mathewhe/aqua_rat huggingface dataset:
Question: How many 11-digits number are Palindromic numbers? A Palindromic number reads the same forward and backward, example 12345654321.
(A) 100
(B) 610
(C) 729
(D) 900
(E) 900000
Rationale: Take the task of building palindromes and break it intostages.
Stage 1: Select the 11th digit
We can choose 1, 2, 3, 4, 5, 6, 7, 8, or 9
So, we can complete stage 1 in9ways
Stage 2: Select the 10th 9th,8th, 7th, 6th digit
We can choose 0, 1, 2, 3, 4, 5, 6, 7, 8, or 9
So, we can complete stage 2 in10ways
IMPORTANT: At this point, the remaining digits are alreadylocked in.
Stage 3: Select the , 5th, 4th, 3rd, 2nd, 1st digit
So, we can complete this stage in1way.
By theFundamental Counting Principle(FCP), we can complete all 5 stages (and thus build a 11-digit palindrome) in(9)(10)(10)(10)(10)(10)(1)(1)(1)(1)(1)ways (= 900000 ways)
Answer: E
Answer: (E) 900000
Question: A batsman scored 150 runs which included 3 boundaries and 8 sixes. What percent of his total score did he make by running between the wickets?
(A) 45(4/11) %
(B) 60 %
(C) 45(5/11) %
(D) 44(5/11) %
(E) None of these
Rationale: Explanation :
Total runs scored = 150
Total runs scored from boundaries and sixes = 3 x 4 + 8 x 6 = 60
Total runs scored by running between the wickets = 150 - 60 = 90
Required % = (90/150) × 100 =60%
Answer : Option B
Answer: (B) 60 %
Question: The average monthly salary of 20 employees in an organisation is Rs. 1600. If the manager's salary is added, then the average salary increases by Rs. 100. What is the manager's monthly salary ?
(A) 3700
(B) 3890
(C) 88798
(D) 2789
(E) 2891
Rationale: Explanation:
Manager's monthly salary Rs. (1700 * 21 - 1600 * 20) = Rs. 3700.
Answer: A) 3700
Answer: (A) 3700
Question: If k is an integer and 2 < k < 6, for how many different values of k is there a triangle with sides of lengths 2, 6, and k?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
Rationale: (6-2) < k < (6+2)
4 < k < 8
thus k = 5, 6, 7
Since 2 < k < 6, then k can be 5.
The answer is B.
Answer: (B) 1
Question: A fill pipe can fill 1/2 of cistern in 20 minutes. In how many minutes, it can fill 1/2 of the cistern?
(A) 5min
(B) 10min
(C) 15min
(D) 20min
(E) 25min
Rationale: Required time = 20*2*1/2 = 20 minutes
Answer is D
Answer: (D) 20min
Question: A bag contains 4 red balls, 5 green balls and 6 white balls. A ball is drawn at
random from the box. What is the probability that the ball drawn is either red or green?
(A) 2/5
(B) 3/5
(C) 1/5
(D) 7/15
(E) 8/15
Rationale: Total number of balls = (4 + 5 + 6) = 15.
Therefore, n(S) = 15.
Let E1 = event of drawing a red ball.
and E2 = event of drawing a green ball.
Then, E1 n E2 = f.
P (E1 n E2) = P(E1) + P(E2) = (4/15 + 5/15) = 9/15 = 3/5.
ANSWER:B
Answer: (B) 3/5
Question: The number of permutations of the letters of the word 'BUBBLEGUM' is?
(A) 9!/(2!)2
(B) 9!/2!
(C) 9!/3! 2!
(D) 8!/3! 2!
(E) 9!/2! 1! 1! 1!
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.
The letter pattern 'BUBBLEGUM' consists of 9 letters of which there are 3B's, 2U's, 1L, 1G and 1M.
Number of arrangements = 9!/3! 2!
Answer: C
Answer: (C) 9!/3! 2!
Question: A shop sells two variants of chocolates - one that costs $3 and the other that costs $5. If the shop sold $112 chocolates on a given day, how many different combinations of (number of $3 sold, number of $5 sold) exist?
