mathewhe/aqua_rat huggingface dataset:
Question: If 3/w + 3/x = 3/y and wx = y, then the average (arithmetic mean) of w and x is
(A) 1/2
(B) 1
(C) 2
(D) 4
(E) 8
Rationale: Given: 3/w + 3/x = 3/ywx=y
Find: (w+x)/2 = ?
3(1/w + 1/x) = 3(1/y) - divide both sides by 3
(1/w + 1/x) = 1/y
(x+w)/wx = 1/wx - sub'd in y=wx
x+w - 1 = 0
x+w = 1
Therefore (w+x)/2 = 1/2
Ans: A
Answer: (A) 1/2
Question: Points A, B, and C lie, in that order, on a straight railroad track. The distance from point A to point B is twice the distance from point B to point C. A train traveled from point A to point C without stopping. The train's average speed when traveling from point A to point B was 50 miles per hour and the train's average speed when traveling from point B to point C was 25 miles per hour. What was the train's average speed, in miles per hour, when traveling from point A to point C?
(A) 20
(B) 25
(C) 30
(D) 35
(E) 15
Rationale: Average speed = distance/time
Because we are looking for average speed we can pick a distance for the variable d.
Speed A-B = 50
Speed B-C = 25
Average Speed = total distance/total rate
rate = distance/time
A====================B==========C
If A-B is twice the length of B-C then let A-B = 2d and let B-C = d
Average speed = 3d/(2d/50) + (d/25)
3d/(2d/50) + (2d/50)
3d/(4d/50)
150d/10d
Average speed = 15
ANSWER: E
Answer: (E) 15
Question: In the xy-plane, the points (c, d), (c, -d), and (-c, -d) are three vertices of a certain square. If c < 0 and d > 0, which of the following points P is in the same quadrant as the fourth vertex of the square?
(A) (-5, -3)
(B) (-5, 3)
(C) (5, -3)
(D) (3, -5)
(E) (3, 5)
Rationale: The question:In the xy-plane, the points P=(c, d), (c, -d), and (-c, -d) are three vertices of a certain square.If c < 0 and d > 0,which of the following points is in the same quadrant as the fourth vertex of the square?
I marked the tricky part in red. It seems c is anegativenumber and d is a positive number. This means
Vertex #1 = (c, d) is in QII (that is, negative x and positive y)
Vertex #2 = (c, -d) is in QIII (that is, both xy negative)
Vertex #3 = (-c, -d) is in QIV (that is y is negative, but x is positive)
That means the last vertex should be in the first quadrant --- the only first quadrant point is (5, 3), answer =E.
Answer: (E) (3, 5)
Question: A certain shirt was marked down 10% the first week and another 20% the next week. What percent of the regular price was the final cost of the shirt after the two markdowns?
(A) 30%
(B) 36%
(C) 40%
(D) 72%
(E) 80%
Rationale: If the price of the shirt is 100, and it is marked down by 10% and then 20% or charged 90% of the price first and 80% of the price of reduced price, the final price is :-
100*90*80/10000= 72
72% is the final price of old price.
D is the answer
Answer: (D) 72%
Question: The average of 65 numbers is 40. If two numbers, 25 and 60 are discarded, then the average of the remaining numbers is nearly
(A) 28.32
(B) 39
(C) 39.92
(D) 29
(E) 30
Rationale: Explanation :
Total sum of 63 numbers = (65 * 40) - (25 + 60) = 2600 - 85= 2515
Average = 2515/63 = 39.92
Answer : C
Answer: (C) 39.92
Question: what will be the next number in the following series??
1,4...48,100,180,294
(A) 32
(B) 46
(C) 24
(D) 18
(E) 30
Rationale: 1x1x1=1;
2x2x1=4;
3x3x2=18;
4x4x3=48;
5x5x4=100;
6x6x5=180;
7x7x6=294;
so answer is 18.
ANSWER:D
Answer: (D) 18
Question: The length of a rectangular plot is thrice its breadth. If the area of the rectangular plot is 675 sq m, then what is the breadth of the rectangular plot?
(A) 16
(B) 17
(C) 18
(D) 15
(E) 14
Rationale: Let the breadth of the plot be b m.
