mathewhe/aqua_rat huggingface dataset:
Question: Car Q and Car Y traveled the same 80-mile route. If Car Q took 2 hours and Car Y traveled at an average speed that was 50 percent faster than the average speed of Car Q, how many hours did it take Car Y to travel the route?
(A)  2/3
(B)  1
(C)  4/3
(D)  8/5
(E)  3
Rationale: The speed of car Q is (distance)/(time) = 80/2 = 40 miles per hour.
The speed of car Y = 3/2*40 = 60 miles per hour --> (time) = (distance)/(speed) = 80/60 = 4/3 hours.
Answer: C.
Or: to cover the same distance at 3/2 as fast rate 2/3 as much time is needed --> (time)*2/3 = 2*2/3 = 4/3 hours.
Answer: C.
Answer: (C)  4/3
Question: The price of stock increased by 8% last year and decreased by 6% this year. What is the net percentage change in the price of the stock?
(A) 0.2%
(B) 0.8%
(C) 1.2%
(D) 1.52%
(E) 2%
Rationale: (100% + 8%) * (100% - 6%) = 1.08 * 0.94 =1.0152 = 101.52%.
The net percentage change in the price of the stock is (+) 1.52%
The answer is D
Answer: (D) 1.52%
Question: A trader sells 85 meters of cloth for Rs. 8925 at the profit of Rs. 15 per metre of cloth. What is the cost price of one metre of cloth?
(A) 22
(B) 28
(C) 90
(D) 27
(E) 23
Rationale: SP of 1m of cloth = 8925/85 = Rs. 105
CP of 1m of cloth = SP of 1m of cloth - profit on 1m of cloth
= Rs. 105 - Rs. 15
= Rs.90.
Answer:C
Answer: (C) 90
Question: The distance between Delhi and Mathura is 110 kms. A starts from Delhi with a speed of 20 kmph at 7 a.m. for Mathura and B starts from Mathura with a speed of 25 kmph at 8 p.m. from Delhi. When will they meet?
(A) 11
(B) 77
(C) 16
(D) 10
(E) 98
Rationale: D = 110 – 20 = 90
RS = 20 + 25 = 45
T = 90/45 = 2 hours
8 a.m. + 2 = 10 a.m..Answer: D
Answer: (D) 10
Question: Three is the largest number that can be divided evenly into 27 and the positive integer x, while 10 is the largest number that can be divided evenly into both 100 and x. Which of the following is the largest possible number that could be divided into x and 1500
(A) 30
(B) 70
(C) 210
(D) 300
(E) 150
Rationale: 27 = 3*3*3, and its GCF with x is 3, which implies that x has ONE factor of 3, but not TWO factors of 3.
100 and x have a GCF of 10, which implies that x has ONE factor of 10, but not TWO factors of 10.
Then we want to know what is the largest possible GCF of x and 2100.
Well 1500 = 3 *5 * 10 * 10
We want x to include as many factors in common with 2100 as possible, to make the GCF with 2100 as big as possible.
We know x has one factor of 3, but not two factors --- that takes the 3.
We know x has one factor of 10, but not two factors --- we can take one of those 10's, but we have to leave the other
No other restrictions, so we can also grab that factor of 7 --- nothing saying that we can't, and it's there for the taking.
3*5*10 = 150
If we allow x to include as many factors as possible, within the constraints given, that is the most x could have in common with 2100.
E
Answer: (E) 150
Question: Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 23 seconds. The ratio of their speeds is?
(A) 3/6
(B) 3/2
(C) 3/4
(D) 3/1
(E) 3/6
Rationale: Let the speeds of the two trains be x m/sec and y m/sec respectively. Then, length of the first train = 27 x meters, and length of the second train
= 17 y meters. (27 x + 17 y) / (x + y) = 23 ==> 27 x + 17 y
= 23 x + 23 y
==> 4 x = 6 y ==> x/y
= 3/2.
Answer: B
Answer: (B) 3/2
Question: The H.C.F of two numbers is 23 and the other two factors of their L.C.M are 14 and 15. The larger of the two numbers is:
(A) 338
(B) 278
(C) 345
(D) 231
(E) 121
Rationale: Clearly, the numbers are (23 * 14) and (23 * 15). Larger number
= (23 * 15) = 345.
