mathewhe/aqua_rat huggingface dataset:
Question: What is the value of n if the sum of the consecutive odd intergers E from 1 to n equals 169?
(A) 47
(B) 25
(C) 37
(D) 33
(E) 29
Rationale: Before you tackle this question you must first understand that the question is comprised of two key parts, 1st is finding out how manytermsis in that sequence and 2nd whatactual number valuethat term is. In an arithmetic progression, in this case consecutive odd integers 1, 3, 5, ...., there are two set of rules.
Rule #1 (Arithmetic Sequence): xn = a + d(n-1) Identifies what the actual # in the sequence would be. Each number in the sequence has a term such as 1(is the first term), 3(is the second term) and so on. So if I were to ask you to find out what the 10th term is of that sequence you would use that formula to find that value.
a=1 (first term)
d=2 (the common difference) remember in the sequence 1, 3, 5, 7 the common difference is always 2
*On a side note we use n-1 because we don't have d in the first term, therefore if we were solving for the first term we would get 0 as n-1 and 0 times d would give us 0, leaving only the first term. This works regardless what your first term is in any sequence.
But remember the question asksWhat is thevalueof n if the sum of the consecutive odd integers from 1 to n equals 169?which means we first need a consecutive sequence that sums up to 169 and than find what the value of the n is, in this case it would be the last number in that sequence. In order to find that we first need to knowhow many terms(how many of the n there is) in order to be able to plug n in this formula given we know what the sum is. For that to happen we need to use Rule #2.
Rule #2 (Summing an arithmetic series): 169 = n/2(2a+(n-1)d). Given the question gives us what the sum is (169 in this case) we would simply use this formula to solve for n. Once we solve for n (13 in this case) we can simply plug n into the first formula (rule 1) and find the value.
It feels very confusing and difficult at first, but once you identify the steps all you need to do is plug and play. We have the sum (169) of a sequence, the number of terms in that sequence is (unknown). Rule #2 tells us how many numbers there are in that sequence and Rule #1 gives us what that last term is.
Answer: (B) 25
Question: A class is 6 meters 24 centimeters in length and 4 meters 32 centimeters in width. Find the least number of square tiles of equal size required to cover the entire floor of the class room ?
(A) 115
(B) 117
(C) 116
(D) 114
(E) 113
Rationale: Explanation:
Length = 6 m 24 cm = 624 cm
Width = 4 m 32 cm = 432 cm
HCF of 624 and 432 = 48
Number of square tiles required = (624 x 432)/(48 x 48) = 13 x 9 = 117.
ANSWER IS B
Answer: (B) 117
Question: If two dice are thrown together, the probability of getting an even number on one die and an odd number on the other is
(A) 1/4
(B) 1/2
(C) 3/4
(D) 3/5
(E) None of these
Rationale: The number of exhaustive outcomes is 36.
Let E be the event of getting an even number on one die and an odd number on the other. Let the event of getting either both even or both odd then = 18/36 = 1/2
P(E) = 1 - 1/2 = 1/2.
Answer : B
Answer: (B) 1/2
Question: How many terms are there in 2, 4, 8, 16,..., 16384?
(A) 14
(B) 11
(C) 12
(D) 10
(E) 8
Rationale: 2, 4, 8, 16, ..., 16384 is a G.P with a =2
and r =4/2 =2
Let the number of terms be n. Then
2 x 2 ^n-1 = 16384
or 2^n-1 = 8192 = 2^13
Thus n - 1 =13
n= 14
ANSWER:A
Answer: (A) 14
Question: The probability that A speaks truth is 3/5 and that of B speaking truth is 2/7. What is the probability that they agree in stating the same fact?
(A) 18/35
(B) 18/38
(C) 18/36
(D) 16/35
(E) 18/31
Rationale: If both agree stating the same fact, either both of them speak truth of both speak false.
