate = [100 * 1 / 22/3 * 3/2] % = 9 9/1%.
Answer C
Answer: (C) 9 1/9 %
Question: If f(m)=m^2 and m is a positive integer, which of the following CANNOT be the value of f(f(m))?
(A) 256
(B) 16
(C) 1296
(D) 625
(E) 300
Rationale: f(m)=m^2
f(f(m)) = (m^2)^2 = m^4
Therefore f(f(m)) will be numbers that are 4th power of other numbers.
Checking the options:
256 = 4^4
16 = 2^4
1296 = 6^4
625 = 5^4
300. This cannot be written as the 4th power of any number
Answer: E
Answer: (E) 300
Question: Solution Y is 30 percent liquid O and 70 percent water. If 2 kilograms of water evaporate from 8 kilograms of solutions Y and 2 kilograms of solution Y are added to the remaining 6 kilograms of liquid, what percent of this new liquid solution is liquid O?
(A) 30%
(B) 33 1/3%
(C) 37 1/2%
(D) 40%
(E) 50%
Rationale: Answer:C
Took time to solve this one, the statement2 kilograms of solution Y are added to the remaining 6 kilograms of liquidwas confusing to me. After thinking more deeply, it was clear to me that new 2 kg of solution Y will also be 30% liquid O and 70% water, and then I was able to get the answer. That was a bit tricky and nice question=C
Answer: (C) 37 1/2%
Question: Find the compound interest on $20000 in 2years at 4% per annum, the interest being compounded half-yearly?
(A) $645.56
(B) $1648.64
(C) $954.26
(D) $745.69
(E) $1020.45
Rationale: Principle = $20000
Rate = 2% half yearly = 4 half years
Amount = 20000*(1 + 2/100)^4 = 20000 * 51/50 * 51/50 * 51/50 * 51/50
= $21648.64
C.I. = 21648.64-20000 = $1648.64
Answer is B
Answer: (B) $1648.64
Question: Riya and Priya set on a journey. Riya moves eastward at a speed of 18kmph and Priya moves westward at a speed of 24 kmph.How far will be priya from Riya after 15 minutes
(A) 25kms
(B) 11kms
(C) 50kms
(D) 30kms
(E) 40kms
Rationale: total eastward distance= 18kmph*1/4hr=4.5 km
total westward distance= 24kmph*1/4hr=6 km
total distn betn them= 4.5+6=10.5m
ans 11km
ANSWER:B
Answer: (B) 11kms
Question: John makes $60 a week from his job. He earns a raise andnow makes $70 a week. What is the % increase?
(A) 16%
(B) 16.66%
(C) 22%
(D) 24%
(E) 24.5%
Rationale: Increase = (10/60)*100 = (1/6)*100 = 16.66%.
B
Answer: (B) 16.66%
Question: Given a Number 123456, from this number put any three values in numerator and remaining three are in denominator. So how many values you can make from this number less than 1/5.
(A) 4
(B) 5
(C) 6
(D) 7
(E) 8
Rationale: 123/645 ,123/654 ,124/635 ,124/653
,125/634 ,125/643 ,
ans is 6.
ANSWER:C
Answer: (C) 6
Question: If Jack walked 9 miles in 1 hour and 15 minutes, what was his rate of walking in miles per hour?
(A)  4
(B)  4.5
(C)  6
(D)  6.25
(E)  7.2
Rationale: Distance walked in 1 hour and 15 mins = 9 miles
Speed per hour = Distance/Time = 9/(5/4) = 7.2 miles per hour
Answer E
Answer: (E)  7.2
Question: In 110 m race, A covers the distance in 36 seconds and B in 45 seconds. In this race A beats B by:
(A) 20 m
(B) 25 m
(C) 22 m
(D) 9 m
(E) 12 m
Rationale: Distance covered by B in 9 sec. =	110/45 x 9	m = 22 m.
A beats B by 20 metres.
Answer: Option C
Answer: (C) 22 m
Question: 4, 12, 48, 240, (...)