Length of the plot = 3 b m
(3b)(b) = 675
3b2 = 675
b2 = 225
b = 15 m.
Answer: Option D
Answer: (D) 15
Question: 50% of the apartments in a certain building have windows and hardwood floors. 25% of the apartments without windows have hardwood floors. If 40% of the apartments do not have hardwood floors, what V percent of the apartments with windows have hardwood floors?
(A) 10
(B) 16 2/3
(C) 40
(D) 50
(E) 83 1/3
Rationale: yup you need to construct a matrix
X********| Windows'|No Windows'''| total
hardFl****'|50*****''|10*********'|60
Not hardFl*|10******|30*********'|40
Total*****|60******'|40*********'|100
so V percent of the apartments with windows have hardwood floors = 50/60 *100
= 83 1/3
so E is the answer.[/u]
Answer: (E) 83 1/3
Question: Sandy leaves her home and walks toward Ed's house. Two hours later, Ed leaves his home and walks toward Sandy's house. The distance between their homes is 52 kilometers, Sandy's walking speed is 6 km/h, and Ed's walking speed is 4 km/h. How many kilometers will Sandy walk before she meets Ed?
(A) 33
(B) 34
(C) 35
(D) 36
(E) 37
Rationale: Sandy walks 12 km in the first two hours so there are 40 km remaining.
When Ed starts walking, they complete a total of 10 km per hour.
They will meet four hours after Ed starts walking.
Since Sandy walks for 6 hours, she walks 36 km.
The answer is D.
Answer: (D) 36
Question: Two pipes A and B can fill a cistern in 20 and 30 minutes respectively, and a third pipe C can empty it in 40 minutes. How long will it take to fill the cistern if all the three are opened at the same time?
(A) 17 1/9 min
(B) 17 1/8 min
(C) 17 1/7 min
(D) 17 8/7 min
(E) 17 3/7 min
Rationale: 1/20 + 1/30 - 1/40
= 7/120
120/7 = 17 1/7
Answer:C
Answer: (C) 17 1/7 min
Question: How much pure alcohol should be added to 400ml of a 15% solution to make the strength of solution 30%?
(A) 100 ml
(B) 60 ml
(C) 120 ml
(D) 130 ml
(E) 150 ml
Rationale: we can also go by answer choices
Tke 100 ml for eg
400 (old)+100 (new concentr)ml
500*30/100 = 150 ml (50ml is de old concentration +100 ml (newly added)
Answer E
Answer: (E) 150 ml
Question: The probabilities of solving a question by 3students A, B & C are 1/2,1/3 &1/4, respectively. The probability that the problem will be solved is?
(A) 1/2
(B) 3/4
(C) 1/5
(D) 3/5
(E) 4/7
Rationale: Sol. First, we find the probability of not solving the problem x PTO x = (1 — D x - D x - D
1 2 3 1 =iXiX71=4;
1 3 Required probability 3/4
B
Answer: (B) 3/4
Question: A die is tossed. Find the probability of getting a multiple of 2 ?
(A) 1/5
(B) 2/3
(C) 1/6
(D) 1/3
(E) 1/2
Rationale: S = {1,2,3,4,5,6}
E= event of getting a multiple of 2 = {2,4,6}
P(E) = 3/6 = 1/2
Answer is E
Answer: (E) 1/2
Question: A chair is bought for Rs.300/- and sold at a loss of 20% find its selling price
(A) Rs.500/-
(B) Rs.510/-
(C) Rs.515/-
(D) Rs.230/-
(E) Rs.240/-
Rationale: Loss = 300*20/100 = 60
S.P = C.P - Loss
= 300- 60
=Rs.240/-
Answer :E
Answer: (E) Rs.240/-
Question: Solve 7y – 5 = 3y + 11
(A) 4
(B) 6(1/3)
(C) 7(1/3)
(D) 3
(E) 9(1/3)
Rationale: Sol.
7y – 5 = 3y + 11
=> 7y – 3y = 11 + 5
=> 4y = 16 => x = 4
Answer A
Answer: (A) 4
Question: There were two candidates in an election. Winner candidate received 60% of votes and won the election by 240 votes. Find the number of votes casted to the winning candidate?