Probability
= 3/5 * 2/7 + 2/5 * 5/7
= 6/35 + 10/35
= 16/35
Answer: D
Answer: (D) 16/35
Question: If the TV is selling for $1200 its cost price is $800. Then what is the profit percentage
(A) 60%
(B) 70%
(C) 80%
(D) 90%
(E) 50%
Rationale: Explanation:
Let the S.P = 1200
then C.P. = 800
Profit = 400
Profit% = (400/800) * 100 = 50%. Answer: E
Answer: (E) 50%
Question: A hotel has 4 available rooms. One room has a view to the garden and the others has a view to the pool. If you sleep in the hotel, what is the probability that you get a room in the side of the garden?
(A) 1/4
(B) 1/2
(C) 1/3
(D) none
(E) 2
Rationale: the total number of rooms is 4
and the number of rooms in the side of the garden is 1
then, in one chance the probability to pick a room in the side of the garden is
1/4
Answer A
Answer: (A) 1/4
Question: If 425/999=0.125, what is the 81st digit to the right of the decimal point in the decimal equivalent of the fraction?
(A) 0
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: 0.[u]125[/u = 0.425425425.....
Every 3rd digit is 5 and every multiple of 3 will be the digit 5. Since 81 is multiple of 3, the 81st digit is 5.
Answer E
Answer: (E) 5
Question: In what time will a train 80 m long cross an electric pole, it its speed be 144 km/hr?
(A) 2.0 sec
(B) 2.8 sec
(C) 7.5 sec
(D) 2.3 sec
(E) 1.5 sec
Rationale: Speed = 144 * 5/18
= 40 m/sec
Time taken = 80/40
= 2.0 sec.
Answer:A
Answer: (A) 2.0 sec
Question: A company selected 250 zip codes in Northeastern, Florida, Arizona and California in order to mail a product catalog. The number of Northeastern zip codes was twice Florida's, and four times Arizona's, and 4/3 California's. 300,000 catalogues were mailed to California and 25% resulted in product orders. What is the ratio of the number of orders to the number of California's zip codes?
(A) a) 500
(B) b) 750
(C) c) 1,000
(D) d) 1,250
(E) e) 1,500
Rationale: Since N = 2F, no of Florida zip codes (F) will be N/2.
Since N = 4A, no of Arizona zip codes (A) will be N/4
Since N = (4/3)C, no of California zip codes (C) will be 3N/4
N + N/2 + N/4 + 3N/4 = 5N/2 = 250
N = 100
C = 3N/4 = 75
No of orders is 25% of 300,000 = 75,000
So required ratio = 75,000/75 = 1000
Answer C
Answer: (C) c) 1,000
Question: If 2^(2w) = 8^(w−6), what is the value of w?
(A) 12
(B) 15
(C) 18
(D) 21
(E) 24
Rationale: 2^(2w) = 8^(w−6)
2^(2w) = 2^(3*(w−6))
2^(2w) = 2^(3w-18)
Let's equate the exponents as the bases are equal.
2w = 3w-18
w = 18
The answer is C.
Answer: (C) 18
Question: The average mark of the students of a class in a particular exam is 80. If 5 students whose average mark in that exam is 20 are excluded, the average mark of the remaining will be 90. Find the number of students who wrote the exam.
(A) 15
(B) 25
(C) 35
(D) 45
(E) 55
Rationale: Let the number of students who wrote the exam be x.
Total marks of students = 80 x.
Total marks of (x - 5) students = 90(x - 5)
80x - (5 * 20) = 90(x - 5)
350 = 10x => x = 35
ANSWER:C
Answer: (C) 35
Question: Monica planned her birthday party. She prepared 5 muffins for each of her guests and kept aside two additional muffins in case someone will want extra. After the party, it turned out that one of the guests didn't come but every one of the guests that did come ate six muffins and 2 muffins remained. How many guests did Monica plan on?
(A) 3.
(B) 4.
(C) 5.
(D) 6.
(E) 7.
Rationale: Let x be the number of guests.
Number of muffins prepared = 5x + 2
Number of muffins eaten + Number of muffins remaining = Number of muffins prepared
6(x - 1) + 2 = 5x + 2
6x - 4 = 5x + 2
x = 6
Answer: D
Answer: (D) 6.
