mathewhe/aqua_rat huggingface dataset:
Question: How many words, with or without meaning, can be formed using all letters of the word EQUATION using each letter exactly once?
(A) 38,320
(B) 39,320
(C) 40,320
(D) 38,400
(E) 39,400
Rationale: The Word EQUATION has exactly 8 letters which are all different.
Therefore the number of words that can be formed = Number of permutations of 8 letters taken all at a time.
= P (8, 8) = 8!
= 8 × 7 x 6 × 5 x 4 x 3 x 2 × 1
= 40,320
ANSWER:C
Answer: (C) 40,320
Question: 325 metres long yard, 26 trees are palnted at equal distances, one tree being at each end of the yard. What is the distance between 2consecutive trees
(A) 13
(B) 12
(C) 14
(D) 16
(E) 18
Rationale: 26 trees have 25 gaps between them,
Required distance (325/25) = 13
A
Answer: (A) 13
Question: A boy runs 200 metres in 24 seconds. What is his speed ?
(A) 20 km/hr
(B) 24 km/hr
(C) 28.5 km/hr
(D) 30 km/hr
(E) 35 km/hr
Rationale: 200/24 * 18/5 = 30 km/hr
Answer: D
Answer: (D) 30 km/hr
Question: What is the sum R of all 3 digit numbers that leave a remainder of '2' when divided by 3?
(A) 897
(B) 164,850
(C) 164,749
(D) 149,700
(E) 156,720
Rationale: The series is => 101+...998
Number of terms => 300
sum => 300/2 * [101+998]
hence sum R=> 164850 i.e. option B
Answer: (B) 164,850
Question: David walks to a viewpoint and returns to the starting point by his car and thus takes a total time of 2 hours 20 minutes. He would have gained 1 hour by driving both ways. How long would it have taken for him to walk both ways.
(A) 4 h
(B) 3 h
(C) 5 h
(D) 3 h 20 min
(E) 6 h 20 min
Rationale: 1.Walking to to a viewpoint+Driving back=2 hours 20 minutes
2.Driving to a viewpoint+Driving back=2 hours 20 minutes - 1 hours=1 hours 20 minutes, thereforeone way driving=1 hours 20 minutes/2 = 40 minutes.
3. From 1.one way driving=2 hours 20 minutes-40 minutes=1 hour 40 minutes.
4.Walking to to a viewpoint+Walking back=1 hours 40 minutes+1 hours 40 minutes=3 hours 20 minutes.
Answer: D
Answer: (D) 3 h 20 min
Question: A basket has 5 apples and 4 oranges. Three fruits are picked at random. The probability that at least 2 apples are picked is
(A) 25/42
(B) 25/48
(C) 25/45
(D) 25/47
(E) 25/43
Rationale: Total fruits = 9
Since there must be at least two apples,
(5C2 * 4C1)/9C3 + 5C3/9C3 = 25/42.
Answer:A
Answer: (A) 25/42
Question: Arnold and Danny are two twin brothers that are celebrating their birthday. The product of their ages today is smaller by 17 from the product of their ages a year from today. What is their age today?
(A) 2.
(B) 4.
(C) 5.
(D) 7.
(E) 8.
Rationale: ad = (a+1) (d+1) -17
0= a+d-16
a+d = 16
a=d (as they are twin brothers)
a=d=8
E is the answer
Answer: (E) 8.
Question: If anitha rows 65 km upstream and 105 km down steam taking 13 hours each, then the speed of the stream
(A) 8.4 kmph
(B) 5.5 kmph
(C) 6 kmph
(D) 8 kmph
(E) 8.2 kmph
Rationale: Speed upstream = 65/13 = 5 kmph
Speed down stream = 105/5 = 21 kmph
Speed of stream = ½ (21-5) = 8 kmph
ANSWER:D
Answer: (D) 8 kmph
Question: Of the 20 participants in a certain competition, half are male, and half of the males are younger than 18 years of age. If half of the female competitors are also younger than 18 years of age, into how many distinct groups of 4 competitors could the participants be divided if each group must contain two males under 18 years of age and 2 females over 18 years of age?
