mathewhe/aqua_rat huggingface dataset:
Question: If (1/2)^16 (1/81)^k = 1/18^16, then k =
(A) 8
(B) 12
(C) 16
(D) 24
(E) 36
Rationale: I'm going to focus on denominator only..
(2^16) . ((3^4)^k = 18^16
(2^16) . ((3^4k) = (2. 3^2)^16
(2^16) . ((3^4k) = (2^24) . (3^2)^16
hence
4k =32
k = 8
answer A
I hope it's quite clear
Answer: (A) 8
Question: If log	a/b	+	log	b/a= log (a + b), then:
(A) a + b = 1
(B) a - b = 1
(C) a = b
(D) a2 - b2 = 1
(E) None of these
Rationale: Explanation:
log	a/b	+ log	b/a= log (a + b)
=>log (a + b) = log a/b	x	b/a = log 1.
So, a + b = 1.
ANSWER IS A
Answer: (A) a + b = 1
Question: Rectangle A has sides a and b, and rectangle B has sides c and d. If a/c=b/d=2/3, what is the ratio of rectangle A’s area to rectangle B’s area?
(A) 4/9
(B) 2/3
(C) 3/2
(D) 9/2
(E) 9/4
Rationale: The area of rectangle A is ab.
c=3a/2 and d=3b/2.
The area of rectangle B is cd=9ab/4.
The ratio of rectangle A's area to rectangle B's area is ab / (9ab/4) = 4/9.
The answer is A.
Answer: (A) 4/9
Question: 21 ball numbered 1 to 21. A ballis drawn and then another ball is drawn without replacement.
(A) 9/41
(B) 3/42
(C) 9/42
(D) 7/41
(E) 7/40
Rationale: The probability that first toy shows the even number,
=1021=1021
Since, the toy is not replaced there are now 9 even numbered toys and total 20 toys left.
Hence, probability that second toy shows the even number,
=920=920
Required probability,
=(1021)×(920)=(1021)×(920)
=9/42
C
Answer: (C) 9/42
Question: Seven carpenters can individually complete a particular task in 3, 4, 5, and 7 hours, respectively. What is the maximum fraction of the task that can be completed in forty-five minutes if six of the carpenters work together at their respective rates ?
(A) 11/15
(B) 3/5
(C) 11/30
(D) 47/70
(E) 5/9
Rationale: Farmer A, B, C, and D
A's rate: 1/3 job/hour
B's rate: 1/4 job/hour
C's rate: 1/5 job/hour
D's rate: 1/7 job/hour
By intuition we know that the three fastest farmers are A B and C.
As such
(1/3 + 1/4 + 1/5)*(6/7) = ?
47/70 or (D)
Answer: (D) 47/70
Question: If f(a)=6a+6, what is the value of (f(2a)+f(a)) ?
(A) 2a-4
(B) 8a-7
(C) 10a+12
(D) 12a+12
(E) 3a+5
Rationale: f(a)=6a+6
f(2a)= 8a+6
(f(2a)+f(a)) = 8a+6+2a+6 = 10a+12
Answer is C
Answer: (C) 10a+12
Question: If x = 6 and y = −2, what is the value of (x − 2y)^y?
(A) −100
(B) 0.01
(C) 0.25
(D) 4
(E) 8
Rationale: (x−2 y)^y=(6−2(−2))^−2 = 1/(6+4)^2= 1/100 = 0.01
ANSWER:B
Answer: (B) 0.01
Question: Ted’s score was in the 80th percentile out of 200 students in one class. In another class of 100 students there were 15 scores higher than ted’s. If nobody had Ted’s score, then Ted’s was what percentile of the two classes combined?
(A) 86
(B) 84
(C) 82
(D) 80
(E) 78
Rationale: Being in 80% percentile out of 200 grades means Ted was 161st (from the least scores) in the class (as long as nobody had Ted’s grades), he outscored 160.
In another class his score would rank him 76 (from the least grade out of 101, 100+Ted), 75 had the grades higher than Ted.
So in combined classes he outscored 160+75=235. There are 300 students 235/300=0.78
Answer: E (78%)
Generally being in x% means that x% has the grades less than you.