(A) 228
(B) 720
(C) 255
(D) 199
(E) 231
Rationale: W = 60% L = 40%
60% - 40% = 20%
20% -------- 240
60% -------- ? => 720
Answer:B
Answer: (B) 720
Question: Jo's collection contains US, Indian and British stamps. If the ratio of US to Indian stamps is 5 to 2 and the ratio of Indian to British stamps is 5 to 1, what is the ratio of US to British stamps?
(A) 10 : 5
(B) 15 : 2
(C) 20 : 2
(D) 25 : 2
(E) None of thees
Rationale: Explanation:
Indian stamps are common to both ratios. Multiply both ratios by factors such that the Indian stamps are represented by the same number.
US : Indian = 5 : 2, and Indian : British = 5 : 1. Multiply the first by 5, and the second by 2.
Now US : Indian = 25 : 10, and Indian : British = 10 : 2
Hence the two ratios can be combined and US : British = 25 : 2
Answer: D
Answer: (D) 25 : 2
Question: Two spherical balls lie on the ground touching. If one of the balls has a radius of 6 cm, and the point of contact is 10 cm above the ground, what is the radius of the other ball (in centimeters)?
(A) 12
(B) 16
(C) 20
(D) 24
(E) 30
Rationale: A straight line will join the two centers and the point of contact, thus making similar triangles.
4/6 = (r-10)/r
4r = 6r - 60
r = 30
The answer is E.
Answer: (E) 30
Question: Car X began traveling at an average speed of 35 miles per hour. After 36 minutes, car Y began traveling at an average speed of 38 miles per hour. When both cars had traveled the same distance, both cars stopped. How many miles did car X travel from the time car Y began traveling until both cars stopped?
(A) 105
(B) 140
(C) 175
(D) 210
(E) 245
Rationale: In 36 minutes, car X travels 21 miles.
Car Y gains 3 miles each hour, so it takes 7 hours to catch car X.
In 7 hours, car X travels 245 miles.
The answer is E.
Answer: (E) 245
Question: If n ≠ 0, which of the following must be greater than n?
I. n^4
II. 2n
III. 2 - n
(A) I only
(B) II only
(C) I and II only
(D) II and III only
(E) None
Rationale: n ≠ 0 => n = negative or n = positive
if n = negative:
2n < n (n = -1 then 2n = -2 => -2 < -1)
n^2 > n (n =-1 then n^2 = 1 => n^2 > n)
2 - n > n (n = -1 then 2--1 = 2+1=3 => 2-n > n)
but if n = positive:
n^2 > n (n = 2 then n^2 = 4 => n^2 > n) => II
2 - n < n(n =2 then 2-2 = 0)
=> only I
=>answer is A
Answer: (A) I only
Question: A rectangular lawn of dimensions 120 m * 60 m has two roads each 10 m wide running in the middle of the lawn, one parallel to the length and the other parallel to the breadth. What is the cost of traveling the two roads at Rs.3 per sq m?
(A) s.5100
(B) s.3900
(C) s.3228
(D) s.3922
(E) s.3928
Rationale: Area = (l + b – d) d
(120 + 60 – 10)10 => 1700 m2
1700 * 3
= Rs.5100
Answer:A
Answer: (A) s.5100
Question: How much water should be added to 15 liters of a 20%-solution of alcohol to reduce the concentration of alcohol in the solution by 75% ?
(A) 25 liters
(B) 27 liters
(C) 30 liters
(D) 32 liters
(E) 35 liters
Rationale: Let x ltr water to be added
2ltr alcohol to be represented as (20(1-3/4(new soln.=15+x)))
2=5%*(15+x)-------->x=25
Ans A
Answer: (A) 25 liters
Question: how many four digits numbers are formed such that the digits are in decreasing order
(A) 170
(B) 180
(C) 190
(D) 200
(E) 210
Rationale: START with 3 = 3_ _ _. You can fill in with digits 0,1,2. Hence 3C3 = 1
START with 4 = 4_ _ _. (0,1,2,3). hence 4C3= 4
START with 5, you have (0,1,2,3,4) to fill in the blanks behind 5, hence 5C3 = 10
START with 6, 6C3=20
7... = 7C3 = 35
8...=8C3 = 56
9...= 9C3 = 84
so ans=1+4+10+20+35+56+84=210
ANSWER:E
Answer: (E) 210
Question: If 6 coins are tossed, how many different coin sequences will have exactly 3 tails, if all tails have to occur in a row?