(A) 3
(B) 4
(C) 6
(D) 100
(E) 20
Rationale: M under 18 - 5
F above 18 - 5
How many distinct groups can be formed now: 5c2 * 5c2 = 100
Answer : D
Answer: (D) 100
Question: A cycle is bought for Rs.930 and sold for Rs.1210, find the gain percent?
(A) 70%
(B) 30%
(C) 40%
(D) 50%
(E) 80%
Rationale: Explanation:
930---- 280
100 ---- ? => 30%
Answer: B
Answer: (B) 30%
Question: A shopkeeper sells his goods at cost price but uses a faulty meter that weighs 900 grams. Find the profit percent.
(A) 12.11
(B) 11.11
(C) 13.11
(D) 14.11
(E) 15.11
Rationale: Explanation:
(100 + g) / (100 + x) = True measure / Faulty measure
x = 0
true measure = 1000
faulty measure = 900
100 + g / 100 + 0 = 1000 / 900
100+g = 10/9*100
g = 11.11
ANSWER: B
Answer: (B) 11.11
Question: How many leading zeros (zeros after the decimal point but before the first nonzero digit of a number) are in 1/5!?
(A) 1
(B) 2
(C) 5
(D) 6
(E) 9
Rationale: 5! =120
1/1000 < 1/120 < 1/100
0.0001 < 1/120 < 0.001
So 1/120 has 2 leading zeros
Answer: B
Answer: (B) 2
Question: 0.35 represents what percent of 0.05?
(A) 0.05%
(B) 0.5%
(C) 5%
(D) 700%
(E) 5000%
Rationale: One more method
0.35 represents what percent of 0.05?
Adjusting the decimal
35 represents what percent of 5?
Divide by 5
7 represents what percent of 1?
Answer = 7*100 = 700% = D
Answer: (D) 700%
Question: 70 is what percent of 125?
(A) 35%
(B) 40%
(C) 45%
(D) 50%
(E) 56%
Rationale: 70/125×100=56% ANSWER : E
Answer: (E) 56%
Question: If 13 = 13w/(1-w) ,then (5w)2 =
(A) 1/4
(B) 5
(C) 1
(D) 2
(E) 3
Rationale: 13-13w=13w
26w=13
w=1/2
5w=5/2
5w*2=5/2*2=5
ANSWER:B
Answer: (B) 5
Question: John, Vikram and Keerthana started a Pizza shop with capitals of Rs. 2000, Rs. 10000 and Rs. 12000 respectively. At the end of the year, the profit share of John is Rs. 500. The difference between the profit shares of Vikram and Keerthana is?
(A) 480
(B) 600
(C) 500
(D) 280
(E) 160
Rationale: Ratio of investments of John, Vikram and Keerthana is 2000 : 10000 : 12000 = 1 : 5 : 6
And also given that, profit share of John is Rs. 500
=> 1 part out of 12 parts is Rs. 500
Now, required difference is 6 - 5 = 1 part
Required difference = 1/1 (500) = Rs. 500.Answer: C
Answer: (C) 500
Question: Evaluate: 6202.5 + 620.25 + 62.025 + 6.2025 + 0.62025
(A) 6819.59775
(B) 6981.59775
(C) 6918.59775
(D) 6198.59775
(E) 6891.59775
Rationale: 6202.5
620.25
62.025
6.2025
+ 0.62025
---------------
6891.59775
Answer is E.