(A) 1440
(B) 10080
(C) 6200
(D) 10020
(E) 12500
Rationale: Explanation :
Go on multiplying the given numbers by 3, 4, 5, 6,
Answer : Option A
Answer: (A) 1440
Question: 4000 was divided into two parts such a way that when first part was invested at 3% and the second at 5%, the whole annual interest from both the investments is Rs.144, how much was put at 3%?
(A) 8279
(B) 2890
(C) 2800
(D) 2730
(E) 3702
Rationale: (x*3*1)/100 + [(4000 - x)*5*1]/100 = 144
3x/100 + 200 – 5x/100 = 144
2x/100 = 56 è x = 2800
Answer: C
Answer: (C) 2800
Question: What number should be added to each of the numbers 8, 21, 13 and 31 so that the resulting numbers, in this order form a proportion?
(A) 2
(B) 3
(C) 5
(D) 7
(E) 9
Rationale: Explanation :
(8+x)/(21+x) = (13+x)/(31+x)
Then, (8 + x)(31 + x) = (13 + x)(21 + x)
or39x + 248 = 34x + 273 or 5x=25 or x = 5.
Answer : C
Answer: (C) 5
Question: In a contest, a bowl contains 7 keys, one of which will open a treasure chest and Six of which will not. If a contestant selects the key that opens the treasure chest, she wins the contents of that chest. If Sita is allowed to draw two keys, simultaneously and at random, from the bowl as the first contestant, what is the probability that she wins the prize?
(A) 1/8
(B) 1/9
(C) 2/7
(D) 3/19
(E) 3/23
Rationale: The total possibilities existing while withdrawing two keys are: 7C2 = 21
For Sita to win, 6 combinations exist assuming Key 1 to unlock the treasure E.g(1,2), (1,3)....(1,6)
P = 6/21= 2/7
Option C
Answer: (C) 2/7
Question: By how much does the larger root of the equation 2c^2+5c = 12 exceed the smaller root?
(A)  5/2
(B)  10/3
(C)  7/2
(D)  14/3
(E)  11/2
Rationale: For 2c^2+5c = 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: How many ways can six friends be arranged around a circular dinner table?
(A) 16
(B) 48
(C) 96
(D) 120
(E) 720
Rationale: The number of arrangements of n distinct objects in a row is given by n!n!.
The number of arrangements of n distinct objects in a circle is given by (n−1)!(n−1)!.
The difference between placement in a row and that in a circle is following: if we shift all object by one position, we will get different arrangement in a row but the same relative arrangement in a circle. So, for the number of circular arrangements of n objects we have:
n!n=(n−1)!n!n=(n−1)!.
So, the answer is (6 - 1)! = 5! = 120.
Answer: D.
Answer: (D) 120
Question: On planet Jupiter the people use a certain number system to the base ‘n’ (n > 2), Jerk, a resident of the planet, one day received twice his daily wage because the digits of this wage, which was a 2 digit number, were reversed. If the value of ‘n’ is the least possible value there the decimal representation of the difference between Jerk’s correct wage for the day is
(A) 8
(B) 9
(C) 10
(D) 11
(E) 12
Rationale: Sol:
Let the base of the number system be n and the two digit number be ab
given 2(ab)n = (ba)n
⇒⇒ nb + a = 2na + 2b
⇒⇒ a(2n - 1) = b(n - 2)
⇒a/b= n−2 /2n−1
Now the maximum possible value of a or b is (n - 1) (base n) for n = 3 we get
a/b=1/5 which is not possible as in base 3, 5 won't exist.
Similarly, for n = 4
but for n = 5
We get a/b=3/9 i.e.1/3
a = 1, b = 3 is the only number possible when n is the least possible.