Ted in 80% --> he outscored 80% of of 200=160 (Joseph is 161st).
Of the 100 scores from another class, 15 were higher than Ted 's, and the rest were lower --> rest is 75, hence Ted outscored 75.
So out of total 200+100=300, Ted outscored 160+75=235. Hence he is in 235/300=78%.
Answer: (E) 78
Question: Twenty people at a meeting were born during the month of September, which has 30 days. The probability that at least two of the people in the room share the same birthday is closest to which of the following?
(A) 10%
(B) 33%
(C) 67%
(D) 90%
(E) 99%
Rationale: The probability that at least two people sharing the same birthday = 1 - the probability that none of them sharing the same birthday
A = The number of ways of none of them sharing the same birthday = 30P20 = 30!/(30-20)! = 30!/10! = 11*12*...*29*30
B = The total number of possible ways of 20 people born in September = 20*20*....*20*20 = 20^30 ( each day has 20 options)
A/B = the probability that none of them sharing the same birthday
since B is much greater than A, A/B may equal 1%
--> The probability that at least two people sharing the same birthday = 1 - 1% = 99%
Answer E
Answer: (E) 99%
Question: An aeroplane covers a certain distance at a speed of 120 kmph in 5 hours. To cover the same distance in 1 2/3 hours, it must travel at a speed of:
(A) 520
(B) 620
(C) 820
(D) 740
(E) 720
Rationale: Distance = (120 x 5) = 600 km.
Speed = Distance/Time
Speed = 600/(5/3) km/hr. [We can write 1 2/3 hours as 5/3 hours]
Required speed = (600 x 3/5) km/hr = 360 km/hr
Answer A) 360 Km/hr
Answer: (A) 520
Question: A person was asked to state his age in years. His reply was , "Take my age 5 years hence, multiply it by 3 and subtract 3 times my age 5 years ago and you will know how old I am." What was the age of the person ?
(A) 18
(B) 92
(C) 27
(D) 26
(E) 30
Rationale: Explanation:
Let the present age of person be x years.
Then, 3(x + 5) - 3(x - 5) = x <=> (3x + 15) - (3x - 15) = x <=> x = 30..
Answer: E
Answer: (E) 30
Question: A boy needs to deliver three different newspaper to three different house. The problem is that he doesn't know which newspaper belong to which house. Find the probability that the boy only got one house with the wrong newspaper.
(A) 0
(B) 1/3
(C) 2/3
(D) 4/27
(E) 1/27
Rationale: This one is a trick question. There are three house and three different newspapers. If he only got one wrong delivery, it means that he got the other two house correct. This is not possible because there are only three newspaper. If there are two correct delivery made the remaining one must also be correct. So the possibility of getting o my one of the delivery made wrong is impossible ore 0
Answer: A
Answer: (A) 0
Question: Find the total number of prime factors in the expression (4)^11 x (7)^7 x (11)^2
(A) 31
(B) 22
(C) 25
(D) 27
(E) 29
Rationale: (4)^11x (7)^7 x (11)^2
= (2 x 2)^11 x (7)^7 x (11)^2
= 2^11 x 2^11 x7^7x 11^2
= 2^22 x 7^7 x11^2
Total number of prime factors = (22 + 7 + 2) =31.
Answer is A.
Answer: (A) 31
Question: If ‘n‘ integers taken at random and multiplied together, then what is the probability that the last digit of the product is 1, 3, 7 or 9 ?
(A) (2/5)^n
(B) (1/5)^n
(C) (3/5)^n
(D) (4/5)^n
(E) (6/5)^n
Rationale: Last digit may be 0,1,2,3,4,5,6,7,8,9 = 10
condition is 1,3,7,9 = 4
and n random no. so
probability is 4^n/10^n=(4/10)^n=(2/5)^n
ANSWER:A
Answer: (A) (2/5)^n
Question: A man sold 18 toys for Rs. 18900, gaining thereby the cost price of 3 toy find the cost price of a toy
(A) s. 600
(B) s. 800
(C) s.500
(D) s.900
(E) s. 990
Rationale: Let the cost of one toy = X.
Then, cost of 18 toys = 18X.