Answer: (E) 6891.59775
Question: A and B finish the job in 15 days.while A,B and C can finish it in 6 days . C alone will finish the job in
(A) 10 days
(B) 30 days
(C) 60 days
(D) 70 days
(E) 50 days
Rationale: Explanation:
6 = (15 * x)/(15 + x)
90+6x=15x
9x=90
X=10
Answer: Option A
Answer: (A) 10 days
Question: If taxi fares were $1.00 for the first 1/5 mile and $0.25 for each 1/5 mile there after, then the taxi fare for a 3-mile ride was
(A) $1.56
(B) $2.40
(C) $3.80
(D) $4.50
(E) $2.80
Rationale: In 3 miles , initial 1/5 mile charge is $1
rest of the distance = 3 - (1/5) = 14/5
rest of the distance charge = 14(0.25) = $3.5 (as the charge is 0.25 for every 1/5 mile)
=> total charge for 3 miles = 1+3.5 = 4.5
Answer is D.
Answer: (D) $4.50
Question: John deposited $10,000 to open a new savings account that earned 4 percent annual interest, compounded quarterly. If there were no other transactions in the account, what was the amount of money in John’s account 6 months after the account was opened?
(A) $10,100
(B) $10,101
(C) $10,200
(D) $10,201
(E) $10,400
Rationale: Approach #1:
4 percent annual interest compounded quarterly --> 1% in 3 moths.
For the first 3 moths interest was 1% of $10,000, so $100;
For the next 3 moths interest was 1% of $10,000, plus 1% earned on previous interest of $100, so $100+$1=$101;
Total interest for 6 months was $100+$101=$201, hence balance after 6 months was $10,000+ $201=$10,201.
Answer: D.
Approach #2:
If the interest were compounded every 6 moths instead of every 3 months (quarterly) then in 6 months the interest would be 4%/2=2% of $10,000, so $200. Now, since the interest is compounded quarterly then there would be interest earned on interest (very small amount) thus the actual interest should be a little bit more than $200, only answer choice D fits.
Answer: D.
Answer: (D) $10,201
Question: How many 4 digit numbers are there, if it is known that the first digit is odd, the second is odd, the third is prime, the fourth (units digit) is divisible by 3, and the digit 1 can be used only once?
(A) 20
(B) 150
(C) 384
(D) 300
(E) 320
Rationale: 4 options for the first digit: 1, 3, 5, 7, 9;
5 options for the second digit: 1, 3, 5, 7, 9;
4 options for the third digit: 2, 3, 5, 7;
4 options for the fourth digit: 0, 3, 6, 9.
Four digit # possible without the restriction (about the digit 2): 5*5*4*4=400
Numbers with one 1-s, 1X1X 1*1*4*4=16.
Thus there are 400-16=384 such numbers.
Answer: C.
Answer: (C) 384
Question: Anil bought a T.V with 20% discount on the labeled price . Had he bought it with 25% discount, he would have saved Rs. 500. At what price did he buy the T.V?
(A) Rs. 16000
(B) Rs. 12000
(C) Rs. 10000
(D) Rs. 5000
(E) Rs. 7000
Rationale: Let the labelled price be Rs. X,
S.P = 80/100*X =4X/5
New S.P = 75/100*X = 3X/4
4X/5 –3X/4 500, X = 10000
ANSWER:C
Answer: (C) Rs. 10000
Question: I remember during the school days , the teacher asked the class "can you tell me the sum of the first 50 odd numbers ?".
I ran quickly to the teacher and told her "the answer is 2500". The teacher replied "lucky guess".
She then asked me "can you tell me the sum of first 75 odd numbers ?".
I wait for approx 10 seconds and replied with the correct answer.
How can i answer so quickly and whats the correct answer ?
(A) 5624
(B) 5625
(C) 5626
(D) 5627
(E) None
Rationale: Solution:
5625
n^1
75 * 75 = 5625 (sum of first 75 odd numbers).
50 * 50 = 2500 (sum of first 50 odd numbers).
Answer B
Answer: (B) 5625
Question: A train of length 250 m crosses a bridge of length 180m in 20 seconds. What is the speed of train?
(A) 33
(B) 77.4
(C) 25
(D) 22
(E) 72
Rationale: Sol : (length of train+ length of bridge) = speed of train x Time
(250+180) = 20 x Speed
Speed = 430/20= 21.5 m/s =77.4 km/h
ANSWER=B
Answer: (B) 77.4
Question: On dividing 265 by a number, the quotient is 12 and the remainder is 1. Find the divisor.