Answer: C
Answer: (C) 345
Question: If the ratio of the sum of the first 6 terms of a G.P. to the sum of the first 3 terms of the G.P. is 126, what is the common ratio of the G.P?
(A) 3
(B) 1/3
(C) 2
(D) 5
(E) 1/5
Rationale: 126=(a1+a2+a3+a4+a5+a6)/(a1+a2+a3)
Factorize the same terms
126=1+(a4+a5+a6)/(a1+a2+a3)
Write every term with respect to r
a1=a1
a2=a1*r^1
a3=a1*r^2
.........
126=1+(a1(r^3+r^4+r^5))/(a1(1+r^1+r^2))
125=(r^3 (1+r^1+r^2))/((1+r^1+r^2))
125=r^3
r=5
D
Answer: (D) 5
Question: A company has 50 employees, of which 22 studied accounting, 15 studied finance and 14 studied marketing. Ten employees have done just two courses and only one made ​​the three courses. How many employees have no training?
(A) A)0
(B) B)9
(C) C)10
(D) D)11
(E) E)26
Rationale: Total employees=50
studied accounting=22
studied finance=15
studied marketing=14
10 employees have been double counted and one employee has been counted thrice.
Therefore employees who have received training=22+15+14-10-(2*1)
=51-12
=39
Employees with no training
=50-39
=11
Ans=D
Answer: (D) D)11
Question: A project manager needs to select a group of 4 people from a total of 4 men and 4 women. How many possible group combinations exist such that no group has all men ?
(A) 72
(B) 68
(C) 74
(D) 82
(E) 69
Rationale: Since the order in which the group is selected does not matter, we are dealing with a combinations problem (and not a permutations problem).
The formula for combinations is:
N!/((N-K)!K!)
Where N = the total number of elements from which we will select, 8 people in this case.
Where K = the total number of elements to select, 4 people in this case.
The total number of combinations is therefore:
8!/((8-4)!4!) = 70
However, one of these combinations are not valid since they have all members of men
The correct answer is 70-1 = 69.Ans E
Answer: (E) 69
Question: A train covers a certain distance at a speed of 320kmph in 6 hours. To cover the same distance in 1 2/3 hours, it must travel at a speed of
(A) 1152km/hr
(B) 1120km/hr
(C) 1650km/hr
(D) 1750km/hr
(E) 1850km/hr
Rationale: Explanation:
Distance = 320Ã—6 = 1920km
Required speed = (1920Ã— 3/5) = 1152km/hr
Answer: Option A
Answer: (A) 1152km/hr
Question: Thirty percent of the women in a college class are science majors, and the non-science majors make up 80% of the class. What percentage of the men are non-science majors if 40% of the class are men?
(A) 2%
(B) 5%
(C) 28%
(D) 30%
(E) 95%
Rationale: 3/k + 2/m = 6/t
Assuming total # is 100 :
[Science - Women] will have - 0.3 * 60 = 18
[Non-Science-Women] will have - 42
[Science-Men] will have = 20-18 = 2
[Non-Science-men] will have - 38
S0 38/40 * 100 = 95%
Answer - E
Answer: (E) 95%
Question: The diameters of two spheres are in the ratio 1:2 what is the ratio of their volumes?
(A) 1:7
(B) 1:3
(C) 1:8
(D) 1:1
(E) 1:2
Rationale: 1:8
Answer: C
Answer: (C) 1:8
Question: How many integers are there between 42 and 97, inclusive?
(A) 51
(B) 55
(C) 56
(D) 57
(E) 58
Rationale: I guess the easiest way to answer this is -
Say you have two positive integers, x and y where y > x
Then the number of integers between x and y is given by - (y - x) + 1
In this case, it's (97 - 42) + 1 =56
Option C
Answer: (C) 56
Question: During a trip, Francine traveled x percent of the total distance at an average speed of 20 miles per hour and the rest of the distance at an average speed of 80 miles per hour. In terms of x, what was Francineâ€™s average speed for the entire trip?