(A) 6
(B) 7
(C) 8
(D) 12
(E) 15
Rationale: $112 = 20*$5 + 4*$3
We can find other combinations by reducing the $5 chocolates by 3 (which is -$15)and increasing the $3 chocolates by 5 (which is +$15).
The number of $5 chocolates can be 20, 17, 14,...,2 for a total of 7 combinations.
The answer is B.
Answer: (B) 7
Question: A and B start a business with Rs.6000 and Rs.8000 respectively. Hoe should they share their profits at the end of one year?
(A) 3:9
(B) 3:4
(C) 3:2
(D) 3:1
(E) 3:5
Rationale: Explanation:
They should share the profits in the ratio of their investments.
The ratio of the investments made by A and B =
6000 : 8000 => 3:4
Answer:B
Answer: (B) 3:4
Question: A retailer sells 10 shirts. The first 3 he sells for $20,$22 and $25. If the retailer wishes to sell the 10 shirts for an overall average price of over $20, what must be the minimum average price of the remaining 7 shirts?
(A) $14.00
(B) $16.00
(C) $17.00
(D) $19.00
(E) $23.00
Rationale: First 3 shirts are sold for $20,$22 and $25=$67.
To get average price of $20,total sale should be 10*$20=$200
So remaining 7 shirts to be sold for $200-$67=$133
Answer should be 133/7=$19.00 that is D
Answer: (D) $19.00
Question: Uncle Bruce is baking chocolate chip cookies. He has 36 ounces of dough (with no chocolate) and 20 ounces of chocolate. How much chocolate is left over if he uses all the dough but only wants the cookies to consist of 10% chocolate?
(A) 18
(B) 20
(C) 16
(D) 22
(E) 24
Rationale: First, you must find the total weight of the mixture given that 80% of it will be dough.
90%*Total = 36 => (9/10)Total=36=> Total=360/9 => Total=40 oz,
From there, you must find 10% of the total 40 oz of the mixture.
10%*Total => (1/10)(40)= 4 oz choclate used,
Not forgetting that the question asks how much chocolate is left over we must subtract the chocolate used from the initial chocolate. 20-4 = 16 oz chocolate left over.
Answer : C
Answer: (C) 16
Question: If 4 men can color 48 m long cloth in 2 days, then 6 men can colour 36 m long cloth in
(A) 1 day
(B) 2 days
(C) 3 days
(D) 4 days
(E) 5 days
Rationale: The length of cloth painted by one man in one day = 48 / 4 × 2 = 6 m
No. of days required to paint 36 m cloth by 6 men = 36/ 6 × 6 = 1 day.
A
Answer: (A) 1 day
Question: A certain no. when divided by 20 leaves a remainder 25, what is the remainder if the same no.be divided by 15?
(A) 3
(B) 4
(C) 6
(D) 8
(E) 9
Rationale: Explanation:
20 + 25 = 45/15 = 3 (Remainder)
A
Answer: (A) 3
Question: A box contains nine slips that are each labeled with one number: 1, 2, 3, 8, 13, 21, 34 and 55. Two of the slips are drawn at random from the box without replacement. What is the probability that the sum of the numbers on the two slips is equal to one of the numbers left in the box?
(A) 7/72
(B) 1/6
(C) 7/36
(D) 15/36
(E) 1/7
Rationale: Probability = No: of desired outcomes / Total No: of outcomes.
You are picking two slips out of 8 slips. So
Total No: of outcomes = 8C2 = 28
Desired outcome : sum of the numbers on the two slips is equal to one of the numbers left in the box. How many such outcomes are there?
If you look at the numbers closely, you will see that the following pair of numbers will give you the desired outcome.
(1,2) (8,13) (13,21) (21,34) . There are 4 such pairs. If the two numbers which I pick is from any of these 4 pairs, then I get my desired outcome.
So No: of desired outcomes = 4
Probability = 4/28=1/7
Answer :E
Answer: (E) 1/7
Question: Kim has 7 pairs of shoes; each pair is a different color. If Kim randomly selects 2 shoes without replacement from the 14 shoes, what is the probability that she will select 2 shoes of the same color?
