mathewhe/aqua_rat huggingface dataset:
Question: How many 4 letter combinations can be made from the letters of the word VERMONT if the first letter has to be a vowel and the last letter has to be a consonant, and each letter can be used only once?
(A) 21
(B) 42
(C) 120
(D) 600
(E) 200
Rationale: Vowel: E O
Consonants: V R M N T
First letter can be filled in 2 Ways ( As the question states thatfirst letter has to be a vowel)
Fourth letter can be filled in 5 Ways ( As the question states thatthe last letter has to be a consonant)
Now since each letter can be used only once, and 2 letters out of 7 letters are already used in First and fourth letter
Second letter can be filled in 5 Ways
Third letter can be filled in 4 Ways
So, Total number of ways = 2 Ways x 5 Ways x 4 ways x 5 ways = 200
Answer E
Answer: (E) 200
Question: At a party, there were five times as many girls as boys and three times as many adults as children. Which of the following could NOT be the number of people at the party?
(A) 258
(B) 259
(C) 216
(D) 120
(E) 72
Rationale: Five times as many girls as boys --> F = 5M.
Three times as many adults as children --> (F + M) = 3C.
The number of people at the party = F + M + C = 3C + C = 4C.
The number of people at the party must be a multiple of 4. The only answer choice which is NOT a multiple of 4 is A.
Answer: A.
Answer: (A) 258
Question: The price of rice falls by 20%. How much rice can be bought now with the money that was sufficient to buy 10 kg of rice previously?
(A) 5 kg
(B) 12,5 kg
(C) 25 kg
(D) 30 kg
(E) None
Rationale: Solution: Let Rs. 100 be spend on rice initially for 10 kg.
As the price falls by 20%, new price for 10 kg rice,
= (100 -20% of 100) = 80
New price of rice = 80/10 = Rs. 8 per kg.
Rice can bought now at = 100/8 = 12,5 kg.
Answer: Option B
Answer: (B) 12,5 kg
Question: If a population of women in a town is 80% of men . What is the population of men as a % of population of women ?
(A) A)200%
(B) B)100%
(C) C)50%
(D) D)65%
(E) E)125%
Rationale: We're told that the number of Women in a town is equal to 50% of the number of Men in that town.
IF....
Men = 10
Women = 8
We're asked for the number of Men, as a percentage of the number of Women.
M/W = 10/8 = 5/4 = 125%
Answer is E
Answer: (E) E)125%
Question: What proximate value should come in place of the question mark (?) in the following question?
8.595 Ã— 1084 + 2568.34 â€“ 1708.34 = ?
(A) 6,000
(B) 12,000
(C) 10,000
(D) 10148
(E) 12312
Rationale: ? â‰ˆ 8.6 Ã— 1080 + 2560 â€“ 1700 â‰ˆ 9288 + 860 â‰ˆ 10148
Answer D
Answer: (D) 10148
Question: A financier claims to be lending money at simple interest, But he includes the interest every six months for calculating the principal. If he is charging an interest of 10%, the effective rate of interest becomes.
(A) 9.25%
(B) 10%
(C) 10.25%
(D) 9%
(E) None of these
Rationale: Explanation :
Let the sum is 100.
As financier includes interest every six months , then we will calculate SI for 6 months, then again for six months as below:
SI for first Six Months = (100*10*1)/(100*2) = Rs. 5
Important: now sum will become 100+5 = 105
SI for last Six Months = (105*10*1)/(100*2) = Rs. 5.25
So amount at the end of year will be (100+5+5.25)
= 110.25
Effective rate = 110.25 - 100 = 10.25
Answer : C
Answer: (C) 10.25%
Question: What percent of 120 are 90?
(A) 33
(B) 66
(C) 75
(D) 44
(E) 31
Rationale: (?% /100) * 120 = 90
? = 75%
Answer: C
Answer: (C) 75
Question: for doing any work A take 50% more time than B.if both together finish the work in 18 days,then B alone in how much days finish the work?