Question: The average weight of three men A, B and C is 84 Kg. The average weight becomes 80 Kg when D joins them. If E whose weight is 3 Kg more than D joins the group replacing A, then the average weight of B, C, D and E becomes 79 Kg. The weight of A is:
(A) 65kg
(B) 70kg
(C) 75kg
(D) 80kg
(E) 85kg
Rationale: Wt of ABC = 84*3= 252 kg
wt of ABCD= 80*4=320 kg
wt of D= 68 kg
wt of E = 71 kg
wt of ABCDE = 320+71=391 kg
wt of BCDE = 79*4=316 kg
wt of A = 391-316=75 kg
ANSWER:C
Answer: (C) 75kg
Question: Choose the missing terms out of the given alternatives.
AD, EH, IL, ?, QT
(A) MP
(B) LM
(C) MN
(D) OP
(E) OM
Rationale: A
MP
The letters move four steps forward.
Answer: (A) MP
Question: A firm has 4 senior partners and 6 junior partners. How many different groups S of 3 partners can be formed in which at least one member of the group is a senior partner. (2 groups are considered different if at least one group member is different)
(A) 48
(B) 100
(C) 120
(D) 288
(E) 600
Rationale: What seems to work as well, though its tougher to come up with this solution:
(10*9*8) * 2/3 + (10*9*4)*1/3 = 600. Divided by all possible permutations (=3!) yields 100.
Explanation: For the first spot you have 10 possible canditates, for the 2nd 9. For the 3rd spot you need to differentiate if a senior partner has been picked for one of the first 2 spots or not. If yes, then you can pick one of the 8 remaining guys, so 10*9*8. If no senior partner has been picked yet, you need 10*9*4.
Now you need to weight the 2 cases with the corresponding probabilities: probability of no senior partner being picked in the first 2 draws = 6/10*5/9=1/3, so you weight 10*9*4 with 1/3. For the complementary case (senior partner was picked in the first 2 draws) you just take the complementary prob (1-1/3)= 2/3 and weight 10*9*8 with it.
Now you just need to divide the answer (600) by the number of different positions (=3!) and get S=600/6=100.B
Answer: (B) 100
Question: In the last set of tests, a student scored marks in each of 5 subjects in the ratio 4:5:6:7:8 and got an overall average score of 48%. If a mark of 50% in a subject is a pass and the maximum marks of each subject is the same, how many subjects did the student pass?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: The tests scores are 4k, 5k, 6k, 7k, and 8k.
The sum of the test scores is 30k.
The average test score is 30k/5 = 48. Then k = 8.
The test scores are 32, 40, 48, 56, and 64.
The student passed 2 subjects.
The answer is B.
Answer: (B) 2
Question: Two numbers N and 12 have LCM = 54 and GCF = 8. Find N.
(A) 24
(B) 34
(C) 36
(D) 54
(E) 64
Rationale: The product of two integers is equal to the product of their LCM and GCF. Hence.
12 × N = 54 × 8
N = 54 × 8 / 12 = 36
correct answer C
Answer: (C) 36
Question: Seats for Maths, Physics and Biology in a school are in the ratio 5:7:8. There is a proposal to increase these seats by 40%,50% and 75%. What will be the ratio of increased seats?
(A) 1:2:3
(B) 2:3:4
(C) 2:4:5
(D) 3:6:7
(E) 5:7:9
Rationale: Let the number of seats of M,P,B be 5x,7x,8x
Number of increased seats are 140% of 5x , 150% of 7x , 175% of 8x
5x*140/100 , 7x*150/100 and 8x*175/100
i.e. 7x, 21x/2 and 14x
Required ratio = 7x:21x/2 : 14x = 14x:21x:28x = 2:3:4
Answer is B
Answer: (B) 2:3:4
Question: Find the value of (2 − 1/3) (1 − 1/4)(1 − 1/5)……… (1 − 1/99)(1 − 1/100)
(A) 1/20
(B) 1/15
(C) 1/16
(D) 1/19
(E) 1/24
Rationale: (2 − 1/3) (1 − 1/4)(1 − 1/5)..... (1 − 1/99)(1 − 1/100)
5/3 × 3/4 × 4/5 × ....... 98/99 × 99/100 = 5/100 = 1/20
A
Answer: (A) 1/20
Question: The Hobo Music Orchestra is comprised of, 3/5 wind instrument musicians, 1/4 string instrument musicians, and the rest are percussion instrument musicians. If half of the string instrument musicians are violinists, and the conductor doubles the number of violinists, what proportion of the orchestra are now wind instrument musicians?