(A) (180-x)/2
(B) (x+60)/4
(C) (300-x)/5
(D) 600/(115-x)
(E) 8,000/(400-4x)
Rationale: E....
X% traveeled at 80 mph
100-X% traveeled at 20 mph
total timt taken = x/80 +(100-x)/20 = (400-4x)/80
Total distance = x+(100-x) = 100
Av speed = Tot Dis/Time Taken which is E
Answer: (E) 8,000/(400-4x)
Question: Which of the following describes all values of x for which 2–x^2 >= 0?
(A)  x >= 1
(B)  x <= –1
(C)  0 <= x <= 2
(D)  x <= –1 or x >= 1
(E)  –2 <= x <= 2
Rationale: Which of the following describes all values of x for which 2–x^2 >= 0?
(A) x >= 1
Plugged in 2. 2–(3)^2 >= 0 -7>=0? NO. Wrong
(B) x <= –1
Plugged in -3. 2–(-3)^2 >= 0 -7>=0? NO. Wrong
(C) 0 <= x <= 2
Plugged in 0, 1, and 2. All of them work. But E is better because it describes all the values of x
(D) x <= –1 or x >= 1
A and B answer this. Wrong.
(E) –2 <= x <= 2
X is a positive or negative fraction or a zero.
x = -2 x = 2 x = 0
Plug all of them. They work.
Answer is E.
Answer: (E)  –2 <= x <= 2
Question: A man buys an item at Rs. 800 and sells it at the loss of 20 percent. Then what is the selling price of that item
(A) Rs. 640
(B) Rs. 760
(C) Rs. 860
(D) Rs. 960
(E) None of these
Rationale: Explanation:
Here always remember, when ever x% loss,
it means S.P. = (100 - x)% of C.P
when ever x% profit,
it means S.P. = (100 + x)% of C.P
So here will be (100 - x)% of C.P.
= 80% of 800
= 80/100 * 800
= 640
Option A
Answer: (A) Rs. 640
Question: A freight elevator can carry a maximum load of 1200 pounds. Sean, who weighs 200 pounds, is in the elevator with two packages weighing 150 pounds and 280 pounds. If he needs to fit three more packages in the elevator that weigh as much as possible without exceeding the elevator limit, what is the difference between their average and the average of the two packages already in the elevator?
(A) 25
(B) 85
(C) 190
(D) 215
(E) 210
Rationale: The average of existing 2 package is (150 + 280)/2 = 430/2 = 215
Remaining allowed weight = 1200 - 200 - 430 = 570
.
allowed per package = 570 / 3 = 190
So difference in average of existing and allowable = 215 - 190 = 25
Hence A
Answer: (A) 25
Question: A bag contains five white and four red balls. Two balls are picked at random from the bag. What is the probability that they both are different color?
(A) 5/7
(B) 5/9
(C) 5/1
(D) 5/2
(E) 5/5
Rationale: Two balls can be picked from nine balls in ⁹C₂ ways.
We select one white ball and one red ball from five white balls and four red balls. This can be done ⁵C₁ . ⁴C₁ ways.
The required probability
= (5 * 4)/⁹C₂ = 20/36 = 5/9
Answer:B
Answer: (B) 5/9
Question: Sujit incurred a loss of 45% on selling an article for Rs.3410/-. What was the cost price of the article?
(A) Rs.6200/-
(B) Rs.5080/-
(C) Rs.6250/-
(D) Rs.6750/-
(E) None of these
Rationale: Explanation:
45% loss means SP of Rs.3410/- is 55% of CP
:. CP = 3410x100/55 = Rs.6200/-
Answer: Option A
Answer: (A) Rs.6200/-
Question: Find the least number must be subtracted from 5474827 so that remaining no.is divisible by 12?
(A) 3
(B) 5
(C) 4
(D) 7
(E) 2
Rationale: On dividing 5474827 by 12 we get the remainder 7, so 7 should be subtracted
D
Answer: (D) 7
Question: Tap 'A' can fill the tank completely in 6 hrs while tap 'B' can empty it by 12 hrs. By mistake, the person forgot to close the tap 'B', As a result, both the taps, remained open. After 7 hrs, the person realized the mistake and immediately closed the tap 'B'. In how much time now onwards, would the tank be full?