(A) 35 days
(B) 30 days
(C) 40 days
(D) 45 days
(E) 50 days
Rationale: let B take x days in finishing work
then,A take=150x/100 days=3x/2 days
so,1/x+2/3x=1/18,5/3x=1/18,3x=90,x=30
hence,whole work B finish in 30 days
answer B
Answer: (B) 30 days
Question: A shopkeeper has 100 kg of apples. He sells 50% of these at 25% profit and remaining 50% at 30% profit. Find his % profit on total.
(A) 27.5%
(B) 25.6%
(C) 31.5%
(D) 35.9%
(E) 29.5%
Rationale: Total number of apples = 100
Let the cost price be x
Selling price at 25% profit = 1.25x
Selling price at 30% profit = 1.3x
Profit % = ((SP - CP)/CP)*100
Profit % = ((1/2)*100*1.25x + (1/2)*100*1.3x - 100x)/100x * 100 = (255-200)/2
= 27.5%
Answer is A
Answer: (A) 27.5%
Question: Tough and Tricky questions: Word Problems.
It takes Sarah 14 minutes to do one oil change, and it takes Alice 10 minutes. If Sarah and Alice both begin doing oil changes at exactly 9:00 a.m. without pausing, when is the first time at which they will finish changing the oil of a car simultaneously?
(A) 10:00 a.m.
(B) 10:42 a.m.
(C) 12:00 a.m.
(D) 1:00 p.m.
(E) 2:00 p.m.
Rationale: LCM of 1014
10 = 2 * 5
14 = 2 * 7
LCM = 2 * 5 * 7 = 70 = 1 hour 10 minutes
1010AM
B
Answer: (B) 10:42 a.m.
Question: John’s salary is reduced by 40% and then reduced salary is increased by 40%. Find ,how many percentage his present salary is less as compared to his previous salary?
(A) 12%
(B) 14%
(C) 16%
(D) 18%
(E) 20%
Rationale: 40*40
-------- = 16%
100
Answer: C
Answer: (C) 16%
Question: What is the ratio between perimeters of two squares one having 3 times the diagonal then the other?
(A) 3: 2
(B) 3: 0
(C) 4: 1
(D) 3: 1
(E) 2: 2
Rationale: d = 3d d = d
a√2 = 3d a√2 = d
a = 3d/√2 a = d/√2 => 3: 1
Answer: D
Answer: (D) 3: 1
Question: Distance between two stations A and B is 778 km. A train covers the journey from A to B at 84 km per hour and returns back to A with a uniform speed of 56km per hour. Find the average speed of the train during the whole journey?
(A) 67.0 km /hr
(B) 67.2 km /hr
(C) 69.0 km /hr
(D) 69.2 km /hr
(E) 69.8 km /hr
Rationale: let us assume A =x,B=y
distance between two stations a and b=2*x*y= 2xy
but,train cover a journey of
A=56 km/hr B=84 km/hr
Average speed =[2xy/x+y]km/hr
= 2*84*56/(84+56) km/hr
=[2*84*56/140] km/hr
= 67.2 km/hr
ANSWER:B
Answer: (B) 67.2 km /hr
Question: What is the least possible product of 4 different integers, each of which has a value between –1 and 10, inclusive?
(A) –5040
(B) –3600
(C) –720
(D) –600
(E) –120
Rationale: Maximize the total product with a -ve sign
so -1 * 10 * 9 * 8 = 720 * -1 = -720
Answer is C.
Answer: (C) –720
Question: The average weight of 16 kids in a class is 50.25 kg and that of the remaining 8 kids is 45.15 kg. Find the average weights of all the kids in the class.
(A) A)48.55
(B) B)49
(C) C)51
(D) D)61
(E) E)62
Rationale: Required average
= (50.25 x 16 + 45.15 x 8)/(16 + 8)
= (804 + 361.20)/24
= 1165.20/24
= 48.55kg
Answer is A
Answer: (A) A)48.55
Question: At what time between 5.30 and 6 will the hands of a clock be at right angles?
(A) 43	7/12	min. past 5.
(B) 43	7/13	min. past 5.
(C) 42	7/11	min. past 5.
(D) 42	7/18	min. past 5.
(E) 43	7/11	min. past 5.
Rationale: At 5 o'clock, the hands are 25 min. spaces apart.
To be at right angles and that too between 5.30 and 6, the minute hand has to gain (25 + 15) = 40 min. spaces.