(A) 9/10
(B) 6/11
(C) 7/15
(D) 1/2
(E) 6/7
Rationale: Wind = 3/5 = 12/20
String = 1/4 = 4/20
Percussion = 1 - (12/20 + 4/20) = 1 - 16/20 = 4/20
Violinists = (1/2)(4/20) = 2/20
If Violinists doubled => (2)(2) = 4; then, total = 12 + 6 + 4 = 22,
and 12 are Wind => proportion = 12/22 = 6/11.
Answer: B
Answer: (B) 6/11
Question: A salesman sold twice as much pears in the afternoon than in the morning. If he sold 360 kilograms of pears that day, how many kilograms did he sell in the morning and how many in the afternoon?
(A) 120 kg
(B) 240 kg
(C) 360 kg
(D) 480 kg
(E) 520 kg
Rationale: Let x be the number of kilograms he sold in the morning.Then in the afternoon he sold 2x kilograms. So, the total is x+2x=3x. This must be equal to 360.
3x=360
x=3603
x=120
Therefore, the salesman sold 120 kg in the morning and 2⋅120=240 kg in the afternoon.
correct answer B
Answer: (B) 240 kg
Question: A 10% stock yielding 8% is quoted at?
(A) 125
(B) 170
(C) 175
(D) 180
(E) 185
Rationale: Assume that face value = Rs.100 as it is not given
To earn Rs.8, money invested = Rs.100
To earn Rs.10, money invested = 100×10/8 = Rs.125
ie, market value of the stock = Rs.125
Answer is A.
Answer: (A) 125
Question: Two trains are moving in the same direction at 72 kmph and 36 kmph. The faster train crosses a man in the slower train in 27 seconds. Find the length of the faster train?
(A) 270 m
(B) 176 m
(C) 197 m
(D) 167 m
(E) 187 m
Rationale: Relative speed = (72 - 36) * 5/18 = 2 * 5 = 10 mps.
Distance covered in 27 sec = 27 * 10 = 270 m.
The length of the faster train = 270 m.
Answer:A
Answer: (A) 270 m
Question: how many square are there between 2001....2300 I don't remember the exact series.
(A) 1
(B) 4
(C) 2
(D) 3
(E) 5
Rationale: series was from 2001 to 2300
45^2=2025
46^2=2116
47^2=2209
48^2=2304 (so exclude 48)
so ans is 3 (45,46 and 47)
ANSWER:D
Answer: (D) 3
Question: A bag contains 7 green balls and 7 white balls. If two balls are drawn simultaneously, what is the probability that both balls are the same colour?
(A) 4/13
(B) 6/13
(C) 8/21
(D) 11/21
(E) 17/42
Rationale: The total number of ways to draw two balls is 14C2 = 91
The number of ways to draw two green balls is 7C2 = 21
The number of ways to draw two white balls is 7C2 = 21
P(two balls of the same colour) = 42/91 = 6/13
The answer is B.
Answer: (B) 6/13
Question: If f(x) = ax^4 + x^3 + 2ax + 5, then f(b) – f(-b) will equal:
(A) 0
(B) 2ab
(C) 2ab^4 – 8b^2 – 6
(D) -2ab^4 + 8b^2 + 6
(E) 2b^3 + 4ab
Rationale: f(x)=ax^4 + x^3 + 2ax + 5
f(b) = ab^4 + b^3 + 2ab + 5
f(-b) = ab^4 - b^3 - 2ab + 5
f(b) - f(-b) = ab^4 + b^3 + 2ab + 5 - ab^4 + b^3 + 2ab - 5
=2b^3 + 4ab
Answer E
Answer: (E) 2b^3 + 4ab
Question: The profit obtained by selling an article for Rs. 56 is the same as the loss obtained by selling it for Rs. 42. What is the cost price of the article?