Gain = 3X.
SP of 18 toys = Rs. 18900.
Gain = SP â€“ CP
3X = 18900 â€“ 18X
21X = 18900
X = Rs. 900.
ANSWER : OPTION D
Answer: (D) s.900
Question: the sum of the ages of 5 children born at the intervals of 3 year each is 40 year. what is the age of the eldest child ?
(A) 14 year
(B) 8 year
(C) 10 year
(D) None of these
(E) 9 year
Rationale: Solution
let the ages of the children be x,(x + 3),(x + 6),(x + 9) and (x + 12) year.
then, x + (x + 3) + (x + 6) + (x + 9) + (x + 12) = 40 â‡” 5 x = 10 â‡” x= 2.
âˆ´ Age of the youngest child = x + 12= 2 + 12 = 14 years. Answer A
Answer: (A) 14 year
Question: Joan took out a mortgage from hel local bank. Each monthly mortgage payment she makes must be triple the amount of the previous month's payment. If her first payment is $100, and the total amount she must pay back is $914800, how many months will it take Joan to pay back her mortgage?
(A) 6
(B) 8
(C) 10
(D) 9
(E) 13
Rationale: Joan starts off with 100 $ .. which is to be tripled every month
Her monthly payments look like this :
100 , 300 , 900 , 2700 ......... Upto 914800
This can be re written as :
100 x 1 , 100 x 3 , 100 x 9 , 100 x 27 ...... 100 x 9148
So we have 1 , 3 , 9 , 27 ..... 914800 in GP
We know that a =1 , and r = 3 ( its easy to figure it out by looking at the question , but regardless of it being mentioned in the question we can still compute the value of r using the formula Tn = a3^n-1 ...)
Therefore to find the Sum of n terms of a GP we use this formula :
Sn = a (1-r^n) / 1 -r
Using this and plugging in the information we get ...
9148 = 1 - 3^n / 1-3 ; 1-3^n / -2
Cross multiplying we get
9148 x -2 = 1- 3^n
- 19682 = 1 - 3^n
- 19682 = - 3 ^n
19683 = 3 ^n (negatives cancel out)
19863 can also be re written as 3 ^ 9
Therefore ; 3 ^9 = 3 ^n
Thus n = 9 (D)
Answer: (D) 9
Question: If A and B get profits of Rs.18,000 and Rs.15,000 respectively at the end of year then ratio of their investments are
(A) 6 : 5
(B) 1:4
(C) 3:2
(D) 2:3
(E) 2:5
Rationale: Ratio = 18000/15000 = 6 : 5
Answer : A
Answer: (A) 6 : 5
Question: The value of P, when 4864 x 9P2 is divisible by 12, is
(A) 2
(B) 5
(C) 8
(D) NOne of these
(E) Cannot be determined
Rationale: Sol.
Since 4864 is divisible by 4, So 9P2 must be divisible by 3.
∴ (11 + 9) must be divisible by 3.
∴ Least value of P is 1.
Answer D
Answer: (D) NOne of these
Question: Nine men went to a theater. Eight of them spent Rs.3 each over their tickets and the ninth spent Rs.2 more than the average expenditure of all the nine. Determine the total money spent by them?
(A) 29
(B) 29.25
(C) 31
(D) 31.23
(E) 32
Rationale: Average of 9 = x
9x = 8 * 3 + x * 2 x = 3.25
Total = 9 * 3.25 = 29.25
B
Answer: (B) 29.25
Question: which of the following inequalities indicates the set of all values of d for which the lengths E of the three sides of a triangle can be 3,4, and d?
(A) 0<d<1
(B) 0<d<5
(C) 0<d<7
(D) 1<d<5
(E) 1<d<7
Rationale: This question is a good way to apply one of the most basic relation between the 3 sides of a triangle. In a triangle (ANY TRIANGLE), any side MUST be greater than the positive difference of the other two sides and less than than the sum of the other 2 sides. Let the sides of a triangle be a,b,c .
Thus,
|a-b| < c < a+b
|b-c| < a < b+c
|c-a| < b < a+c
Thus, if the sides of the triangle are 3,4 and d,
4-3<d<4+3 ---> 1<d<7. Thus E is the correct answer.