55 min. spaces are gained in 60 min.
40 min. spaces are gained in 60/55 x 40 min = 43 7/11 min.
Required time = 43	7/11	min. past 5.
Answer: E
Answer: (E) 43	7/11	min. past 5.
Question: A tradesman by means of his false balance defrauds to the extent of 10%? in buying goods as well as by selling the goods. What percent does he gain on his outlay?
(A) 29%
(B) 17%
(C) 44%
(D) 46%
(E) 21%
Rationale: g% = 10 + 10 + (10*10)/100
= 21%
Answer: E
Answer: (E) 21%
Question: How many natural numbers are there between 23 and 100 which are exactly divisible by 6 ?
(A) 134
(B) 12
(C) 11
(D) 14
(E) 15
Rationale: A
13
Required numbers are 24, 30, 36, 42, ..., 96
This is an A.P. in which a = 24, d = 6 and l = 96
Let the number of terms in it be n.
Then tn = 96a + (n - 1)d = 96
24 + (n - 1) x 6 = 96
(n - 1) x 6 = 72
(n - 1) = 12
n = 13
Required number of numbers = 13.
Answer: (A) 134
Question: Evaluate: 6502.5 + 650.25 + 65.025 + 6.5025 + 0.65025
(A) 6819.59775
(B) 6981.59775
(C) 7224.92775
(D) 6198.59775
(E) 6891.59775
Rationale: 6502.5
650.25
65.025
6.5025
+ 0.65025
---------------
7224.92775
Answer is C.
Answer: (C) 7224.92775
Question: A water tank is three-fifth full.Pipe A can fill a tank in 10 minutes and pipe B can empty it in 6 minutes.If both the pipes are open,how long will it take to empty or fill the tank completely?
(A) 6 min.to empty
(B) 9 min.to empty
(C) 5 min.to empty
(D) 4 min.to empty
(E) 7 min.to empty
Rationale: Explanation:
Clearly,pipe B is faster than pipe A and so,the tank will be emptied.
part to be emptied = 3/5
part emptied by (A+B) in 1 minute=(1/6-1/10)=1/15
so, the tank will be emptied in 9 min
Answer: B
Answer: (B) 9 min.to empty
Question: Look at this series: 1,4,9,16,... What number should come next?
(A) 18
(B) 27
(C) 30
(D) 25
(E) 24
Rationale: Explanation: This is a series of perfect square numbers.
1*1 = 1
2*2 = 4
3*3 = 9
4*4 = 16
5*5 = 25 and so on.
Answer: Option D
Answer: (D) 25
Question: 4 weavers can weave 4 mats in 4 days. At the same rate, how many mats would be woven by 10 weavers in 10 days?
(A) 10
(B) 15
(C) 20
(D) 25
(E) 30
Rationale: 1 weaver can weave 1 mat in 4 days.
10 weavers can weave 10 mats in 4 days.
10 weavers can weave 25 mats in 10 days.
The answer is D.
Answer: (D) 25
Question: A train having a length of 240 m passes a post in 24 seconds. How long will it take to pass a platform having a length of 660 m?
(A) 120 sec
(B) 99 sec
(C) 89 sec
(D) 90 sec
(E) 85 sec
Rationale: Explanation:
v = 240/24 (where v is the speed of the train) = 10 m/s
t = (240+660)/10 = 90 seconds
Answer: Option D
Answer: (D) 90 sec
Question: A metallic sphere of radius 12 cm is melted and drawn into a wire, whose radius of cross section is 16 cm. What is the length of the wire?
(A) 6 cm
(B) 5 cm
(C) 2 cm
(D) 7 cm
(E) 9 cm
Rationale: Volume of the wire (in Cylindrical shape) is equal to the volume of the sphere.
π(16)2 * h
= (4/3)π (12)3 => h
= 9 cm
Answer: E
Answer: (E) 9 cm
Question: The price of 5 kilograms of premium fertilizer is the same as the price of 14 kilograms of regular fertilizer. If the price of premium fertilizer is y cents per kilogram more than the price of regular fertilizer, what is the price, in cents, per kilogram of premium fertilizer?