(A) A)12
(B) B)14
(C) C)16
(D) D)18
(E) E)22
Rationale: d = (D-R)/Q
= (265 - 1)/12
= 264/12 = 22
E)
Answer: (E) E)22
Question: The average runs scored by a batsman in 20 matches is 40. In the next 10 matches the batsman scored an average of 13 runs. Find his average in all the 30 matches?
(A) 31
(B) 67
(C) 88
(D) 69
(E) 12
Rationale: Total score of the batsman in 20 matches = 800.
Total score of the batsman in the next 10 matches = 130.
Total score of the batsman in the 30 matches = 930.
Average score of the batsman = 930/30 = 31.
Answer:A
Answer: (A) 31
Question: if an article with marked price of rs.400 is sold at successive discount of 10%,25% and 15%,what is the price the customer has to pay?
(A) 360
(B) 300
(C) 230
(D) 270
(E) 290
Rationale: discount=0.9*.75*.85=.57
so .57*400=230
ANSWER:C
Answer: (C) 230
Question: The ratio of the present ages of Ram and Rahim is 3 : 2. The ratio of the present ages of Rahim and Aman is 5 : 2. What is the ratio of the present ages of Ram and Aman?
(A) 4 : 15
(B) 15 : 4
(C) 9 : 5
(D) Cannot be determined
(E) None of these
Rationale: ram/rahim=3/2;
rahim/aman=5/2;
rahim=5aman/2;
ram/(5aman/2)=3/2;
ram=(3/2)*5aman/2;
ram/aman = (3/2)*5/2;
ram/aman = 15/4
ANSWER:B
Answer: (B) 15 : 4
Question: In a class of 25 students in an examination in maths 3 students scored 95 marks each, 3 get zero each and the average of the rest was 45. What is the average of the whole class?
(A) 47
(B) 45.6
(C) 44
(D) 48
(E) 49
Rationale: Explanation:
Total marks obtained by a class of 25 students
= 3*95 + 3*0 + 19 * 45 =1140
Average marks of whole class = 1140/25 =45.6
Answer: Option B
Answer: (B) 45.6
Question: The difference between the compound interest compounded annually and simple interest for 2 years at 20% per annum is Rs.432. Find the principal?
(A) 2277
(B) 2667
(C) 3600
(D) 9766
(E) 10800
Rationale: P = 432(100/5)^2 => P = 10800
Answer: E
Answer: (E) 10800
Question: Three (rather lazy) men A, B and C working together can do a work in 5 days. They start the work together and A works for 1 day and takes rest on the second day, B works for 2 days and takes rest on the next two days and C works for 2 days and takes rest on the next three days. In how many days will the work be completed ? (A, B, C work at the same rate)
(A) 7 days
(B) 8 days
(C) 9 days
(D) 10 days
(E) 11 days
Rationale: Total work is 3*5 = 15 units.
A does 1 day of work every 2 days.
B does 2 days of work every 4 days.
C does 2 days of work every 5 days.
Test the options.
In 7 days:
A will do 1*3 + 1 = 4 units (3 complete cycles and 1 day of work).
B will do 2*1+ 2= 4 units (1 complete cycle, 2 days of work, and 1 day of rest).
C will do 2*1 + 2 =4 units (1 complete cycle and 2 days of work).
Total = 4 + 4 + 4 = 12 units.
In 8 days:
A will do 1*4 = 4 units (4 complete cycles).
B will do 2*2= 4 units (2 complete cycles).
C will do 2*1 + 2 =4 units (1 complete cycle, 2 days of work, and 1 day of rest).
Total = 4 + 4 + 4 = 12 units.
In 9 days:
A will do 1*4 + 1 = 5 units (4 complete cycles and 1 day of work).
B will do 2*2+ 1 = 4 units (2 complete cycles and 1 day of work).