(A) 2.5 hours
(B) 4.5 hours
(C) 5.5 hours
(D) 1.5 hour
(E) None of these
Rationale: Explanation :
Tap A can fill the tank completely in 6 hours
=> In 1 hour, Tap A can fill 1⁄6 of the tank
Tap B can empty the tank completely in 12 hours
=> In 1 hour, Tap B can empty 1⁄12 of the tank
i.e., In one hour, Tank A and B together can effectively fill 1⁄6 - 1⁄12 = 1⁄12 of the tank
=> In 7 hours, Tank A and B can effectively fill 1⁄12 × 7 = 7/12 of the tank.
Time taken to fill the remaining 1−(7/12) = 5/12 of the tank = (5/12)/(1/6) = 2.5 hours. Answer : Option A
Answer: (A) 2.5 hours
Question: Among 250 viewers interviewed who watch at least one of the three TV channels namely A, BC. 116 watch A, 127 watch C, while 107 watch B. If 60 watch exactly two channels. How many watch exactly one channel?
(A) 185
(B) 180
(C) 170
(D) 190
(E) 195
Rationale: 250 = n(Exactly 1 channel) + n(Exactly 2 channels) + n(Exactly 3 channels)
250 = n(Exactly 1 channel) + 60 + n(Exactly 3 channels)
Let's find the value of n(Exactly 3 channels) = x
250 = n(A) + n(B) + n(C) - n(A and B) - n(B and C) - n(C and A) + n(A and B and C)
Note that each of n(A and B) is the sum of 'number of people watching exactly two channels A and B' and 'number of people watching all three channels'.
250 = 116 + 127 + 107 - n(Exactly 2 channels) - 3x + x
250 = 116 + 127 + 107 - 60 - 2x
x = 25
250 = n(Exactly 1 channel) + 60 + 25
n(Exactly 1 channel) = 170
Answer (C)
Answer: (C) 170
Question: In a dairy farm, 40 cows eat 40 bags of husk in 40 days. In how many days one cow will eat one bag of husk?
(A) 32
(B) 36
(C) 38
(D) 40
(E) 50
Rationale: Assume that in x days, one cow will eat one bag of husk.
More cows, less days (Indirect proportion)
More bags, more days (direct proportion)
Hence we can write as
(cows)40:1
(bags)1:40
x:40
=40×1×40=1×40×x
=x=40
ANSWER : D
Answer: (D) 40
Question: A grocer has a sale of Rs. 6435, Rs. 6927, Rs. 6855, Rs. 7230 and Rs. 6562 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Rs. 6500?
(A) Rs. 4991
(B) Rs. 5991
(C) Rs. 6001
(D) Rs. 6991
(E) Rs. 7991
Rationale: Total sale for 5 months = Rs. (6435 + 6927 + 6855 + 7230 + 6562) = Rs. 34009.
Required sale = Rs. [ (6500 x 6) - 34009 ]
= Rs. (39000 - 34009)
= Rs. 4991.
ANSWER:A
Answer: (A) Rs. 4991
Question: If the wages of 6 men for 15 days be Rs.2100, then find the wages of
for 12 days.
(A) Rs. 2530
(B) Rs. 2520
(C) Rs. 2500
(D) Rs. 1520
(E) Rs. 3520
Rationale: Let the required wages be Rs. x.
More men, More wages	(Direct Proportion)
Less days, Less wages	(Direct Proportion)
Men 6: 9 : :2100:x
Days 15:12
Therefore (6x15 x x)=(9x12x2100) <=> x=(9x12x2100)/(6x15) =2520
Hence the required wages are Rs. 2520.
Answer is B.
Answer: (B) Rs. 2520
Question: what is the smallest integer that is multiple of 5,7,11
(A) A)70
(B) B)35
(C) C)385
(D) D)280
(E) E)140
Rationale: It is the lcm of 5, 7 and 11 which is 385.
The answer is C.