(A) y/30
(B) 5/6*y
(C) 6/5*y
(D) 5y
(E) 14y/9
Rationale: Usingpfor premium andrfor regular, I got two equations from the question stem:
5p = 14r and p = r+y
Substitute for p: 5(r+y) = 14r
Distribute: 5r + 5y = 14r
Subtract 5r from both sides: 5y = 9r
Plug back into the first equation: 5p = 14(5y/9)
Distribute: 5p = 70y/9
Divide both sides by 5: p = 14y/9
The answer is E.
Answer: (E) 14y/9
Question: Of the 800 employees of Company X, 70 percent have been with the company for at least ten years. If y of theselong-termmembers were to retire and no other employee changes were to occur, what value of y would reduce the percent oflong-termemployees in the company to 50 percent ?
(A) 320
(B) 160
(C) 112
(D) 80
(E) 56
Rationale: The # oflong-termemployees is 70%*800=560.
After y of them retire new # oflong-termemployees would become 560-y.
Total # of employees would become 800-y.
We want 560-y to be 50% of 800-y --> 560-y=(800 -y)*50% --> y = 320.
Answer: A.
Answer: (A) 320
Question: A man can row with a speed of 24 kmph in still water. If the stream flows at 6 kmph, then the speed in downstream is?
(A) 27
(B) 23
(C) 30
(D) 28
(E) 12
Rationale: M = 24
S = 6
DS = 24 + 6 = 30
Answer: C
Answer: (C) 30
Question: The average weight of A, B and C is 43 kg. If the average weight of A and B be 40 kg and that of B and C be 43 kg, then the weight of B is:
(A) 33 kg
(B) 31 kg
(C) 32 kg
(D) 36 kg
(E) 37 kg
Rationale: Let A, B, C represent their respective weights.
Then, we have: A + B + C = (45 x 3) = 129 .... (i)
A + B = (40 x 2) = 80 .... (ii)
B + C = (43 x 2) = 86 ....(iii)
Adding (ii) and (iii), we get: A + 2B + C = 166 .... (iv)
Subtracting (i) from (iv), we get : B = 37.
B's weight = 37 kg.
E
Answer: (E) 37 kg
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. 2
(B) Rs. 2(2/9)
(C) Rs. 3(2/9)
(D) Rs. 4
(E) Rs. 4(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 basket contains 5 blue, 5 red and 5 yellow marbles. If 5 marbles are extracted from the basket at random, what is the probability that a marble of each color is among the extracted?
(A) 2/21
(B) 3/25
(C) 25/91
(D) 9/28
(E) 11/24
Rationale: 15/15*10/14*5/13 = 50/182 = 25/91
the answer is (C)
Answer: (C) 25/91
Question: The average weight of 8 person's increases by 2.5 kg when a new person comes in place of one of them weighing 65 kg. What might be the weight of the new person?
(A) 80
(B) 82
(C) 85
(D) 87
(E) 88
Rationale: Total weight increased = (8 x 2.5) kg = 20 kg.
Weight of new person = (65 + 20) kg = 85 kg.
ANSWER C
Answer: (C) 85
Question: Two sides of a certain triangle have lengths 3 and 4 respectively, which of the following could be the length of the third side of the triangle?
I. 0
II. 10
III. 2
(A) I only
(B) II only
(C) III only
(D) II and III only
(E) I, II and III
Rationale: Following the triangle inequality rule, which states: the length of a side of a triangle is less than the sum of the lengths of the other two sides and greater than the difference of the lengths of the other two sides:
Difference of other 2 sides < any side < sum of other two sides. Let the third side of triangle be AB.
So, 4 - 3 < AB < 4+3,
and 1 < AB < 7
Check if any of the answers are between 1 and 7.
I: 0 ; could not be a possible value.
II: 10 ; could not be a possible value.
III: 2; could be a possible value.
Answer :C
Answer: (C) III only
Question: If d is the standard deviation x, y, and z, what is the standard deviation of x + 10, y + 10, z + 10 ?
(A) d
(B) 3d
(C) 15d
(D) d + 5
(E) d + 15
Rationale: If we add or subtract a constant to each term in a set:
Mean will increase or decrease by the same constant.
SD will not change.