(A) Rs. 40
(B) Rs. 50
(C) Rs. 49
(D) Rs. 59
(E) None of these
Rationale: S.P 1- C.P = C.P – S.P 2
56 - C.P = C.P - 42
2 C.P = 56 + 42;
C.P = 98/2 = 49
ANSWER:C
Answer: (C) Rs. 49
Question: (1/5)^q * (1/4)^18 = 1/(2(10)^35). What is q?
(A) 17
(B) 18
(C) 34
(D) 35
(E) 36
Rationale: We need to arrive at a common base. -->
(5)^(-q) * 2^(-36) = 2^(-36)*5^(-35)
5^(-q)=5^(-35)
-q=-35
q=35=D
Answer: (D) 35
Question: A can give B a start of 50 metres or 10 seconds in a kilometer race. How long does A take to complete the race?
(A) 200 seconds
(B) 140 seconds
(C) 220 seconds
(D) 190 seconds
(E) None
Rationale: Solution:
A can give B a start of 50 metres or 10 seconds in a 1000 m race.
That is, B takes 10 seconds to run 50 metres.
Therefore, B will take (10/50) * 1000 = 200 seconds to run 1000 metres.
A who can give B a start of 10 seconds will take 10 seconds lesser to run the 1000m.
Hence, the time taken by A = 190 seconds.
Answer D
Answer: (D) 190 seconds
Question: For which of the following does f(m)−f(n)=f(m−n) for all values of m and n?
(A) f(y)=y^2
(B) f(y)=y/2
(C) f(y)=y+5
(D) f(y)=2y−1
(E) f(y)=|y|
Rationale: To solve this easiest way is just put the value and see that if it equals or not.
with option 1. f(m) = m^2 and f(n) = n^2
so L.H.S = m^2 - n^2
and R.H.S = (m-n)^2 ==> m^2 + n^2 -2mn.
so L.H.S not equal to R.H.S
with option 2. f(m) = m/2 and f(n) =n/2
L.H.S = m/2 - n/2 ==> 1/2(m-n)
R.H.S = (m-n)/2
so L.H.S = R.H.S which is the correct answer.
B
Answer: (B) f(y)=y/2
Question: Two trains are moving at 65 kmph and 70 kmph in opposite directions. Their lengths are 150 m and 100 m respectively. The time they will take to pass each other completely is?
(A) 6 2/3 sec
(B) 7 1/7 sec
(C) 7 2/2 sec
(D) 8 1/2 sec
(E) 7 1/9 sec
Rationale: 70 + 65 = 135 * 5/18 = 75/2 mps
D = 150 + 100 = 250 m
T = 250 * 2/75 = 20/3 - 6 2/3 sec
Answer: A
Answer: (A) 6 2/3 sec
Question: Two numbers are in the ratio 3:5. If 9 be subtracted from each, they are in the ratio of 9:17. The first number is:
(A) 36
(B) 98
(C) 34
(D) 35
(E) 62
Rationale: (3x-9):(5x-9) = 9:17
x = 12 => 3x = 36
Answer:A
Answer: (A) 36
Question: The graph of a quadratic function and the graph of a linear function in the xy plane can intersect in at most how many points
(A) one
(B) Two
(C) Three
(D) Four
(E) More than four
Rationale: i also thought 2 but i think we need to consider linear function like y=|X| then it could intersect at 6 points.
E
Answer: (E) More than four
Question: A train traveling at 72 kmph crosses a platform in 33 seconds and a man standing on the platform in 18 seconds. What is the length of the platform in meters?
(A) 240 meters
(B) 360 meters
(C) 420 meters
(D) 300 meters
(E) Cannot be determined
Rationale: Speed of train = 72 * (5/18) = 20 m/s
Lets consider the man as a stationery point on the platform.
Crossing the point gives us the length of the train.
Lt = 20 * 18 = 360 m.
Crossing the platform gives us the length of trainlength of platform.
L(t+p) = 20 * 33 = 660 m.
So, length of platform = 660 - 360 = 300 m
IMO, Answer
D
Answer: (D) 300 meters
Question: What is the greatest number of four digits which is divisible by 15, 25, 40 and 75 ?