The correct wage = (13)5=(8)10
The actual wage paid = (31)5=(16)10
So difference = 8
Answer A
Answer: (A) 8
Question: A man bought 40 shares of Rs. 60 at 6 discount, the rate of dividend being 12 1/2%The rate of interest obtained is
(A) 13.89%
(B) 15.5%
(C) 14%
(D) 14.25%
(E) 14.95%
Rationale: Explanation :
Face Value of a share = Rs.60
He bought each share at Rs.60 - Rs.6 = Rs.54
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 × 54)
Interest obtained = 40×7.5×100/40×54=13.89%
Answer : Option A
Answer: (A) 13.89%
Question: The average age 12 monkeys in a tree is 16 years. Out of these, the average age of 6 monkeys is 18 years and that of the other 6 monkeys is 13 years. The age of the 12th monkey is?
(A) 10
(B) 9
(C) 4
(D) 6
(E) 7
Rationale: Age of the 12th monkey= 12*16 - (6*18+6*13) = 192-186= 6 years
Answer is D
Answer: (D) 6
Question: In the following number sequence how many such even numbers are there which are exactly divisible by its immediate preceding number but not exactly divisible by its immediate following number?
3 8 4 1 5 7 2 8 3 4 8 9 3 9 4 2 1 5 8 2
(A) Two
(B) Three
(C) Four
(D) More than four
(E) One
Rationale: correct answer is a
283,489
ANSWER:B
Answer: (B) Three
Question: If (68-a)(68-b)(68-c)(68-d)(68-e)=725
then a+b+c+d=?
(A) 231
(B) 231
(C) 233
(D) 234
(E) 235
Rationale: we will first break 725 in prime factor=(5*5*29*1*1) a/c to whatever factors is here
then we we will compare like
(68-63)(68-63)(68-39)(68-67)(68-67)i.e.5*5*29*1*1
a=63
b=63
c=39
d=67
and now sum is =a+ b+ c+ d=232
ANSWER:B
Answer: (B) 231
Question: What should come in place of question mark(?) in the following equation?
8597 – ? = 7429 – 4358
(A) 5706
(B) 5526
(C) 5426
(D) 5626
(E) None of these
Rationale: 8597 – ? = 7429 – 4358
∴ ? = 5526
Answer B
Answer: (B) 5526
Question: For 6-digit integer 46x,y12, when x and y are drawn at random from {3,5,8}, what is the probability E that the integer drawn is divisible by 8?
* A solution will be posted in two days.
(A) 1/6
(B) 1/3
(C) 1/2
(D) 2/3
(E) 5/6
Rationale: In general, the remainder divided by integer n is the same as the remainder that up to tens of n is divided by 8.
Thus, in order for 46,x,y12 to be divided by 8, y12 should be divided by 8.
Amongst 3,5,8, 3 and 5 can be divided by 8.
Therefore,E= two out of three can be divided and the answer is D.
Answer: (D) 2/3
Question: Hector runs a one-product widget shop. Each month, his fixed costs, whether he produces anything or not, amount to x dollars. The marginal cost of producing and selling one widget is a constant y dollars, regardless of the number he produces. He generally can sell widgets for s dollars each. What is the minimum number of widgets he must produce, assuming he sells every widget he produces, to break even (neither make a profit nor incur a loss) in a given month?
(A) x/(y - s)
(B) x/(s - y)
(C) x
(D) x/s
(E) x/y
Rationale: Two ways...
1) let t be the total number, so cost = t*y+x and selling price=t*s..
No profit no loss....t*y+x=t*s.....T=x/(s-y)...
B
Answer: (B) x/(s - y)
Question: 123 school girls are to be transported in small vans. Each van can carry 8 girls only. What is the smallest possible number of vans that are needed to transport all 123 school girls?
(A) 16 vans
(B) 26 vans
(C) 12 vans
(D) 17 vans
(E) 10 vans
Rationale: To find the number of vans, we divide 123 by 8.
123 / 8 = 15 and remainder = 3
So 15 vans are needed to transport 15 x 8 = 120 girls, and 1 van is needed to transport the 3 remaining girls. A total of 16 vans are needed.
correct answer A
Answer: (A) 16 vans
Question: A, B and C invested Rs.6300, Rs.4200 and Rs.10500 respectively, in a partnership business. Find the share of A in profit of Rs.12500 after a year?