(A) 4
(B) 8
(C) 16
(D) 20
(E) 24
Rationale: xactly 3 tails and have to occur in row
We have 6 coins we use the glue method so we say all 3 tails as 1
so we have 4! ways, however we need to reduce duplicate for 3 Heads as well
HHH{T} therefore using anagram method
4!/3! = 4
Answer: A
Answer: (A) 4
Question: The average score of a cricketer in 10 matches is 60 and in other 15 matches is 70. Then find the average score in all the 25 matches?
(A) 50
(B) 48
(C) 65
(D) 66
(E) 72
Rationale: Average in 25 matches = (10*60 + 15*70)/10+15 = 66
Answer is D
Answer: (D) 66
Question: Ramu bought an old car for Rs. 43000. He spent Rs. 13000 on repairs and sold it for Rs. 64900. What is his profit percent?
(A) A)14%
(B) B)16%
(C) C)18%
(D) D)22%
(E) of these
Rationale: Total CP = Rs. 43000 + Rs. 13000 = Rs. 56000 and SP = Rs. 64900
Profit(%) = (64900 - 56000)/55000 * 100 = 16%
ANSWER:B
Answer: (B) B)16%
Question: A shop keeper sell an article gets profit of 20% had he bought it for 20% less and sold it for Rs 120 less he would have still bought profit of 20% what is the cost price of article
(A) 500
(B) 600
(C) 700
(D) 750
(E) 450
Rationale: let c.p be x,
1st s.p =(120/100)x=6x/5
2nd s.p=(80/100)x=4x/5
filnal profit 20% so
120/100 * 4x/5
120 rs less so
6x/5 - 24x/25 =120
x=500
ANSWER:A
Answer: (A) 500
Question: The area of a triangle will be when a = 1m, b = 2m, c = 5m, a, b, c being lengths of respective sides?
(A) 3
(B) 6
(C) 4
(D) 9
(E) 1
Rationale: S = (1 + 2 + 5)/2= 4 Answer:C
Answer: (C) 4
Question: If the speed of x meters per second is equivalent to the speed of Y mile per hour, what is y in terms of x? (1 mile = 1609.34 meter)
(A) 1.21x
(B) 1.33x
(C) 2.23x
(D) 2.84x
(E) 3.13x
Rationale: x meters per second -->
--> 3,600x meters per hour(as there are 3,600 seconds in one hour);
--> 3,600x/1,609.34=2.236x miles per hour (as there are 1,609.34 meters in one mile).
Answer: C.
Answer: (C) 2.23x
Question: Number X is 30% more than that of Number Y . Find what percent of Number Y is less than Number X ?
(A) 25 1/3%
(B) 26 1/3%
(C) 24 1/3%
(D) 23 1/3%
(E) 23 2/3%
Rationale: Explanation:
y=100 x=130
130---------30
100---------? => 23 1/3%
Answer D
Answer: (D) 23 1/3%
Question: A house of 4 rooms is designed from 4 types of bedrooms and 3 types of bathrooms. The house must have at least 2 types of bedrooms and at least 1 type of bathroom. How many ways can this house be designed?
(A) 3
(B) 4
(C) 12
(D) 30
(E) 38
Rationale: Solution: We have two possibilities 3Bed 1Bath or 2Bed 2Bath
(4C3)(3C1)+(4C2)(3C2)=30
D) 30
Answer: (D) 30
Question: Ram and Krishna start from A and B respectively at the same time and travel towards each other at constant speeds along the same route. Ram meets Krishna at point C on the road which is 1000m away from starting point A and 500m away from point B. The time taken by Ram to reach point B is 10minutes. Find the time taken by krishna to go from B to A.?
(A) 45 minutes
(B) 35 minutes
(C) 50 minutes
(D) 52 minutes
(E) None of the above.