Answer: (E) 1<d<7
Question: A family consists of two grandparents, two parents and three grandchildren. The average age of the grandparents is 67 years, that of the parents is 35 years and that of the grandchildren is 6 years. What is the average age of the family?
(A) 200/7years
(B) 222/7years
(C) 225/7years
(D) 245/7years
(E) None of these
Rationale: Multiply avg age of grand parents, parents and grand childrens with respectively to the no of persons in the family.
i.e,
Total Age of the family => (67*2)+(35*2)+(3*6)=222
Total no of persons in family = 7
Now the avg age of the family = 222/7 years
ANSWER:B
Answer: (B) 222/7years
Question: Two fair die with sides numbered 1 to 6 are tossed. What is the probability that the sum of the exposed faces on the die is a prime number?
(A) 5/11!
(B) 7/8!
(C) 5/9!
(D) 15/21!
(E) 4/9!
Rationale: Two dices are thrown ! So we may get 1+1 or 1+2 ... or 1+6.. or 2+6 or 3+6 etc
Therefore the total different sum values we can get are :2,3,4,5,6,7,8,9,10,11,12[Sample space] ----------------(1)
Out of these values, 5 numbers are primes i.e.2,3,5,7,11[Favorable events] --------------------(2)
From (1)(2)
The answer is5/11!!
Ans: A
Answer: (A) 5/11!
Question: From (1, 2, 3, 4, 5, 6), one number is picked out and replaced and one number is picked out again. If the sum of the 2 numbers is 9, what is the probability that the 2 numbers included the number 5?
(A) 1/2
(B) 2/5
(C) 3/10
(D) 3/5
(E) 1/4
Rationale: We know that the sum of two numbers picked was 9. So, there could be the following cases:
(3, 6);
(6, 3);
(4, 5);
(5, 4);
Total of 4 cases out of which 2 have 5, thus the probability is 2/4=1/2.
Ans A
Answer: (A) 1/2
Question: A can do a piece of work in 4 days. B can do it in 5 days. With the assistance of C they completed the work in 2 days. Find in how many days can C alone do it?
(A) 33
(B) 20
(C) 88
(D) 77
(E) 11
Rationale: C = 1/2 - 1/4 - 1/5 = 1/20
=> 20 days
Answer:B
Answer: (B) 20
Question: Mike's age is 57 years. If he is 5 more than twice the age of his son, find the age of his son.
(A) 20 years
(B) 26 years
(C) 16 years
(D) 18 years
(E) 19 years
Rationale: Let Mike's son age be x.
5 + 2 x = 57
x = 26
Hence Mike's son age is 26years
Answer : B
Answer: (B) 26 years
Question: Subtracting 2% of A from A is equivalent to multiplying A by how much ?
(A) 0.98
(B) 9.4
(C) 0.094
(D) 94
(E) None
Rationale: Answer
Let A - 2% of A = AB.
⇒ (98 x A) / 100 = AB
∴ B = 0.98
Correct Option: A
Answer: (A) 0.98
Question: P, Q, R, S and T are five speakers who have to speak on a particular day, not necessarily in the same order. R is neither the first nor the last speaker. There are three speakers after S and three speakers ahead of T. If P speaks after Q, then who is the last speaker to speak?
(A) S
(B) T
(C) P
(D) Q
(E) Cannot be determined.
Rationale: Explanation:
There are three speakers after S. So, S is the 2nd speaker.
There are three speakers before T. So, T is the 4th speaker.
R is neither the 1st nor the 5th. So, R is the 3rd speaker.
P speaks after Q, So P is the 5th and Q is the 1st speaker. So, P is the last speaker.
ANSWER IS C
Answer: (C) P
Question: A rectangular floor is covered by a rug except fo a strip p meters along each of the four edges. If the floor is m meters by e meteres, What is the area of the rug in square meters?
(A) mn - p(m+n)
(B) mn – 2p(m+n)
(C) mn – p^2
(D) (m - p)(n - p)
(E) (m - 2p)(e - 2p)
Rationale: The answer must be E.
Plug in M 100
N 50
e 10.