(A) 3630
(B) 2881
(C) 2887
(D) 3750
(E) 2212
Rationale: 6300:4200:10500
3:2:5
3/10 * 12100 = 3750.Answer: D
Answer: (D) 3750
Question: If x is equal to the sum of the integers from 30 to 50, inclusive, and y is the number of even integers from 30 to 50, inclusive, what is the value of x + y ?
(A) 810
(B) 811
(C) 830
(D) 850
(E) 851
Rationale: 21 integers from 30 to 50 inclusive
so 11th integer is mean, it is 40
21*40=840
from 21 integers 11 ones is even
840+11=851
ANSWER:E
Answer: (E) 851
Question: A certain sum of money at simple interest amounted Rs.840 in 10 years at 3% per annum, find the sum?
(A) 971
(B) 973
(C) 268
(D) 646
(E) 365
Rationale: 840 = P [1 + (10*3)/100]
P = 646
Answer: D
Answer: (D) 646
Question: The owner of a wood furniture shop charges his customer 24% more than the cost price. If a customer paid Rs. 8339 for a computer table, then what was the cost price of the computer table?
(A) 6535
(B) 6532
(C) 6725
(D) 6874
(E) 6972
Rationale: C
6725
CP = SP * (100/(100 + profit%))
= 8339(100/124) = Rs. 6725
Answer: (C) 6725
Question: A discount of 10 percent on an order of goods followed by a discount of 40 percent amounts to
(A) the same as one 46 percent discount
(B) the same as one 40 percent discount
(C) the same as one 36 percent discount
(D) the same as one 30 percent discount
(E) the same as one 25 percent discount
Rationale: 0.9*0.6*x=0.54x from initial value, meaning 0.46 or 46% discount
A
Answer: (A) the same as one 46 percent discount
Question: A foreign language club at Washington Middle School consists of n students, 3/5 of whom are boys. All of the students in the club study exactly one foreign language. 1/3 of the girls in the club study Spanish and 4/5 of the remaining girls study French. If the rest of the girls in the club study German, how many girls in the club, in terms of n, study German?
(A) 2n/5
(B) n/3
(C) 4n/75
(D) 2n/15
(E) n/15
Rationale: 3/5 of the students are boys, thus 2/5 of the students are girls.
1/3 of the girls in the club study Spanish and 4/5 of the remaining girls study French.
Thus 1/5 of 2/3 = 2/15 of the girls study German.
Since girls comprise 2/5 of the students, then 2/5*2/15=4/75 are girls who study German.
The answer is C.
Answer: (C) 4n/75
Question: A telephone number contains 10 digit, including a 3-digit area code. Bob remembers the area code and the next 5 digits of the number. He also remembers that the remaining digits are not 0, 1, 2, 7, or 8. If Bob tries to find the number by guessing the remaining digits at random, the probability that he will be able to find the correct number in at most 2 attempts is closest to which of the following ?
(A) 1/625
(B) 2/625
(C) 50/625
(D) 75/625
(E) 90/625
Rationale: I think most of the answers are missing a point. Let me try to put it across:
Total number of possible numbers are : 5x5 = 25
Correct number =1
Case 1: When he gets it right in first attempt: P(E1) = 1/25
Case 2: He gets 1st attempt wrong and second right:
When he gets it wrong then the probability of getting wrong is 24/25.
Now there are 24 cases with him and he chooses the right one this time.
Probability of right case is 1/24
Thus, P(E2) = 24/25 x 1/24
=1/25
Probability of getting it right in at most two cases = P(E1) + P(E2)
= 1/25 + 1/25
= 2/25
= 50/625
Option (C) is therefore right as most of you mentioned but the method employed was wrong.
Answer: (C) 50/625
Question: The value of a stock is X dollars. On Sunday the stock's value grew by half of its value, but on Monday its value dropped to a third of its new value. What is the stock's value at the end of Monday?