Answer: (C) C)385
Question: A and B together can complete one-ninth of a job in a day. What is the difference between the maximum and minimum number of days A could take to complete the job alone, if A and B take whole number of days to complete the job alone?
(A) 45
(B) B.60
(C) C.80
(D) D.90
(E) be determined
Rationale: A and B together can complete one-ninth of a job in a day means that AB together does one whole work in 9 days.
1/A +1/B = 1/9
The minimum value A can take is 10 days (Anything less than 10 days is not possible because in other case, no of days taken by B will become negative, which is not possible practically)
When A takes least time (10Days) then B would take the Max time (90 days) to complete the work alone.
In order to find the Max time taken by A, find out the min time taken by B as we did earlier.
The minimum value B can take is 10 days (Anything less than 10days is not possible because in other case, no of days taken by A will become negative, which is not possible practically)
When B takes least time (10Days) then A would take the Max time (90 days) to complete the work alone.
So the required difference = Max Time taken-Min Time taken
= 90 - 10
=80 Days
Option C
Answer: (C) C.80
Question: What is the rate percent when the simple interest on Rs.910 amount to Rs.260 in 4 Years?
(A) 7.14
(B) 6.14
(C) 5.14
(D) 3.14
(E) 2.14
Rationale: 260 = (910*4*R)/100
R = 7.14%
Answer: A
Answer: (A) 7.14
Question: Evaluate permutation
8P8
(A) 40290
(B) 40300
(C) 40310
(D) 40320
(E) 40330
Rationale: Explanation:
nPn=n!
8P8=8*7*6*5∗4∗3∗2∗1=40320
Option D
Answer: (D) 40320
Question: 1. If the product of 6 integers is negative, at most how many of the integers can be negative?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
Rationale: We're told that the product of 6 numbers is negative (the fact that they're integers is actually irrelevant). We're asked for the MAXIMUM number of those 6 that COULD be negative. We'll start with the largest and work our way down..
6 are negative: (-1)(-1)(-1)(-1)(-1)(-1) = + 1...which is NOT a negative product
5 are negative: (-1)(-1)(-1)(-1)(-1)(+1) = -1...which IS a negative product
D
Answer: (D) 5
Question: The ratio of the incomes of Rajan and Balan is 7:6 and the ratio of their expenditure is 6:5. If at the end of the year, each saves $1000 then the income of Rajan is?
(A) $7600
(B) $7000
(C) $8000
(D) $9000
(E) $5000
Rationale: Let the income of Rajan and Balan be $7x and $6x
Let their expenditures be $6y and $5y
7x-6y = 1000-------1)
6x-5y = 1000-------2)
From 1) and 2)
x = 1000
Rajan's income = 7x = 7*1000 = $7000
Answer is B
Answer: (B) $7000
Question: In a apartment, 30% of the people speak English, 20% speak Hindi and 10% speak both. If a people is selected at random, what is the probability that he has speak English or Hindi?
(A) 1/3
(B) 2/3
(C) 2/5
(D) 2/9
(E) 3/7
Rationale: P (E) = 30 / 100 = 3 / 10 , P (H) = 20 / 100 = 1 / 5 and P (E ∩ H) = 10 / 100 = 1 / 10
P (E or H) = P (E U H)
= P (E) + P (H) - P (E ∩ H)
= (3 / 10) + (1 / 5) - (1 / 10) = 4 / 10 = 2/5
C
Answer: (C) 2/5
Question: If a and b are integers and (a*b)^5 = 128y, y could be:
(A) 1
(B) 2
(C) 4
(D) 8
(E) 16
Rationale: Distribute the exponent.
a^5 * b^5 = 128 y
Find the prime factorization of 96. This is 2^5 *2^2.
We need 2^3 (or some other power of 2 that will give us a multiple of 2^5 as our second term).
2^3 = 8
The answer is D.
Answer: (D) 8
Question: A car rental company charges for mileage as follows: 10 dollars per mile for the first n miles and 11 dollars per mile for each mile over n miles. How much will the mileage charge be, in dollars, for a journey of d miles, where d > n ?