Answer: (E) (m - 2p)(e - 2p)
Question: Simple interest on a sum at 4% per annum for 2 years is Rs.80. The C.I. on the same sum for the same period is?
(A) 81.6
(B) 81.7
(C) 81.2
(D) 81.3
(E) 81.1
Rationale: SI = 40 + 40
CI = 40 + 40 + 1.6 = 81.6
Answer: A
Answer: (A) 81.6
Question: A charity collected $4,199 from donors during the last month. If each donor gave at least $20, what is the greatest possible number of donors the charity could have?
(A) 209
(B) 205
(C) 200
(D) 250
(E) 215
Rationale: Min fund = 20
Total = 4199
The closest multiple of 20 to 4199 is : 208
Which implies 208 people gave 20 and 1 person gave 39
Ans. A
Answer: (A) 209
Question: Tanaka and Sam worked all summer mowing lawns to earn money for college. They combined what they made everyday and at the end of summer they split all of their earnings evenly (50/50) between themselves. If Sam earned an even number of dollars, and the product of Tanaka and Sam's earnings is an even number, then which of the following is true?
(A) Tanaka made $522.
(B) Tanaka made $306.
(C) Tanaka made $333.
(D) Tanaka made $666.
(E) Tanaka made $500.
Rationale: From Parity Mathematics Rule: If the sum of two numbers is odd, then the product is even. x + y = odd; then, xy = even.
And, the sum of an even and odd number are odd, but the sum of two even numbers is even.
Sam's earning are even, so Tanakas must be odd.
Answer: C
Answer: (C) Tanaka made $333.
Question: x men working x hours per day can do x units of a work in xx days. How much work can be completed by y men working y hours per day in y days?
(A) x2/y2 units
(B) y3/x2 units
(C) x3/y2 units
(D) y2/x2 units
(E) None
Rationale: Explanation:
Let amount of work completed by y men working y hours per in y days = w units
More men, more work(direct proportion)
More hours, more work(direct proportion)
More days, more work(direct proportion)
Hence we can write as
(men)x:y
(hours)x:y
(days)x:y }::x:w
⇒x^3w=y^3x
⇒w=y^3x/x^3
=y^3/x^2
Answer: Option B
Answer: (B) y3/x2 units
Question: Max planned to buy bike, sales man advised him to buy within this month, If he purchase next month means State Tax will be increasing 10% than its cost and it would be 82500. What is the bike's Selling price in this month
(A) 70000
(B) 73000
(C) 75000
(D) 77000
(E) 79000
Rationale: SP* (110/100) = 82500
SP= 750 * 100 => SP = 75000
Answer:C
Answer: (C) 75000
Question: Which one of the following numbers is exactly divisible by 11?
(A) A)11
(B) B)13
(C) C)14
(D) D)15
(E) E)16
Rationale: (4 + 5 + 2) - (1 + 6 + 3) = 1, not divisible by 11.
(2 + 6 + 4) - (4 + 5 + 2) = 1, not divisible by 11.
(4 + 6 + 1) - (2 + 5 + 3) = 1, not divisible by 11.
(4 + 6 + 1) - (2 + 5 + 4) = 0, So, 415624 is divisible by 11.
A
Answer: (A) A)11
Question: If two of the four expressions x + y , x + 3y , x - y , and 3x - y are chosen at random, what is the probability that their product will be of the form of x^2-(by)^2, where b is an integer?
(A) 1/2
(B) 1/6
(C) 1/5
(D) 1/3
(E) 1/4
Rationale: Total number of expressions if 2 are multiplied = 4C2 = 4!/2!*2! = 6
now we have to find the expressions that are in form of x^2 - (by)^2
one is (x+y)(x-y) = x^2 - (1y)^2
If you see any other combination we are always going to have one term of xy since 3x and 3y are there, so there can be only one type of combination like this.
therefore, probablity is 1/6
Answer : B
Answer: (B) 1/6
Question: Which is the smallest no which divides 2880 and gives a perfect square?