(A) 1/13
(B) 1/15
(C) 11/9
(D) 1/10
(E) 1/25
Rationale: Can be tackled in this way as well: Probability of selecting any 1 out of 14 shoes = 14/14 = 1
Probability of selecting the next shoe (out of 14 available) having the same color = 1/14 (as after selecting the 1st one, there is only 1 another shoe left with the same color).
Thus the total probability = 1*1/13=1/13.
A is the correct answer.
Answer: (A) 1/13
Question: A train 225 m in length crosses a telegraph post in 15 seconds. The speed of the train is?
(A) 37 kmph
(B) 34 kmph
(C) 32 kmph
(D) 38 kmph
(E) 76 kmph
Rationale: S = 225/25 * 18/5
= 32 kmph
Answer: C
Answer: (C) 32 kmph
Question: A trader owes a merchant $10000 due 1 year hence. The trader wants to settle the account after 2 months. If the rate of interest 12% per annum, how much cash should he pay?
(A) $9090.90
(B) $9010.90
(C) $7090.90
(D) $8090.90
(E) $9000.90
Rationale: Required money	= P.W. of $10000 due 10 months hence
= $((10000*100) / 100+ (12*10/12) )
= $9090.90
ANSWER:A
Answer: (A) $9090.90
Question: Which of these lines in the xy-plane does not contain any point with two negative coordinates?
(A) y = 3x
(B) y = x + 7
(C) y = x^2 - 4
(D) y = x^3 + 3x
(E) y = x^6
Rationale: x^6 is 0 when x is 0 and positive for all other values of x.
The answer is E.
Answer: (E) y = x^6
Question: Each of the 20 boxes in a certain shipment weighs either 10 pounds or 20 pounds, and the average (arithmetic mean) weight of the boxes in the shipment is 18 pounds. If the average weight of the boxes in the shipment is to be reduced to 15 pounds by removing some of the 20-pound boxes, how many 20-pound boxes must be removed?
(A) 10
(B) 12
(C) 14
(D) 16
(E) 18
Rationale: If the average of 10-pound and 20-pound boxes is 18, the ratio of 10-pound boxes:20-pound boxes is 1:4.
So out of 20 boxes, 4 are 10-pound boxes and 16 are 20-pound boxes.
If the average of 10 and 20-pound boxes is to be 15, the ratio of 10-pound boxes:20-pound boxes should be 1:1.
The number of 10 pound boxes remains the same so we still have 4 of them.
To get a ratio of 1:1, the number of 20-pound boxes must be 4.
We need to remove 12 of the 20-pound boxes.
The answer is B.
Answer: (B) 12
Question: The cash realised on selling a 14% stock is Rs.104.25, brokerage being 1/4% is?
(A) 104
(B) 106
(C) 102
(D) 192
(E) 122
Rationale: Cash realised= Rs. (104.25 - 0.25)
= Rs. 104.
Answer: A
Answer: (A) 104
Question: The triplicate ratio of 2:5 is?
(A) 1:0
(B) 8:125
(C) 1:7
(D) 1:2
(E) 1:1
Rationale: 23: 53 = 8:125
Answer: B
Answer: (B) 8:125
Question: There are 2000 students in a school and among them 10 % of them attends chess class. 50% of the students who are in the chess class are also enrolled for swimming. No other students are interested in swimming so how many will attend the swimming class if all enrolled attends?
(A) 1
(B) 10
(C) 100
(D) 50
(E) 20
Rationale: 10% of 2000 gives 200. so 200 attends chess and 50% of 200 gives 100
so 100 enrolled for swimming
Answer: C
Answer: (C) 100
Question: If y is an integer, then y(y - 1)( y- k) must be evenly divisible by three when k is any of the following values EXCEPT
(A) -4
(B) -6
(C) -1
(D) 2
(E) 5
Rationale: if we put k=-1 we get:
y(y-1)(y+1) rearrange:(y-1)y(y+1)
so it looks like a sequenc,
if we assume that y=2 and put number from the answer then we get:
(y – 1)y(y – k)
k=5 =1.2.-3
k=2 =1.2.0
k=-1 =1.2.3
k=-4 =1.2.6
but when we put
k=-6 =1.2.8 not satisfied
so,the answer is B
Answer: (B) -6
Question: The grocer ordered deliveries of apples on each weekday. The numbers of apples he ordered per day were 80, 30, 100, 90 and x. If the median apple delivery was 10 apples larger than the average (arithmetic mean) number of apples delivered, which of the following could be x?