(A) X.
(B) X/2.
(C) 2X/3
(D) X/3
(E) X/4.
Rationale: Given the value of stock is X dollars.
Then on Sunday the stock's value is increased by half i.e. X + X/2 = 3X/2 ( this is the new value)
Then on Monday its value dropped by 1/3 of new value = 1/3(3X/2) = 3X/6
Then 3X/2 - 3X/6 = 6X/6 = 6. (new value - 1/3 value)
Ans: A is correct option..
Answer: (A) X.
Question: Jim travels the first 3 hours of his journey at 60 mph speed and the remaining 5 hours at 24 mph speed. What is the average speed of Jim's travel in mph?
(A) 35.5mph
(B) 37.5mph
(C) 38.5mph
(D) 39.5mph
(E) 36.5mph
Rationale: 3 hours of his journey at 60 mph means 180 miles in 3 hours
5 hours at 24 mph speed means 120 miles in 5 hours. In total 300 miles in 8 hours.
Average Speed is ((3*60)+(5*24))/8 = 37.5mph
ANSWER:B
Answer: (B) 37.5mph
Question: If p is a positive integer and 10p/96 is an integer, then the minimum number ofuniqueprime factors p could have is H:
(A) H=1
(B) H=2
(C) H=3
(D) H=4
(E) H=5
Rationale: 10p/96 should resolve to a integer => 5p/48 should resolve to an integer.
Hence p/48 should resolve to a integer.
48 -- > 2^4 * 3.
Hence p should have atleast 2^4*3 for p/48 to resolve to a int.
The unique prime factors in 2^4 * 3 is 2, 3 and hence the answer is B(2).
Answer: (B) H=2
Question: 5358 x 51 = ?
(A) 273258
(B) 273158
(C) 273268
(D) 283258
(E) 262268
Rationale: 5358 x 51	= 5358 x (50 + 1)
= 5358 x 50 + 5358 x 1
= 267900 + 5358
= 273258
Answer is A.
Answer: (A) 273258
Question: How many possible integer values are there for x if |4x - 3| < 6 ?
(A) One
(B) Two
(C) Three
(D) Four
(E) Five
Rationale: Solution: |4x-3| < 6
let 4x=a therefore we have |a-3| < 6 ==> read this as origin is at +3 and we have to move +6 to the right and -6 to the left
(the less than sign represents that the a must be within boundaries )
(3-6)----------3----------(3+6)
now, we have -3<a<9
but a =4x ==> -3<4x<9
dividing all values by +4 we have -0.75 <x < 2.24
Now question says Integer values (not rational ) therefore we have 0,1,2
ANSWER:C
Answer: (C) Three
Question: what is the distance between two parallel chords of length 32 cm and 24 cm in a circle of radius 20 cm ?
(A) 1 or 7
(B) 3 or 21
(C) 4 or 28
(D) 2 or 14
(E) 5 or 14
Rationale: since the chord length=2sqrrt(r^2-d^2)
chord length=32,r=20 then we get d=12
chord length=24,r=20 then we get d=16
then we add/subtract we get option c) 4 or 28
ANSWER:C
Answer: (C) 4 or 28
Question: 0.0006688/0.0000150 x 19.85 = ?
(A) 850
(B) 900
(C) 950
(D) 1000
(E) 2000
Rationale: Explanation :
? = 6688/150 x 19.85 = 45 x 20 = 900
Answer : Option B
Answer: (B) 900
Question: Two stations A and B are 110 km apart on a straight line. One train starts from A at 7 a.m. and travels towards B at 20 kmph. Another train starts from B at 8 a.m. and travels towards A at a speed of 25 kmph. At what time will they meet?
(A) 16 a.m
(B) 10 a.m
(C) 17 a.m
(D) 76 a.m
(E) 11 a.m
Rationale: Suppose they meet x hours after 7 a.m.
Distance covered by A in x hours = 20x km.
Distance covered by B in (x - 1) hours = 25(x - 1) km.