(A) 4
(B) 9
(C) 3
(D) 5
(E) 7
Rationale: 2880=20*144(because w.k.t 144 is perfect square)
=2*10*144
=2*2*5*144
=4*5*144(here 4 and 144 are perfect square)
so the smallest number is 5
ANSWER:D
Answer: (D) 5
Question: A and B together can complete a piece of work in 6 days. B and C can complete the same work in 8 days.A and C can finish it in 12 days. If they all work together, how long it will take to finish the work
(A) 48/9 days
(B) 58/9 days
(C) 68/9 days
(D) 78/9 days
(E) 88/9 days
Rationale: Solution: Work done by A,B & C together in one day= ½(1/6 +1/8 + 1/12)=9/48
=> days taken to complete the work by A,B & C together =48/9 days
Answer A
Answer: (A) 48/9 days
Question: If k, m, and n are consecutive integers such that k > m > n and the sum of k, m, and n is a multiple of 10, which of the following could be the value of k?
(A) 0
(B) 1
(C) 9
(D) 10
(E) 12
Rationale: We're given a very specific set of restrictions in this prompt:
1) K, M and N are CONSECUTIVE INTEGERS
2) K > M > N
3) K+M+N = a multiple of 10
We're asked which of the 5 answer COULD be the value of K given these restrictions. Rather than staring at the screen or doing layered math, we canbrute forcethe answers until we find one that fits these restrictions..
Answer A: K = 0
In this case, the numbers would be 0, -1, and -2. The sum = -3 which is NOT a multiple of 10. Eliminate A.
Answer B: K = 1
In this case, the numbers would be 1, 0, and -1. The sum = 0 which IS a multiple of 10. B IS the answer.
Final Answer:
B
Answer: (B) 1
Question: If the cost price is 90% of sp then what is the profit %
(A) 1.10%
(B) 1.11%
(C) 1.15%
(D) 1.17%
(E) 1.27%
Rationale: Sol. sp=Rs100 : then cp=Rs 90:profit =Rs 10.
Profit={(10/90)*100}%=1.11%
Answer is B.
Answer: (B) 1.11%
Question: The sum of ages of 5 girls born at the intervals of 3 years each is 70 years. What is the age of the youngest girl?
(A) years
(B) years
(C) years
(D) years
(E) years
Rationale: Let the ages of children be x, (x + 3), (x + 6), (x + 9) and (x + 12) years.
Then, x + (x + 3) + (x + 6) + (x + 9) + (x + 12) = 70
5x = 40
x = 8.
Age of the youngest child = x = 8years.
A)
Answer: (A) years
Question: There is a five digit code consist of letters and digit. the code can have one digit from 1,2,3 and any four letters from A,b,c,d,e. first and last code must be a letter and all letters can be repeated. How many combinations can be possible?
(A) 625
(B) 3840
(C) 5625
(D) 11,520
(E) 11,620
Rationale: 5c1*(5c1*5c1*3c1)*3!/2!*5c1=5625
First fix the 1st and last digit, that can be filled with any of the 5 letters in 5c1 ways
Remaining 3 digits includes a no which can be filled in 3c1 ways
Remaining 2 digits are again letters and can be filled in 5c1 ways
these 3 digits can be arranged among themselves in 3!/2! ways
5625 is the answer!
ANSWER:C
Answer: (C) 5625
Question: If apples cost x dollars per m dozen, how many dollars will it cost to buy n apples?
(A) xn/(12m) dollars
(B) xn/m
(C) m/(xn)
(D) 12m/(xn)
(E) 12mn/x
Rationale: let it 2 dollars for 2 dozens(24) and we are asked to find the value n apples...let n be 4...
In order to buy 24 apples it took 2 dollars...then for 4 apples it'll take 4*2/12*2 = 1/3.. i.e. n*x/12*m.
Answer: option A is correct answer...
Answer: (A) xn/(12m) dollars
Question: What is the next number of the following sequence
1,2,3,5,8,13,?
(A) 25
(B) 21
(C) 20
(D) 24
(E) 28
Rationale: 1+2=3
2+3=5
3+5=8
5+8=13
8+13=21
therefore next no. is 21
ANSWER:B
Answer: (B) 21
Question: A child must place 3 different toys in 4 different bins. If any of the toys can go in any of the bins, in how many ways can the child place the toys into the bins?