(A) 50
(B) 55
(C) 60
(D) 65
(E) 70
Rationale: Look at the options available
Value of x seems to 50 < = x < = 70
A. 50
B. 55
C. 60
D. 65
E. 70
So position of x is second
30 , x , 80 , 90 , 100
Median = 80
Median number of apples was 10 points higher than the average, so average = 70
30 + x + 80 + 90 + 100 = 350
x = 50 = Answer = A
Answer: (A) 50
Question: In the simple subtraction problem below some single digits are replaced by letters .Fined the value of 7A+5D+6CD?
(A) 288
(B) 3799
(C) 277
(D) 278
(E) 240
Rationale: 15 - 7 = 8 So D = 8
10 + (C -1) - 8 = 4 So C = 3
10 + (5-1) - B = 7 So B = 7
(A-1) - 1 = 6 So A = 8
7A + 5D + 6CD = 56 + 40 + 144 = 240
Answer:E
Answer: (E) 240
Question: There are 3 teams each with 6 basket players. How many combinations are there if we were to pick 2 players from the 3 teams such that no team was picked twice?
(A) 50
(B) 23
(C) 108
(D) 28
(E) 45
Rationale: There are altogether three arrangements, which are we can select two members each from team A and B, each from team A and C, and each from team B and C. For each arrangement, there are altogether 36 possibilities (6*6) since each team has 6 players. So there are a total of 108 possibilities (36*3). I hope this method is easier for you to understand.
Answer: (C) 108
Question: For any 8 given numbers, which of the following is always equivalent to adding the 3 numbers together and then dividing the sum by 3?
I. Ordering the 3 numbers numerically, from highest to lowest, and then selecting the middle number.
II. Dividing each of the numbers by 3 and then adding the results together.
III. Multiplying each number by 6, adding the resulting products together, and then dividing the sum by 9.
(A) I only
(B) II only
(C) I and II only
(D) II and III only
(E) None of the above
Rationale: Let the 3 numbers be x, y and z.
Question: Which of the following is equivalent to (x + y + z)/3
I. Ordering the 3 numbers numerically, from highest to lowest, and then selecting the middle number. --> Not always equivalent Eg: 111 and 141
II. Dividing each of the numbers by 3 and then adding the results together. --> x/3 + y/3 + z/3 = (x + y + z)/3 --> Equivalent
III. Multiplying each number by 6, adding the resulting products together, and then dividing the sum by 9. --> (6x + 6y + 6z)/9 = 2(x + y + z)/3 --> Not equivalent
Answer: E
Answer: (E) None of the above
Question: A father is now three times as old as his son. Seven years back, he was four times as old as his son. The age of the son (in years) is
(A) A)12
(B) B)15
(C) C)18
(D) D)20
(E) E)21
Rationale: Explanation:
Let son's age be x years. Then, father's age = (3x) years.
Seven years ago, father's age = (3x - 7) years and son's age = (x - 7) years.
So, 3x - 7 = 4 (x - 7)=> 3x - 7 = 4x - 28=> x = 21.
Answer: E
Answer: (E) E)21
Question: In a group of 86 students, each student is registered for at least one of three classes – History, Math and English. Twenty-eight students are registered for History, twenty-three students are registered for Math, and forty-four students are registered for English. If only three students are registered for all three classes, how many students are registered for exactly two classes?