C will do 2*1 + 2 = 4 units (1 complete cycle, 2 days of work, and two days of rest).
Total = 5 + 5 + 4 = 14 units.
In 10 days:
A will do 1*5 = 5 units (5 complete cycles).
B will do 2*2+ 2= 6 units (2 complete cycle and 2 days of work).
C will do 2*2 =4 units (2 complete cycles).
Total = 5 + 6 + 4 = 15 units.
Therefore, the answer is D.
Answer: (D) 10 days
Question: Shipment --- No. of Defective Chips/shipment --- Total Chips in shipment
S1 ---------------------- 2 ------------------------------------------ 5,000
S2 ---------------------- 5 ------------------- ---------------------- 12,000
S3 ---------------------- 6 ------------------------------------------ 18,000
S4 ---------------------- 4 ------------------------------------------ 16,000
A computer chip manufacturer expects the ratio of the number of defective chips to the total number of chips in all future shipments to equal the corresponding ratio for shipments S1, S2, S3, and S4 combined, as shown in the table above. What’s the expected number of defective chips in a shipment of 66,000 chips?
(A) 14
(B) 20
(C) 22
(D) 24
(E) 25
Rationale: for a total of 51000 chips (adding S1,S2,S3,S4) total number of defective chips is 17 ((adding defective chips of S1,S2,S3,S4) so ratio is 17/51000 or 1 every 3000 chips.
Keeping this ratio constant for 60000 chips number of defective chips will be (1/3000) * 66000 = 22
C
Answer: (C) 22
Question: At 3:40, the hour hand and the minute hand of a clock form an angle of
(A) 160°
(B) 180°
(C) 130°
(D) 110°
(E) 150°
Rationale: Angle between hands of a clock
When the minute hand is behind the hour hand, the angle between the two hands at M minutes past H 'o clock
=30(H−M/5)+M/2 degree
When the minute hand is ahead of the hour hand, the angle between the two hands at M minutes past H 'o clock
=30(M/5−H)−M/2 degree
Here H = 3, M = 40 and minute hand is ahead of the hour hand.
Hence the angle
=30(M/5−H)−M/2
=30(40/5−3)−40/2
=30(8−3)−20
=30×5−20 =130°
Answer is C.
Answer: (C) 130°
Question: A factory produces x widgets per day. The factory's fixed costs are $8000 per day. The price per widget is $80 and the variable costs are $30 per widget. How many widgets need to be produced for profits of $5440 a day?
(A) 42.33
(B) 90.33
(C) 168
(D) 224
(E) 268.8
Rationale: profits=5440=50x-8000 --> x=268.80
Answer E.
Answer: (E) 268.8
Question: If a - b = 10 and a2 + b2 = 210, find the value of ab.
(A) 68
(B) 42
(C) 55
(D) 18
(E) 44
Rationale: 2ab = (a2 + b2) - (a - b)2
= 210 - 100 = 110
ab = 55.
Answer: C
Answer: (C) 55
Question: A train of 24 carriages, each of 60 meters length, when an engine also of 60 meters length is running at a speed of 60 kmph. In what time will the train cross a bridge 1.5 km long?
(A) 5 mins
(B) 1 mins
(C) 8 mins
(D) 3 mins
(E) 6 mins
Rationale: D
3 mins
D = 25 * 60 + 1500 = 3000 m
T = 3000/60 * 18/5 = 180 sec = 3 mins
Answer: (D) 3 mins
Question: The length of a rectangular landscape is 4times its breadth. There is a playground in it whose area is 1200 square mtr & which is 1/3rd of the total landscape. What is the length of the landscape?
(A) 80
(B) 100
(C) 120
(D) 130
(E) 140
Rationale: Sol. x * 4x = 3 * 1200
x = 30
Length = 4 * 30 = 120
C
Answer: (C) 120
Question: A pack of “Jameson's” cigarettes contains 20 cigarettes, of which 2 to 5 cigarettes (randomly) are defective. What are the greatest possible chances of picking a non-defective cigarette?