If we increase or decrease each term in a set by the same percent (multiply by a constant):
Mean will increase or decrease by the same percent.
SD will increase or decrease by the same percent.
So in our case SD won't change as we are adding 10 to each term in a set --> SD=d.
Answer: A.
Answer: (A) d
Question: P and Q are the only two applicants qualified for a short-term research project that pays 540 dollars in total. Candidate P has more experience and, if hired, would be paid 50 percent more per hour than candidate Q would be paid. Candidate Q, if hired, would require 10 hours more than candidate P to do the job. Candidate P’s hourly wage is how many dollars greater than candidate Q’s hourly wage?
(A) $9
(B) $15
(C) $18
(D) $21
(E) $27
Rationale: Let Q's hourly wage be x, then P's hourly wage is 1.5x
Let T be the number of hours that Q needs, then P needs T-10 hours to do the job.
Since they both are paid an equal total amount of $540:
x*T=1.5x*(T-10)
T = 30 hours and Q's hourly wage is 540/30 = $18
P's hourly wage is 540/(T-10) = $27 which is $9 per hour more.
The answer is A.
Answer: (A) $9
Question: When x is even, [x] = x/2 + 1, when x is odd [x] = 2x + 1 then [17]*[4] = ?
(A) [22]
(B) [44]
(C) [105]
(D) [88]
(E) [90]
Rationale: [17]*[4]=(2*17+1)(4/2+1)
=[105].
Ans - C
Answer: (C) [105]
Question: 10 men and 15 women together can complete a work in 6 days. It takes 100 days for one man alone to complete the same work. How many days will be required for one woman alone to complete the same work?
(A) 227
(B) 269
(C) 266
(D) 298
(E) 225
Rationale: 1 man's 1 day work = 1/100
(10 men + 15 women)'s 1 day work = 1/6
15 women's 1 day work = (1/6 - 10/100) = 1/15
1 woman's 1 day work = 1/225
1 woman alone can complete the work in 225 days.
Answer: E
Answer: (E) 225
Question: Rani bought more apples than oranges. She sells apples at ₹23 apiece and makes 15% profit. She sells oranges at ₹10 apiece and makes 25% profit. If she gets ₹653 after selling all the apples and oranges, find her profit percentage Z.
(A) 16.8%
(B) 17.4%
(C) 17.9%
(D) 18.5%
(E) 19.1%
Rationale: Given: Selling price of an Apple = 23 --> Cost price = 23/1.15 = 20
Selling price of an orange = 10 --> Cost price = 10/1.25 = 8
A > O
23*(A) + 10*(O) = 653
653 - 23*(A) has to be divisible by 10 --> Units digit has to be 0
Values of A can be 1, 11, 21, 31, .... --> 1 cannot be the value
Between 11 and 21, If A = 11, O = 30 --> Not possible
If A = 21, O = 17 --> Possible
Cost price = 20*21 + 8*17 = 420 + 136 = 556
Profit = 653 - 556 = 97
Profit% Z = (97/556)*100 = 17.4%
Answer: B
Answer: (B) 17.4%
Question: What will come in place of the x in the following Number series? 8, 10, 14, 22, 38, x
(A) 66
(B) 68
(C) 70
(D) 72
(E) 74
Rationale: 88 x 2 - 6 = 1010 x 2 - 6 = 1414 x 2 - 6 = 2222 x 2 - 6 = 3838 x 2 - 6 = 70C
Answer: (C) 70
Question: Let us say that a table tennis tournament was going on with knock out terms which means the one who loses the match is out of the tournament. 100 players took part in that tournament.
How many matches were played?
(A) 90 matches
(B) 95 matches
(C) 99 matches
(D) 85 matches
(E) 87 matches
Rationale: C
99 matches.
The number of matches will always sum up to one less than the number of players in a knock out tournament. You may calculate it in any manner. Thus 99 matches were played.
Answer: (C) 99 matches
Question: We bought 85 hats at the store. Blue hats cost $6 and green hats cost $7. The total price was $548. How many green hats did we buy?
(A) 36
(B) 38
(C) 40
(D) 42
(E) 44
Rationale: Let B be the number of blue hats and let G be the number of green hats.
B+G=85.
B=85-G.
6B+7G=548.