(A) 3
(B) 10
(C) 9
(D) 8
(E) 7
Rationale: A U B U C = A + B + C - AB-BC-AC + ABC
86 = 28 + 23+ 44 -AB-BC-AC +3 => AB+BC+AC = 12
Exactly Two classes = AB+BC+AC - 3ABC = 12 -3*3 = 3
Hence A
Answer: (A) 3
Question: If a person walks at 14 km/hr instead of 10 km/hr, he would have walked 20 km more. The actual distance travelled by him is
(A) 50 km
(B) 56 km
(C) 70 km
(D) 80 km
(E) 90 km
Rationale: Let the actual distance travelled be x km.
Then x/10=(x+20)/14
--> 14x = 10x + 200
--> 4x = 200
--> x = 50 km.
Answer : A.
Answer: (A) 50 km
Question: A test paper has 10 questions each worth 4 marks. While taking the test, a student realises that he has attempted questions worth 16 marks. Assuming that whatever question he attempts is completely correct, how many more questions should he attempt so that he is able to secure 90 percent marks?
(A) 4
(B) 5
(C) 6
(D) 7
(E) 8
Rationale: Since the test paper has 10 questions each worth 4 marks, the maximum marks he can get is 40.
His aim is to secure 90 % marks, this means he wants to secure 90% of 40 = 36 marks.
Out of the 36 marks, he has already attempted questions worth 16 marks, so he should attempt questions worth 36 - 16 = 20 more marks.
As every question is worth 4 marks, so to secure 20 more marks he should attempt (20/4) = 5 more questions.
Ans B
Answer: (B) 5
Question: The average age of three boys is 48 years and their ages are in proportion 2:5:5. What is the age in years of the youngest boy?
(A) 30
(B) 23
(C) 24
(D) 26
(E) 40
Rationale: 2x + 5x + 5x = 144
x =12
2x = 24
Answer: C
Answer: (C) 24
Question: The cash realised on selling a 14% stock is Rs.106.25, brokerage being 1/4% is
(A) 123
(B) 106
(C) 100
(D) 156
(E) 240
Rationale: Explanation:
Cash realised= Rs. (106.25 - 0.25)
= Rs. 106.
Answer: B
Answer: (B) 106
Question: A jogger running at 9 kmph along side a railway track is 270 metres ahead of the engine of a 120 metre long train running at 45 kmph in the same direction. In how much time will the train pass the jogger?
(A) 3.6 sec
(B) 18 sec
(C) 36 sec
(D) 39 sec
(E) None of these
Rationale: Speed of train relative to jogger
= (45 – 9) km/h = 36 km/h
= (36 × 5⁄18) m/sec = 10 m/sec
Distance to be covered = (270 + 120) m = 390 m.
∴ Time taken = (390⁄10) sec = 39 sec.
Answer D
Answer: (D) 39 sec
Question: Find the average of all prime numbers between 80 and 100
(A) 88
(B) 60
(C) 80
(D) 89.6
(E) 92
Rationale: Prime numbers between 80 and 100 are 83, 89, 97
Required average = (83+ 89+ 97)/3 = 269/3 = 89.6
Answer is D
Answer: (D) 89.6
Question: In a birthday party, every person shakes hand with every other person. If there was a total of 28 handshakes in the party, how many persons were present in the party?
(A) 6
(B) 7
(C) 8
(D) 9
(E) 10
Rationale: Suppose there are nn persons present in a party and every person shakes hand with every other person. Then, total number of handshakes
= nC2=n(n−1)/2
n(n−1)=28×2n(n−1)=56
n=8
ANSWER C 8
Answer: (C) 8
Question: A train passes a man standing on the platform. If the train is 180 meters long and its speed is 72 kmph, how much time it took in doing so?
(A) 6 ½ sec
(B) 4 ½ sec
(C) 9 sec
(D) 8 sec
(E) 2 ½ sec
Rationale: D = 180
S = 72 * 5/18 = 20 mps
T = 180/20 = 9 sec
Answer: C
Answer: (C) 9 sec
Question: The average age of a class of 39 students is 15 years. If the age of the teacher be included, then the average increases by3 months. Find the age of the teacher.