(A) 0.1
(B) 0.25
(C) 0.5
(D) 0.75
(E) 0.9
Rationale: greatest chance of picking a non defective will exist when defective pieces are least = 2
greatest chance = (18/20) = 0.9
Answer: Option E
Answer: (E) 0.9
Question: The divisor is 25 times the quotient and 5 times the remainder, if the quotient is 16, the dividend is
(A) 6400
(B) 6480
(C) 400
(D) 480
(E) 520
Rationale: Let the divisor be X
Given, Quotient = X/25
Remainder = X/5
X/25 = 16 ==> X = 25 * 16
Dividend = Divisor x Quotient + Remainder
= X * X/25 + X/5 = X/5(X/5 + 1)
= (16 * 25)/5 * (16 * 25/5 + 1)
= 80(80 + 1) = 81 * 80 = 6480
Answer B.
Answer: (B) 6480
Question: A company, Chauncy Co., has an annual travel budget of $56,000. The accounting department estimates that transportation expenses will increase 5 percent in the coming year, and nontransportation travel expenses will increase by 15 percent in the coming year. Last year, Chauncy Co. spent $19,500 on transportation-related expenses, and $35,000 on nontransportation travel expenses. If the annual travel budget does not increase this year, and if the accounting department’s estimates are correct, how far over the annual travel budget will expenses be this year?
(A) Expenses will not go over the budget.
(B) $500
(C) $4,725
(D) $5,725
(E) $60,725
Rationale: annual travel budget of $56,000
Let, Transportation expenses = T = 19500
and Non-Transportation expenses = N=35000
i.e. Increased Transportation expenses = 1.05T = 20475
and Increased Non-Transportation expenses = 1.15N = 40250
Total Expense = 20475+40250 = 60725
Expense over Budget = Budget - expense = 56000-60725 = 4725
Answer: Option C
Answer: (C) $4,725
Question: For how many integer values of n will the value of the expression 4n + 7 be an integer greater than 1 and less than 200?
(A) 48
(B) 49
(C) 50
(D) 51
(E) 52
Rationale: From first constraint
4n+7 > 1
4n> -6
n > -(3/2)
n> -1.5 (n = -1, 0, 1 ,2 3........ upto infinity)
From second constraint
4n+7 < 200
4n< 193
n < 48. 25
n = (-infinity, .......-3, -2, -1, 0, 1, 2, .........upto 48)
Combining the two
-1.5 < n<48.25
n = 1 to 48 (48 integers)
and n = -1 and 0
so 50 integers.
C is the answer
Answer: (C) 50
Question: Is triangle ABC obtuse angled?
1.a2 + b2 > c2.
2.The center of the circle circumscribing the triangle does not lie inside the triangle.
(A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
(B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
(C) BOTH statements (1) and (2) TOGETHER are sufficient but NEITHER statement ALONE is sufficient to answer the question asked.
(D) EACH statement ALONE is sufficient to answer the question asked.
(E) Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked; additional data specific to the problem is needed.
Rationale: Statements together: a2 + b2 > c2
+
The center of the circle circumscribing the triangle does not lie inside the triangle.
From statement 2 we know that the triangle is not acute. Without knowing whether 'c' is the longest side, we will not be able to conclude whether the triangle is obtuse.
Choice E
Answer: (E) Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked; additional data specific to the problem is needed.
Question: 23, 27, 36, 52,...
(A) 40
(B) 24
(C) 77
(D) 36
(E) 12
Rationale: Explanation :
23
23+2^2=27
23+3^2=36
23+4^2=52
23+5^2=77
ANSWER:C
Answer: (C) 77
Question: What is the rate percent when the simple interest on Rs.1600 amount to Rs.200 in 4 Years?