(A) 7d-n
(B) 5d-n
(C) 3*11d-n
(D) 11d-n
(E) 4d-n
Rationale: Total Distance in miles = d
Millage Charge = 10n + (d-n) 11
10n --> For the first n Miles
(d-n)11--> Total no of miles after traveling the first n miles is d-n and the rate after n miles is 11 .
If we solve the equation , We will get 11d-n
Answer : D
Answer: (D) 11d-n
Question: On dividing a number by 357, we get 39 as remainder.On dividing the same number by 17, what will be the remainder ?
(A) 4
(B) 5
(C) 8
(D) 7
(E) 2
Rationale: Let x be the number and y be the quotient.Then,
x=357*y+39
=(17*21*y)+(17*2)+5
=17*(21y+2)+5.
Required number =5.
Answer is B
Answer: (B) 5
Question: The variables m and n are positive integers. When m is divided by 4, there is a remainder of 5, and when n is divided by 3, there is a remainder of 4. Which of the following are possible values of m + n?
I. 50
II. 70
III. 92
(A) I only
(B) III only
(C) I and II
(D) I​ and III
(E) II and III
Rationale: m = 4k + 5 --> Values are 5, 9, 13, 17
n = 3k + 4 --> Values are 4, 7, 10, 13
I. 16 --> 9 + 7 --> Possible
II. 24 --> Not possible
III. 29 --> Not possible
Answer: A
Answer: (A) I only
Question: If 34 men completed 2/5th of a work in 8 days working 9 hours a day. How many more man should be engaged to finish the rest of the work in 6 days working 9 hours a day?
(A) 100
(B) 102
(C) 104
(D) 106
(E) 108
Rationale: Using the chain rule,
M1 x T1 = M2 x T2
Thus, (34 x 8 x 9) / 2/5 = (M2 x 6 x 9) / 3/5
M2 = 68.
Therefore, required number of men = (68 + 34) = 102
ANSWER:B
Answer: (B) 102
Question: March 11, 2003 is a Tuesday. What will be the day on which march 11 2004 comes??
(A) Thursday
(B) Friday
(C) Saturday
(D) Sunday
(E) Monday
Rationale: 2004 is a leap year that means 29 days in feb.
so march 11,2003 to march 11, 2004 will be 366 days.
366/7=52 weeks + 2 days. Hence Thursday
ANSWER:A
Answer: (A) Thursday
Question: Two electronic musical instruments were purchased for 8000. The first was sold at a profit of 40% and the second at loss of 40%. If the sale price was the same in both the cases, what was the cost price of two electronic musical instruments?
(A) 2000, 5000
(B) 2200, 5500
(C) 2400, 5000
(D) 2400, 5600
(E) None of these
Rationale: Here, SP1 = SP2
⇒ 140 CP1 = 60CP2 ⇒ CP1/CP2=6/14=3/7
∴ CP1 = 3(3+7)×8000=24003(3+7)×8000=2400
and CP2 = 8000 – 2400 = 5600
Answer D
Answer: (D) 2400, 5600
Question: What is the average of first 21 multiples of 7 ?
(A) 49
(B) 77
(C) 66
(D) 57
(E) 50
Rationale: Required average = 7(1+2+....+21) / 21
(7/21)X ( (21x22) / 2 ) (because sum of first 21 natural numbers)
= 77
ANSWER IS B
Answer: (B) 77
Question: A recipe for a large batch of fruit juice at a factory calls for 10% oranges, 20% lemons, and 70% limes. if 200 lemons are used, how many limes are needed?
(A) 100
(B) 200
(C) 300
(D) 700
(E) 1400
Rationale: 20%= 200 fruit
100%=1000 fruit
70% of 1000 fruit=700 fruit
700 limes
ANSWER:D
Answer: (D) 700
Question: What is the compound interest paid on a sum of Rs.4500 for the period of 2 years at 10% per annum.
(A) 945
(B) 620
(C) 610
(D) 600
(E) None of these
Rationale: Solution= Interest % for 1st year= 10
Interest % for 2nd year= 10+ 10% of 10= 10+ 10 *10/100=11
Total % of interest= 10 + 11=21
Total interest = 21 % 4500 = 4500* (21/100)= 945
Answer A
Answer: (A) 945
Question: Combine terms: 8a + 26b -4b – 16a.