(A) 9800
(B) 9600
(C) 9400
(D) 9200
(E) 9300
Rationale: Greatest number of four digits = 9999
LCM of 15, 25, 40 and 75 = 600
9999 ÷ 600 = 16, remainder = 399
Hence, greatest number of four digits which is divisible by 15, 25, 40 and 75
= 9999 - 399 = 9600 Answer: Option B
Answer: (B) 9600
Question: One-fifth of the apples produced by farm are defective and one-quarter of all apples produced are rejected by the quality control technician. If one-tenth of the non defective apples are rejected by mistake, and if all the apples not rejected are sold, then what percent of the apples sold by the farm are defective?
(A) 4%
(B) 5%
(C) 6%
(D) 8%
(E) 12%
Rationale: We have 20% defective and 80% non-defective; we have 25% rejected and 75% not rejected. We also know that 1/10 of the non-defective ones (8%) are rejected, so 72% sold. This means that we have 3% sold that are defective and 17% rejected that are defective. Overall, we have 3%/75% or 1 of every 25 that are sold (not rejected) and defective. Correct answer is A.
Answer: (A) 4%
Question: In a Fish tank there are 8 fishes are there. In how many possibilities to choose 6 fishes from the tank?
(A) 20
(B) 21
(C) 28 possibilities
(D) 8
(E) 30
Rationale: The possible way to select 6 fishes out of 10 fishes in the tank is 8C6.
8C6=8!/2!*6!=8*7*6!/6!*2*1
8C6=28
There are 28 ways to select a 6 fishes from the tank.
Answer: (C) 28 possibilities
Question: Two trains of equal are running on parallel lines in the same direction at 46 km/hr and 36 km/hr. The faster train passes the slower train in 27 sec. The length of each train is?
(A) 50
(B) 37.5
(C) 27
(D) 28
(E) 21
Rationale: Let the length of each train be x m.
Then, distance covered = 2x m.
Relative speed = 46 - 36 = 10 km/hr.
= 10 * 5/18 = 25/9 m/sec.
2x/27 = 25/9 => x = 37.5.
Answer: B
Answer: (B) 37.5
Question: Solve 6x + 4 = 4x - 2
(A) 2
(B) 3
(C) 5
(D) 1
(E) 8
Rationale: Sol.
6x + 4 = 4x - 2
=> 6x – 4x = 4 - 2
=> 2x = 2 => x = 1
Answer D
Answer: (D) 1
Question: Kurt, a French painter, has 9 jars of paint: 4 jars of yellow paint, 2 jars of red paint, and 3 jars of brown paint. Kurt pours the contents of 3 jars of paint into a new container to make a new color, which he will name according to the following conditions:
The paint will be namedBrun Yif it contains 2 jars of brown paint and no yellow.
The paint will be namedBrun Xif the paint contains 3 jars of brown paint.
The paint will be namedJaune Xif the paint contains at least 2 jars of yellow.
The paint will be namedJaune Yif the paint contains exactly 1 jar of yellow.
What is the probability E that the new color will be one of theJaunecolors?
(A) 5/42
(B) 37/42
(C) 1/21
(D) 4/9
(E) 5/9
Rationale: I get B.
Jaune Y = (4 choose 1)*(5 choose 2) = 4*10 = 40
Jaune X = (4 choose 2)*(5 choose 1) + (4 choose 3) = 6*5 + 4 = 34
Total combinations = 9 choose 3 = 84
Probability of Jaune E= (40 + 34)/84 = 37/42.B
Answer: (B) 37/42
Question: Suppose you play a game where you role a single dice and whatever you roll you get that dollar amount. For example, if you roll a 1 you get $1. If you roll a 6 you get $6. If you are unhappy with the first roll, you can roll again. However, if you get lower the second time, you cannot take the first roll. If you are unhappy with the second roll you can roll a third and final time. Again, if you get lower on the third roll, you have to keep this roll and cannot take the first or second roll.
What is the expected value of this game?
(A) 4250
(B) 4500
(C) 467
(D) 512
(E) 850
Rationale: Expected value for one roll is 1/6*(1+2+3+4+5+6)=3.5$. This part is easy.