(A) 22 years
(B) 23 years
(C) 24 years
(D) 25 years
(E) 26 years
Rationale: avg of 39 student = 15 yrs
Total age of 39 students=39*15= 585 yrs
Avg age of 39 students + teacher =15+3/12=15.25 yrs
so the total age of (39 student+1 teacher) or 40 persons=
40*15.25=610 yrs
so age of teacher=610-585=25 years
ANSWER:D
Answer: (D) 25 years
Question: A boat running downstream covers a distance of 44 km in 8 hours while for covering the same distance upstream, it takes 10 hours. What is the speed of the boat in still water?
(A) 5 kmph
(B) 4.95 kmph
(C) 6 kmph
(D) 7 kmph
(E) 8 kmph
Rationale: Explanation:
Speed downstream = 44/8 = 5.5 kmph
Speed upstream = 44/10 = 4.4 kmph
Speed of the boat in still water = (5.5+4.4)/2 = 4.95 kmph
Answer: Option B
Answer: (B) 4.95 kmph
Question: Population of a city in 20004 was 1000000. If in 2005 there isan increment of 15% , in 2006 there is a decrements of 35 % and in 2007 there is an increment of 45%, then find the population of city atthe end of the year 2007
(A) 967532
(B) 977522
(C) 984424
(D) 997454
(E) 1083875
Rationale: Required population = P (1 + R1/100)(1 - R2/100)(1 + R3/100)
= P (1 + 15/100)(1 - 35/100)(1 + 45/100)
= 1083875
E
Answer: (E) 1083875
Question: Two numbers are in the ratio 3 : 4. If the sum of numbers is 63, find the numbers.
(A) 27 and 36.
(B) 25 and 30.
(C) 23 and 44.
(D) 63 and 12.
(E) 12 and 36.
Rationale: Sum of the terms of the ratio = 3 + 4 = 7
Sum of numbers = 63
Therefore, first number = 3/7 × 63 = 27
Second number = 4/7 × 63 = 36
Therefore, the two numbers are 27 and 36.
Answer is A
Answer: (A) 27 and 36.
Question: The residents of the town Q participated in a survey to determine the number of hours per week each resident spent watching television. The distribution of the results of the survey had a mean of 21 hours and a standard deviation of 6 hours. The number of hours that Pat, a resident of town Q, watched television last week was between 1 and 2 standard deviations below the mean. Which of the following could be the number of hours that Pat watched television last week?
(A) - 30
(B) - 20
(C) - 18
(D) - 12
(E) - 6
Rationale: (21-6*2)<number of hours that Pat watched television last week <(21-6*1)
=9<L<15
Only option E (12) satisfies this condition.
Answer: (E) - 6
Question: The average amount with a group of seven numbers is Rs. 20. If the newly joined member has Rs. 50 with him, what was the average amount with the group before his joining the group?
(A) 17
(B) 26
(C) 15
(D) 97
(E) 12
Rationale: Total members in the group = 7
Average amount = Rs. 20
Total amount with them = 7 * 20
= Rs. 140
One number has Rs. 50. So, the amount with remaining 6 people
= 140 - 50 = Rs. 90
The average amount with them = 90/6
= Rs.15.
Answer:C
Answer: (C) 15
Question: A work as fast as B. If B can complete a work in 20days independently,the number of days in which A and B can together finish the work in?
(A) 2days
(B) 3days
(C) 4days
(D) 5days
(E) 6 2/3days
Rationale: Ratio of rates of working of A and B = 2:1
ratio of times taken = 1:2
A's 1day work = 1/10
B's 1day work = 1/20
A+B 1day work = 1/10 + 1/20 = 3/20 => 20/3 = 6 2/3
A and B can finish the work in 6 2/3days
Answer is E
Answer: (E) 6 2/3days
Question: There are 10 orators A, B, C, D, E, F, G, H, I and J. In how many ways can the arrangements be made so that A always comes before B and B always comes before C.
(A) 10! / 3!
(B) 8! / 6!
(C) 5! x 3!
(D) 8! / (5! x 3!)
(E) 8! / (5! x 4!)