Rationale: total distance from A to B-
A - C = 1000m, B - C = 500m;
therefore A-B = 1500m;
Vr=1500/25=60 m/m;
t-time taken by Ram for AB meet,
t=1000/60=16.67 minutes = Time taken by Krishna for AB meet.
therefore,
Vk=500/16.67=30m/m.
time taken by krishna for B-A = 1500/30 =50 minutes
option C
Answer: (C) 50 minutes
Question: Two different solutions of alcohol with respective proportions of alcohol to water of 3:1 and 2:3 were combined. What is the concentration of alcohol in the new solution if the first solution was 9 times the amount of the second solution?
(A) 62
(B) 65.5
(C) 68
(D) 70
(E) 71.5
Rationale: SOL:
Lets assume that 90L of sol1 was mixed with 10L of sol2.
Alcohol in Sol1: 90*3/4 = 67.5L
Alcohol in Sol2: 10*2/5 = 4L
Total Alcohol in the mixed solution of 100L = 67.5 + 4 = 71.5L
Alcohol concentration in the new sol: (71.5/100)*100 = 71.5%
ANSWER:E
Answer: (E) 71.5
Question: In an examination, a student scores 4 marks for every correct answer and loses 1 mark for every wrong answer. If he attempts all 60 questions and secures 130 marks, the no of questions he attempts correctly is :
(A) 33
(B) 38
(C) 99
(D) 27
(E) 71
Rationale: Let the number of correct answers be X.
Number of incorrect answers = (60 – X).
4x – (60 – x) = 130
=> 5x = 190
=> x = 38
Answer: B
Answer: (B) 38
Question: The difference between two numbers is 1365. When the larger number is divided by the smaller one, the quotient is 6 and the remainder is 15. The smaller number is
(A) 240
(B) 270
(C) 295
(D) 360
(E) NOne
Rationale: Sol.
Let the smaller number be x.
Then, larger number = (1365 + x).
∴ 1365 + x = 6x + 15
⇔ 5x = 1350
⇔ x = 270.
Hence, the required number is 270.
Answer B
Answer: (B) 270
Question: Two kinds of Vodka are mixed in the ratio 1:2 and 2:1 and they are sold fetching the profit 25% and 20% respectively. If the vodkas are mixed in equal ratio and the individual profit percent on them are increased by 4/3 and 5/3 times respectively, then the mixture will fetch the profit of
(A) 18%
(B) 20%
(C) 21%
(D) 25%
(E) Cannot be determined
Rationale: Answer: D.
Answer: (D) 25%
Question: How many odd 4-digit positive integers Q that are multiples of 5 can be formed without using the digit 3?
(A) 648
(B) 729
(C) 900
(D) 1296
(E) 3240
Rationale: I choose A.
Possible n° of 1st digit: 8 (0 can't be the first number, or else it wouldn't have 4 digits. 3 is exlcuded)
Possible n° of 2nd digit: 9 (3 is excluded)
Possible n° of 3rd digit: 9 (3 is excluded)
Possible n° of 4th digit: 1 (a number is a multiple of 5 if it ends in 5 or 0, here we are asked for the odd numbers, hence the last digit can't be 0)
So, Q=8*9*9*1=648 (A)
Answer: (A) 648
Question: A shopkeeper cheats both his supplier and customer by using faulty weights. When he buys from the supplier, he takes 20% more than the indicated weight. When he sells to his customer, he gives the customer a weight such that 10% of that is added to the weight, the weight claimed by the trader is obtained. If he charges the cost price of the weight that he claims, find his profit percentage.
(A) 20%
(B) 32%
(C) 23.365%
(D) 22.109%
(E) 2%
Rationale: Anyways, one can infer that he 'steals' 20% from suppliers and then charges 10% extra to customers
So basically 1.2 * 1.1 = 1.32
Given that 1 is start point, we get 32% more
Hence answer is B
Answer: (B) 32%
Question: Among all sales staff at Listco Corporation, college graduates and those without college degrees are equally represented . Each sales staff member is either a level-1 or level-2 employee. Level-1 college graduates account for 10% of Listco's sales staff. Listco employs 72 level-1 employees, 20 of whom are college graduates. How many sales staff members without college degrees are level-2 employees ?