6(85-G)+7G=548.
510-6G+7G=548.
G=548-510=38.
The answer is B.
Answer: (B) 38
Question: In what time will a cart 50 m long cross, if its speed be 36 km/hr?
(A) 25
(B) 5
(C) 15
(D) 20
(E) 30
Rationale: Speed = 36 * 5/18 = 10 m/sec
Time taken = 50/10 = 5 sec.
Answer:B
Answer: (B) 5
Question: The average of first 18 natural numbers is?
(A) 5.6
(B) 9.5
(C) 9.1
(D) 9.8
(E) 5.2
Rationale: Sum of 18 natural no.
= 342/2 = 171
Average = 171/18
= 9.5
Answer:B
Answer: (B) 9.5
Question: What is the area of a square field whose sides have a length of 13 meters?
(A) 225 sq m
(B) 169 sq m
(C) 128 sq m
(D) 267 sq m
(E) 231 sq m
Rationale: 13 * 13 = 169 sq m
The answer is B.
Answer: (B) 169 sq m
Question: Imagine John has 2 blue balls, 3 green balls, 1 black ball and 4 red balls. How many ways can he arrange the balls lining them up?
(A) 10!/(2!)2 1!
(B) 10!/2! 1! 3! 1!
(C) 10!/4! 4!
(D) 9!/4! 3! 2!
(E) 10!/4! 3! 2!
Rationale: n items of which p are alike of one kind, q alike of the other, r alike of another kind and the remaining are distinct can be arranged in a row in n!/p!q!r! ways.
John has 10 balls which are 4 red balls, 3 green balls, 2 blue balls and 1 black ball.
Number of arrangements = 9!/(2!)2 3!
Answer: E
Answer: (E) 10!/4! 3! 2!
Question: Of the total amount that Rose spent on a shopping trip, excluding taxes, she spent 50 percent on clothing, 20 percent on food, and 30 percent on other items. If Rose paid a 4 percent tax on the clothing, no tax on the food, and an 8 percent tax on all other items, then the total tax that she paid was what percent of the total amount that she spent, excluding taxes?
(A) 2.8%
(B) 4.4%
(C) 4.6%
(D) 5.2%
(E) 6.0%
Rationale: Assume she has $200 to spend.
TAX
Clothing = 50% = $100= $4.00
Food = 20% = $ 40 = $0.00
Items = 30% = $ 60 = $ 4.80
Total tax = $8.80
% of total amount = 8.8/200 * 100 = 4.4%
B)
Answer: (B) 4.4%
Question: If two numbers are in the ratio 2:3. If 10 is subtracted from both of the numbers then the ratio becomes 2:4 then find the biggest number?
(A) 20
(B) 22
(C) 27
(D) 28
(E) 30
Rationale: Given Ratio => 2:3
2x - 10 : 3x - 10 = 2 : 4
4[2x - 10] = 2[3x - 10]
8x - 40 = 6x - 20
8x - 6x = 40 - 20
x = 10
Then biggest number is = 3x
3x = 30
Ans = E
Answer: (E) 30
Question: The area of a parallelogram is 242sq m and its altitude is twice the corresponding base. Then the length of the base is?
(A) 8
(B) 9
(C) 7
(D) 11
(E) 2
Rationale: 2x * x = 242 => x= 11
Answer: D
Answer: (D) 11
Question: (1+0.0001)/(0.04+10000)
The value of the expression above is closet to which of the following?
(A) 0.0001
(B) 0.001
(C) 0.1
(D) 1
(E) 10
Rationale: Notice that we need approximate value of the fraction.
Now, the nominator is very close to 1 and the denominator is very close to 10, hence the value of the fraction is very close to 1/10000=0.0001.
Answer: A
Answer: (A) 0.0001
Question: Mr. T has a wrong weighing pan. One arm is lengthier thanother.1 kilogram on left balances 8 melons on right.1 kilogram on rightbalances 2 melons on left. If all melons are equal in weight, what is theweight of a single melon
(A) 100grm
(B) 200grm
(C) 300grm
(D) 400grm
(E) 500grm
Rationale: R L
8m 1kg
1kg 2m
total melons in Right and Left = 10melons
total kilogram in Right and Left = 2kg
for balance
10melons = 2kg
5melons = 1kg
So that weight of 1 melons = 1000/5 = 200grm
ANSWER:B
Answer: (B) 200grm
Question: Let d(n) represent the sum of the digits of the integer n. For example,
d(2016) = 2 + 0 + 1 + 6 = 9:
For how many positive 3-digit integers k is it true that d(k) > d(k + 1)?