Rationale: Select any three places for A, B and C. They need no arrangement amongst themselves as A would always come before B and B would always come before C.
The remaining 7 people have to be arranged in 7 places.
Thus, 10C3 x 7! =10! / 3!
ANSWER:A
Answer: (A) 10! / 3!
Question: A completes 80% of a work in 20 days. Then B also joins and A and B together finish the remaining work in 3 days. How long does it need for B if he alone completes the work?
(A) 37 1/2 days
(B) 22 days
(C) 31 days
(D) 22 days
(E) 25 1/2 days
Rationale: Work done by A in 20 days = 80/100 = 8/10 = 4/5
Work done by A in 1 day = (4/5) / 20 = 4/100 = 1/25 --- (1)
Work done by A and B in 3 days = 20/100 = 1/5 (Because remaining 20% is done in 3 days by A and B)
Work done by A and B in 1 day = 1/15 ---(2)
Work done by B in 1 day = 1/15 – 1/25 = 2/75
=> B can complete the work in 75/2 days = 37 ½ days
Option A
Answer: (A) 37 1/2 days
Question: The present average age of a family of five members is 26 years. If the present age of the youngest member in the family is ten years, then what was the average age of the family at the time of the birth of the youngest member ? (Assume no death occurred in the family since the birth of the youngest)
(A) 22 years
(B) 25 years
(C) 20 years
(D) 28 years
(E) 12 years
Rationale: Present total age of the members = 26(5) = 130 years.
Present age of the youngest member = 10 years
Present total age of the remaining four members = 130 -10 = 120 years
Their average age at the time of the birth of the youngest member = [120 - (4 * 10)] / 4 = 30 - 10 = 20 years.
Answer: C
Answer: (C) 20 years
Question: 8597 - ? = 7429 - 4358
(A) 3567
(B) 6424
(C) 6835
(D) 5526
(E) None of these
Rationale: D
7429-4358=3071
Let 8597 - x = 3071
Then, x = 8597 - 3071 = 5526
Answer: (D) 5526
Question: In an increasing sequence of 8 consecutive integers, the sum of the last 4 integers is 822. What is the sum of the first 4 integers in the sequence?
(A) 800
(B) 808
(C) 806
(D) 802
(E) 804
Rationale: Solution:
In solving this problem we must first remember that when we have 8 consecutive integers we can display them in terms of just 1 variable. Thus, we have the following:
Integer 1: x
Integer 2: x + 1
Integer 3: x + 2
Integer 4: x + 3
Integer 5: x + 4
Integer 6: x + 5
Integer 7: x + 6
Integer 8: x + 7
We are given that the sum of the first 4 integers is 570. This means that:
x+7+ x+6 + x+5 + x+4 = 822
4x + 22 = 822
4x = 800
x = 200
The sum of the last 4 integers can be expressed and simplified as:
x+ x+1 + x+2+ x+3 = 4x + 6
Substituting 141 for x yields:
(4)(200) + 6 = 806
Answer: C
Answer: (C) 806
Question: A lemonade stand sold only small and large cups of lemonade on Tuesday. 3/5 of the cups sold were small and the rest were large. If the large cups were sold for 11/5 as much as the small cups, what fraction of Tuesday's total revenue was from the sale of large cups?
(A) (a) 7/16
(B) (b) 7/15
(C) (c) 10/21
(D) (d) 22/37
(E) (e) 1/2
Rationale: A simpler way i guess would be to think that in total 5 cups were sold. Out of which 3 are small and 2 are large. Now let the small ones cost $5. so the large ones would cost $11.
So,
3*5=15 and 2*11=22.
Total revenue was 15+22=37
and Large cup sales as found above is 22
Therefore answer is 22/37
D
Answer: (D) (d) 22/37
Question: Find the area of the quadrilateral of one of its diagonals is 40 cm and its off sets 11 cm and 9 cm?
(A) 100 cm2
(B) 150 cm2
(C) 333 cm2
(D) 400 cm2
(E) 750 cm2
Rationale: 1/2 * 40(11 + 9)
= 400 cm2
Answer: D
Answer: (D) 400 cm2