(A) 46
(B) 48
(C) 56
(D) 32
(E) 58
Rationale: I'm going in on this one.
So let's say that we have the following
So we know that L1 = 72 and that C and L1 = 0.10X , we should set up a double set matrix btw but anyways, I'm just explaining the point with this problem. Now we are told that 0.1x = 20, therefore the grand total is 200. Now we know that L2 is 200 - 72 = 128. We also learn that C and No C are equally represented thus 100 each. Therefore No C and No L2 will be 100 - 52 = 48.
Thus B is the correct answer choice
Answer: (B) 48
Question: A's salary is 50% more than B's. How much percent is B's salary less than A's?
(A) 25.5%
(B) 33.3%
(C) 45.6%
(D) 50%
(E) 25%
Rationale: B's salary is less than A's salary by 50/(100+50) * 100% = 100/3% = 33.3%
Answer is B
Answer: (B) 33.3%
Question: 66 small identical cubes are used to form a large cube. How many more cubes are needed to add one top layer of small cube all over the surface of the large cube ?
(A) 64
(B) 150
(C) 152
(D) 216
(E) 256
Rationale: 66 small cube will make a large cube with 4 cubes in each line i.e.
Adding one layer will require one cube at each end and hence new cube will have 6 cubes in each line.
Total number of small cubes in new cube = 6^3 = 216
Extra cube required = 216 - 66 = 150
Hence, B is the answer.
Answer: (B) 150
Question: If the sum of two numbers is 20 and the sum of their squares is 200, then the product of the numbers is
(A) 40
(B) 44
(C) 100
(D) 88
(E) 48
Rationale: according to the given conditions x+y = 20
and x^2+y^2 = 200
now (x+y)^2 = x^2+y^2+2xy
so 20^2 = 200 + 2xy
so xy = 200/2 = 100
ANSWER:C
Answer: (C) 100
Question: A container contains 40 liters of milk, From this container 4 liters of milk was taken out and replaced by water. This process was repeated further 2 times. How much milk is now contained by the container?
(A) 25.5 liters
(B) 29.16 liters
(C) 30.98 liters
(D) 42.15 liters
(E) 48.32 liters
Rationale: Amount of milk left after 3 operations = 40 (1 - 4/40)^3 = 40 * 9/10 * 9/10 * 9/10 = 29.16 liters
Answer is B
Answer: (B) 29.16 liters
Question: There are 6 periods in each working day of a school. In how many ways can one organize 5 subjects such that each subject is allowed at least one period?
(A) 1800
(B) 3200
(C) 2600
(D) 3600
(E) None of these
Rationale: There are 5 subjects and 6 periods. Each subject must be allowed in at least one period. Therefore, two periods will have same subject and remaining four periods will have different subjects.
Select the two periods where the same subject is taught. This can be done in 6C2 ways.
Allocate a subject two these two periods(5C1 ways).
Remaining 4 subjects can be arranged in the remaining 4 periods in 4! ways.
Required number of ways
= 6C2 × 5C1 × 4! = 1800
Answer : A.
Answer: (A) 1800
Question: In a 100 m sprint race Kelly was given a 3 m head start by Abel. If Abel lost the race to Kelly by a distance of 0.50 m, how many meters more would Abel need to overtake Kelly?
(A) 20.5
(B) 18.4
(C) 17.5
(D) 19.9
(E) 21.5
Rationale: Distance Abel ran before completion of race---100 m-0.50m=99.5m
Distance gained on Kelly over 99.5m---3m-0.50m=2.50m
then Abel gains 99.5m/2.50m = 1m on Kelly every 39.8 meters.
Therefore 39.8 divided by half a meter ( i.e the 0.50 m Abel was defeated with)
ANSWER: D. 19.9m
Answer: (D) 19.9
Question: Two students appeared at an examination. One of them secured 9 marks more than the other and his marks was 56% of the sum of their marks. The marks obtained by them are:
(A) 39, 30
(B) 41, 32
(C) 42, 33
(D) 43, 34
(E) 41, 44
Rationale: C
Let their marks be (x + 9) and x.
Then, x + 9 = 56/100(x + 9 + x)
25(x + 9) = 14(2x + 9)
3x = 99
x = 33
So, their marks are 42 and 33.