Let's proceed: if it's 3.5$, when will I agree to continue the game and roll the second time? Well obviously if the first roll will give me the value less than 3.5 or 1, 2, 3. In other cases if I get 4, 5 or 6, it won't be clever to continue as I already have from my first roll the value higher than the expected value of the second. So what is the expected value of two rolls:
1/6*6+1/6*5+1/6*4+1/2*3.5=2.5+1.75=4.25
The same for the three rolls: if I know that expected value for two rolls is 4.25$, so I'll continue to roll if the first roll will give me the value less than 4.25 or 1,2,3,4. So for three rolls expected value must be:
1/6*6+1/6*5+2/3*4.25=1.833+2.833=~4.67$	C
Answer: (C) 467
Question: A bakery has 6 employees. It pays annual salaries of $19,000 to each of 2 employees, $21,000 to 1 employee, and $22,000 to each of the remaining 3 employees. Which number is closest to the average (arithmetic mean) annual salary of these employees?
(A) $20,200
(B) $20,500
(C) $20,800
(D) $21,000
(E) $21,400
Rationale: average = 2(19000)+(21000)+3(22000) / 6 = $20,833
The answer is C.
Answer: (C) $20,800
Question: The successive discounts 20% and 15% are equal to a single discount of?
(A) 33
(B) 77
(C) 32
(D) 77
(E) 99
Rationale: Let the CP of an article be Rs. 100
Given that successive discounts are 20% and 15%.
SP = 85% of 80% of 100 = (85/100)(80/100)(100)
=> SP = Rs. 68
Clearly, single discount is 32%.
Answer:C
Answer: (C) 32
Question: Product of two natural numbers is 7. Then, the sum of reciprocals of their squares is
(A) 50/49
(B) 1/289
(C) 290/90
(D) 290/19
(E) None of these
Rationale: Explanation:
If the numbers are a, b, then ab = 7,
as 17 is a prime number, so a = 1, b = 7.
1/a2+1/b2=1/1(2)+1/7(2)
=50/49
Option A
Answer: (A) 50/49
Question: A heap of stones can be made up into groups of 21. When made up into groups of 16, 20, 25 and 45 there are 3 stones left in each case. How many stones at least can there be in the heap?
(A) 7203
(B) 2403
(C) 3603
(D) 4803
(E) 5803
Rationale: LCM of 16, 20, 25, 45 = 3600
1 * 3600 + 3 = 3603 not divisible by 21
2 * 3600 + 3 = 7203 is divisible by 21
ANSWER:A
Answer: (A) 7203
Question: The speed of a boat in upstream is 30 kmph and the speed of the boat downstream is 60 kmph. Find the speed of the boat in still water and the speed of the stream?
(A) 10
(B) 99
(C) 15
(D) 66
(E) 23
Rationale: Speed of the boat in still water = (30+60)/2 = 45 kmph. Speed of the stream = (60-30)/2 = 15 kmph. Answer:C
Answer: (C) 15
Question: GOOD is coded as 164 then BAD coded as 21.if ugly coded as 260 then BED?
(A) 33
(B) 34
(C) 35
(D) 32
(E) 31
Rationale: GOOD=(7+15+15+4)*4=164
BAD= (2+1+4)*3=21
UGLY= (21+7+12+25)*4=260
coding follows
(sum of position of alphabets)*(no. of letters in the given word)
so,
BED=(2+5+4)*3= 33
ANSWER:A
Answer: (A) 33
Question: Solve the given two equations and find the inequality of X and Y. (a) 225X^2-4 = 0 and (b) (225y)^(1/2) +2 = 0
(A) If x>y
(B) If x>=y
(C) If x < y
(D) If x<=y
(E) x=y or relationship cannot be established
Rationale: Solution:-
X= +2/15 and -2/15
Y= 4/225
Comparing we get X>Y and X<y
Hence, no relationship can be established
E)
Answer: (E) x=y or relationship cannot be established
Question: A train 360 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 140 m long?
(A) 40
(B) 37
(C) 32
(D) 39
(E) 28
Rationale: Speed = 45 * 5/18 = 25/2 m/sec
Total distance covered = 360 + 140 = 500 m
Required time = 500 * 2/25 = 40 sec
Answer: A
Answer: (A) 40