(A) 4a + 22b
(B) -28a + 30b
(C) -8a + 22b
(D) 28a + 30b
(E) 5a + 30b
Rationale: Solution:
8a + 26b -4b – 16a.
= 8a – 16a + 26b – 4b.
= -8a + 22b.
Answer: (C)
Answer: (C) -8a + 22b
Question: 8 cups of milk are to be poured into a 4-cup bottle and a 8-cup bottle. If each bottle is to be filled to the same fraction of its capacity, how many cups of milk should be poured into the 8-cup bottle?
(A)  16/3
(B)  7/3
(C)  5/2
(D)  4/3
(E)  3
Rationale: Let x be the # of cups going into the 8 cup bottle.
so.... x/8 = ((8-x)/4)
64 - 8x = 4x
64 = 12x
x = 16/3.
Answer : A
Answer: (A)  16/3
Question: Which number should replace both the asterisks in (* /20) x (*/80) = 1 ?
(A) 20
(B) 40
(C) 60
(D) 80
(E) 120
Rationale: Let (y/20) x (y/80) = 1
y^2 = 20 x 80 = 20 x 20 x 4
y = (20 x 2) = 40
The answer is B.
Answer: (B) 40
Question: Mrs. Rodger got a weekly raise of $148. If she gets paid every other week, write an integer describing how the raise will affect her paycheck.
(A) $140
(B) $141
(C) $142
(D) $148
(E) $145
Rationale: Let the 1st paycheck be x (integer).
Mrs. Rodger got a weekly raise of $ 148.
So after completing the 1st week she will get $ (x+148).
Similarly after completing the 2nd week she will get $ (x + 148) + $ 148.
= $ (x + 148 + 148)
= $ (x + 296)
So in this way end of every week her salary will increase by $ 148.
correct answer D)$148
Answer: (D) $148
Question: In a class there are 20 boys and 24 girls. In how many ways can a boy and a girl be selected?
(A) 508
(B) 480
(C) 800
(D) 570
(E) 503
Rationale: We can select one boy from 20 boys in 20 ways.
We select one girl from 24 girls in 24 ways
We select a boy and girl in 20 * 24 ways i.e., = 480 ways.
Answer:B
Answer: (B) 480
Question: The average temperature in Lincoln in July is 85 degrees. Last
Wednesday, it was 90 degrees. Today it was 15 degrees cooler than
last Wednesday. What was the temperature today?
(A) 15 degrees
(B) 25 degrees
(C) 75 degrees
(D) 45 degrees
(E) 55 degrees
Rationale: The July temperature is extra information. 90 – 15 = 75
It was 75 degrees today.
correct answer C
Answer: (C) 75 degrees
Question: Boys and girls in a class are writing letters. There are twice as many girls as boys in the class, and each girl writes 3 more letters than each boy. If boys write 24 of the 90 total letters written by the class, how many letters does each boy write?
(A) 3
(B) 4
(C) 6
(D) 8
(E) 12
Rationale: There are twice as many girls as boys in the class --> g = 2b.
Each girl writes 3 more letters than each boy --> boys write x letters, girls write x+3 letters.
Boys write 24 letters --> bx = 24.
Girls write 90-24=66 letters --> (2b)(x+3) = 66 --> 2bx + 6b = 66 --> 2*24 + 6b = 66 --> b = 3.
bx = 24 --> 3x = 24 --> x = 8.
Answer: D.
Answer: (D) 8
Question: In how many different orders can the people Alice, benjamin Charlene, David, Elaine, Frederick, Gale, and Harold be standing on line if each of Alice, David, Charlene must be on the line before each of Frederick, Gale, and Harold?
(A) 2016
(B) 1,296
(C) 1,512
(D) 2,018
(E) 2,268
Rationale: Place B and E first: 8 options for B, 7 options for E.
We are left with 6 empty places. A, D and C must take first 3 places and F, G, H must take the remaining three. A, D and C can be arranged in their places in 3! ways. The same for F, G, and H.
Total = 8*7*3!*3! = 2,016.
Answer: A
Answer: (A) 2016