Answer: (C) 42, 33
Question: Rajesh, Sunil and Tarun enter into a partnership. Rajesh invested Rs.25000 and after one year he adds Rs.10,000 more. Sunil initially invests Rs.35,000 and after 2 years he withdraws Rs.10,000 and Tarun invests Rs.19,000 in the beginning only. Then ratio of their profits after 3 years will be
(A) 05:30:00
(B) 05:30:00
(C) 05:30:00
(D) 05:30:00
(E) None
Rationale: Ratio of their profits after 3 years
=25000×1+35000×2 :35000×2+25000×1:19000×3
=25×1+35×2:35×2+25×1:19×3
=95:95:57
=5:5:3
ANSWER:E
Answer: (E) None
Question: What is the tens' digit Q of the sum of the first 40 terms of 1, 11, 111, 1111, 11111, 111111, ...?
(A) Q=2
(B) Q=3
(C) Q=4
(D) 8
(E) 9
Rationale: All of the first 40 terms have 1 at the units place.
Except the first term, the tens digit of all the remaining 39 terms is 1.
So now if you do the addition
1 1
1 1
. . .
. . .
. . .
1 1
0 1
3 0
Answer is B
Answer: (B) Q=3
Question: If q>0, which of the following must be true?
(A) 1 <q
(B) 0 < q < 2
(C) -1 < q < 1
(D) -10 < q
(E) 1/100 < q
Rationale: All we know is that q is some positive number. Right away we can see that D must be true: if q is positive then it MUST be true that it's greater than -10. Still let's check each option.
A. 1 < q. We don't know whether the number is greater than 1, it could be a positive number less than or equal to 1. Discard.
B. 0 < q < 2. The same here: we don't know whether the number is less than 2, it could be more than or equal to 2. Discard.
C. -1 < q < 1. The same as A. Discard.
E. 1/100 < q. We don't know whether the number is greater than 1/100, it could be a positive number less than or equal to 1/100. Discard.
Answer: D.
Answer: (D) -10 < q
Question: If there is an equal probability of a child being born a boy or a girl, what is the probability that a couple who have 7 children have two children of the same sex and one of the opposite sex?
(A) 1/3
(B) 2/3
(C) 1/4
(D) 7/64
(E) 3/5
Rationale: No of ways of selecting a gender - 2C1
No of ways of selecting any 2 children out of 7 = 7C2
Total possible outcomes - 2^7 (each child can be either a girl or a boy)
Probability=2C1*7C2/2^7= 2*7/2*2*2*2*2*2*2=7/64
Ans=D
Answer: (D) 7/64
Question: Two whole numbers whose sum is 100 cannot be in the ratio
(A) 2:23
(B) 5:45
(C) 10:10
(D) 2:6
(E) 2:3
Rationale: D) 2:6
Answer: (D) 2:6
Question: If Dale works at full efficiency he needs a break of 1 day after every 2 days of work and he completes a job in a total of 5 days. If he works at reduced efficiency, he can work without break and finish that same job in 5 days. Dale's output at reduced efficiency is what fraction of his output at full efficiency?
(A) 5/2
(B) 4/1
(C) 9/5
(D) 4/5
(E) 2/5
Rationale: We're told that there are 2 ways for Dale to complete a job:
1) Full Efficiency: 2 days of work followed by 1 dayofffor a total of 5 days.
2) Reduced Efficiency: 5 straight days with no days off.
Working at Full Efficiency creates the following pattern:
2 days on, 1 day OFF, 2 days on, 1 day OFF, 2 days on, 1 day OFF, 2 days on = 2+1+2= 5 days
Totals: 4 days on, 1 days off
Reduced Efficiency means that Dale will do 6 days of work in 5 days, thus those Reduceddaysare 4/1 of Full Efficiency.
Answer : B
Answer: (B) 4/1
Question: If x is divisible by 2, 14, and 11, which of the following must be the least multiple of x?
(A) 308
(B) 154
(C) 70
(D) 44
(E) 0
Rationale: We are looking for the LCM (which is not 0) of 2, 11, 14:
2 * 11 * 7 = 154
ANSWER:B
Answer: (B) 154