Therefore 20x + 25(x - 1) = 110
45x = 135
x = 3.
So, they meet at 10 a.m.
Answer:B
Answer: (B) 10 a.m
Question: The velocity of a falling object in a vacuum is directly proportional to the amount of time the object has been falling. If after 7 seconds an object is falling at a speed of 90 miles per hour, how fast will it be falling after 12 seconds?
(A) 18 miles per hour
(B) 156 miles per hour
(C) 216 miles per hour
(D) 1080 miles per hour
(E) 5400 miles per hour
Rationale: Since Velocity is proportional to Time
Velocity =k*Timewhere k is the constant of proportionality
Time= 7 seconds
Velocity = 7k = 90 miles per Hour
i.e. k = 13
i.e. The relation between Velocity and Time becomes
Velocity =13*Time
Time= 12 seconds
Velocity = 13*12 = 156 miles per hour
Answer: Option B
Answer: (B) 156 miles per hour
Question: In a recent election, Geoff received 1 percent of the 6,000 votes cast. To win the election, a candidate needed to receive more than x% of the vote. If Geoff needed exactly 3000 more votes to win the election, what is the value of x ?
(A)  50
(B)  54
(C)  56
(D)  51
(E)  63
Rationale: Word problems are tricky in somehow more than other problem because you have the additional step to translate.
Breaking the problem: Geoff how many votes he receives ?? 60 votes
he needs 3571 more votes so : 60+3000= 3060
Now what's the problem wants ?? a x %........3060 is what % of total votes 6000........translating: 3060 = x/100 * 6000 ---
x= 51 %..........D
Answer: (D)  51
Question: When you multiply a number by 4 and
then subtract 7, the result is the same as
if you first subtracted 7 from the same
number and then multiplied by 11. What
is the number?
(A) 23
(B) 13
(C) 19
(D) 31
(E) 10
Rationale: Let x equal the number and then change the words into an equation and solve for x:
4x – 7 = 11(x – 7)
4x – 7 = 11x – 77
70 = 7x
10 = x
correct answer E)10
Answer: (E) 10
Question: As a treat for her two crying children, a mother runs to the freezer in which she has five cherry ice pops, three orange ice pops, and four lemon-lime ice pops. If she chooses two at random to bring outside to the children, but realizes as she runs out the door that she cannot bring them different flavors without one invariably being jealous of the other and getting even more upset, what is the probability that she has to return to the freezer to make sure that they each receive the same flavor?
(A) 1/9
(B) 1/6
(C) 5/18
(D) 1/999
(E) 5/6
Rationale: Probability of not getting the same flavor ->
Favourable -> Cherry - orange [ 5C1 * 3C1 [or simply 5*3 ] or Cherry - lemon [ 5*4] or orange - lemon [3*4]
Prob = (5*3 + 5*4 + 3*4 ) / 9C2 = 47/47520 = 1/999
Answer -> D
Answer: (D) 1/999
Question: How many integerskgreater than 100 and less than 1200 are there such that if the hundreds and the units digits ofkare reversed, the resulting integer is k+99?
(A) 50
(B) 60
(C) 70
(D) 80
(E) 100
Rationale: Numbers will be like 102 => 201 = 102 + 99
203 => 302 = 103 + 99
so the hundereth digit and units digit are consecutive where unit digit is bigger than hundred digit.
There will be ten pairs of such numbers
for every pair there will 10 numbers like for 12 => 102, 112,132,142,152, 162,172,182,192.
Total = 10 *10 = 100 hence E
Answer: (E) 100
Question: A mall charges 50 cents for the first hour of parking and $4 for each additional hour until the customer reaches 4 hours, after that the parking fee is $2 per hour. If a Rahul parked his car in the mall for 7 hours and 30 minutes, how much is he going to pay?
(A) $25
(B) $12.
(C) $23.5
(D) $24.5.
(E) $25.5
Rationale: 0.50+4*4+2*4+0.50= $25
Answer: $25
Answer: (A) $25