(A) 90
(B) 100
(C) 120
(D) 140
(E) 40
Rationale: Note that d(k) > d(k + 1) if and only if the units digit of k is 9, because if the units
digit of k is not 9, then d(k) = d(k + 1) - 1 < d(k + 1). Since there are 9 possible hundreds
digits and 10 possible tens digits, there are 9 * 10 = 90 possible values of k.
correct answer A
Answer: (A) 90
Question: A train starts full of passengers at the first station it drops 1/3 of the passengers and takes 280 more at the second station it drops one half the new total and takes twelve more. On arriving at the third station it is found to have 244 passengers. Find the no of passengers in the beginning?
(A) 292
(B) 180
(C) 276
(D) 144
(E) 168
Rationale: Let no of passengers in the beginning be X
After first station no passengers=(X-X/3)+280=2X/3 +280
After second station no passengers =1/2(2X/3+280)+12
1/2(2X/3+280)+12=244
2X/3+280=2*232 = 464 - 280 = 184
2X/3=184
X=276. So the answer is option C) 276.
Answer: (C) 276
Question: If two sides of a triangle have lengths 3 and 7, which of the following could be the perimeter of the triangle?
I. 9
II. 15
III. 19
(A) None
(B) I only
(C) II only
(D) II and III only
(E) I, II, and III
Rationale: Let x be the length of the third side.
7-3 < x < 7+3
4 < x < 10
14 < perimeter < 20
The answer is D.
Answer: (D) II and III only
Question: The population of locusts in a certain swarm doubles every two hours. If 4 hours ago there were 1,000 locusts in the swarm, in approximately how many hours will the swarm population exceed 512,000 locusts?
(A) 18
(B) 15
(C) 13
(D) 14
(E) 12
Rationale: - 4 hours: 1,000
-2 hours: 2,000
Now: 4,000
+ 2 hours: 8,000
+ 4 hours: 16,000
+ 6 hours: 32,000
+ 8 hours: 64,000
+ 10 hours: 128,000
+ 12 hours: 256,000
+ 14 hours: 512,000
Answer : D
Answer: (D) 14
Question: The average age of seven persons sitting in a row facing east is 28 years. If the average age of the first three persons is 21 years and the average age of the last three persons is 34 years, then find the age of the person sitting in the middle of the row?
(A) 22
(B) 31
(C) 17
(D) 12
(E) 91
Rationale: Total age seven persons = (28 * 7)years
Total age of the first three persons and the last three persons are (21 * 3) years and (34 * 3) years respectively.
Age of the person sitting in the middle of the row = 28 * 7 - 21 * 3 - 34 * 3 = 196 - 63 - 102 = 31 years.
Answer: B
Answer: (B) 31
Question: The sides of a square region, measured to the nearest centimeter, are 5 centimeters long. The least possible value of the actual area of the square region is
(A) 25.25 sq cm
(B) 20.25 sq cm
(C) 30.25 sq cm
(D) 36.25 sq cm
(E) 40.25 sq cm
Rationale: Though there might be some technicalities concerning the termnearest(as 4.5 is equidistant from both 4 and 5) the answer still should be : 4.5^2=20.25.
Answer: B
Answer: (B) 20.25 sq cm
Question: A bag is filled with pennies and nickels in the ratio of 4 to 3. There are 45 nickles in the bag, how many coins are there in that bag?
(A) 40
(B) 105
(C) 65
(D) 70
(E) 80
Rationale: A ratio of pennies to nickels of 4 to 3 means that we can write the number of pennies and nickels in the form
number of pennies = 4x and number of nickels = 3x
But we know the number of nickels, 45. Hence
3x = 45
Solve for x
x = 15
The total number of coins is given by
4x + 3x = 4x = 7 × 15 = 105
Answer : B
Answer: (B) 105