(A) 6^6
(B) 6^4
(C) 4^6
(D) 4^3
(E) 6^4-4^6
Rationale: there are 4 different bins and each of the toy can go to any of these bins..
so answer 4âˆ—4âˆ—4=4^3
ANSWER:D
Answer: (D) 4^3
Question: The ratio of two numbers is 3:4 and their sum is 28. The greater of the two numbers is?
(A) 12
(B) 14
(C) 16
(D) 18
(E) 21
Rationale: 3:4
Total parts = 7
= 7 parts --> 28 (7 × 4 = 28)
= 1 part ---->4 (1 × 4 = 4)
= The greater of the two number is = 4
= 4 parts ----> 16 (4 × 4 = 16)
C
Answer: (C) 16
Question: A boat goes 8 km upstream in 24 minutes. The speed of stream is 4 km/hr. The speed of boat in still water is:
(A) 24 km/hr
(B) 29 km/hr
(C) 27 km/hr
(D) 25 km/hr
(E) 26 km/hr
Rationale: Speed upstream =8(24/60) = 20 km/hr
Speed of the stream = 4 km/hr
speed of boat in still water = (20+4) = 24 km/hr
Answer: A
Answer: (A) 24 km/hr
Question: The sale price sarees listed for Rs.500 after successive discount is 10% and 5% is?
(A) 427.5
(B) 277
(C) 342
(D) 882
(E) 212
Rationale: 500*(90/100)*(95/100) = 427.5
Answer: A
Answer: (A) 427.5
Question: A merchant has 1000kg of sugar, part of which he sells at 8% profit and the rest at 18% profit. He gains 14% on the whole. The quantity sold at 18% profit is
(A) 348
(B) 600
(C) 277
(D) 188
(E) 112
Rationale: Rule of Allegation
Answer with Explanation: Profit on I kind (%) (c) Profit of II kind (d) 8 18
Mean Price (m) d-m (18-14) = 4 14 m-c (14-8) = 6
Ratio of Profits on I and II kind = 4:6 = 2:3
Step (ii) Quantity sold at 18% profit = (3/5 x 1000) kg = 600 kg.
Answer:B
Answer: (B) 600
Question: Larry, Michael, and Doug have five donuts to share. If any one of the men can be given any whole number of donuts from 0 to 5, in how many different ways can the donuts be distributed?
(A) 21
(B) 42
(C) 120
(D) 504
(E) 5040
Rationale: If you get confused about combinations, there's a simple way to count these combinations as well, by counting the number of ways 5 can be summed with 3 numbers.
{5,0,0} = 3 possibilities.
{4,1,0} = 6 possibilities.
{3,2,0} = 6 possibilities.
{3,1,1} = 3 possibilities.
{2,2,1} = 3 possibilities.
Total = 21 possibilitieS
ANSWER:A
Answer: (A) 21
Question: A class has three girls and three boys. These students line up at random, one after another.
What is the probability that no boy is right next to another boy, and no girl is right next to
another girl?
(A) 1 /20
(B) 1 /12
(C) 1 /10
(D) 3 /10
(E) 1 /2
Rationale: We pick the students in order. The first choice is always okay. There is a probability
3/5 that the second choice is okay; for example, if you picked a boy first then there are two boys
and three girls left. Similarly the probabilities that the remaining choices are okay is 1/2 , 2/3 , 1/2,1. The answer is 1/10 , the product of all these probabilities.
correct answer C
Answer: (C) 1 /10
Question: In an examination 35% of the students passed and 260 failed. How many students appeared for the examination?
(A) A)540
(B) B)400
(C) C)700
(D) D)650
(E) E)840
Rationale: Let the number of students appeared be x
then, 65% of x = 260
65x/100 = 260
x = 260*100/65 = 400
Answer is B
Answer: (B) B)400
Question: Ram sold two bicycles, each for Rs.990. If he made 10% profit on the first and 10% loss on the second, what is the total cost of both bicycles?
(A) 2000
(B) 2772
(C) 8122
(D) 2888
(E) 2211
Rationale: (10*10)/100 = 1%loss
100 --- 99
? --- 1980 => Rs.2000
Answer: A
Answer: (A) 2000