(A) 4%
(B) 3.125%
(C) 5%
(D) 6%
(E) 7%
Rationale: Interest for 1 year = 200/4 = 50
Interest on Rs 1600 p/a = 50
interest rate = 50/1600*100 = 3.125%
Answer : B
Answer: (B) 3.125%
Question: The length of the bridge, which a train 130 metres long and travelling at 54 km/hr can cross in 30 seconds, is:
(A) 200 m
(B) 225 m
(C) 320 m
(D) 250 m
(E) 240 m
Rationale: Speed = [54 X 5/18] m/sec = [15/1] m/sec
Time = 30 sec
Let the length of bridge be x metres.
Then, (130 + x)/30 = 15 => (130 + x) = 450 => x = 450-130 = 320m
ANSWER:C
Answer: (C) 320 m
Question: If S is the sum of the reciprocals of the consecutive integers from 91 to 100, inclusive, which of the following is less than S?
I. 1/8
II. 1/10
III. 1/9
(A) None
(B) I only
(C) III only
(D) II only
(E) I, II, and III
Rationale: Since we summarize the reciprocals from 100 to 91, we can say also that we add ten numbers who are all (with one exception 1/100) greater than 1/100, so that the sum must be greater than 1/10.
On the other side we can say that we add the reciprocals from 91 to 100, so that the sum has to be less than the sum of ten times 1/91.
We can conclude that the sum has to be less than 1/9 but more than 1/10. That leaves us D as the only possible answer.
Answer: (D) II only
Question: January 1, 2008 is Saturday. What day of the week lies on Jan 1, 2009?
(A) Saturday
(B) Wednesday
(C) Thursday
(D) Tuesday
(E) Monday
Rationale: Explanation:
Number of odd days in 2008 = 2 (since it is a leap year)
(we have taken the complete year 2008 because we need to find out the odd days from 01-Jan-2008 to 31-Dec-2008, that is the whole year 2008)
Given that January 1, 2008 is Saturday.
Hence January 1, 2009 = (Saturday+ 2 odd days) = Monday
Answer: Option E
Answer: (E) Monday
Question: Factor (x + 4)3 - 9x - 36 =
(A) (x - 4)(x + 1)(x + 7)
(B) (x + 6)(x + 2)(x + 9)
(C) (x + 4)(x + 1)(x + 5)
(D) (x + 4)(x + 1)(x + 7)
(E) None
Rationale: (x + 4)3 - 9x - 36=
(x + 4)3 - 9(x + 4)=
(x + 4)[(x + 4)2 - 9]=
(x + 4)(x + 4 - 3)(x + 4 + 3)=
(x + 4)(x + 1)(x + 7
Answer D
Answer: (D) (x + 4)(x + 1)(x + 7)
Question: How many kilograms of sugar costing Rs. 9 per kg must be mixed with 27 kg of sugar costing Rs. 7 per
Kg so that there may be a gain of 10 % by selling the mixture at Rs. 9.24 per Kg ?
(A) 60 Kg
(B) 63 kg
(C) 58 Kg
(D) 56 Kg
(E) 66 Kg
Rationale: Explanation :
Selling Price(SP) of 1 Kg mixture= Rs. 9.24
Profit = 10%
Cost Price(CP) of 1 Kg mixture= 100(100+Profit%)×SP=100(100+10)×9.24=100110×9.24=92.411=Rs.8.4
By the rule of alligation, we have
CP of 1 kg sugar of 1st kind CP of 1 kg sugar of 2nd kind
Rs. 9 Rs. 7
Mean Price
Rs.8.4
8.4 - 7 = 1.4 9 - 8.4 = .6
ie, to get a cost price of 8.4, the sugars of kind1 and kind2 should be mixed in the
ratio 1.4 : .6 = 14 : 6 = 7 : 3
Let x Kg of kind1 sugar is mixed with 27 kg of kind2 sugar
then x : 27 = 7 : 3
⇒x27=73⇒x=27×73=63
Answer : Option B
Answer: (B) 63 kg
Question: In a throw of a coin find the probability of getting a tail?
(A) 1/2
(B) 1/3
(C) 1/4
(D) 2/5
(E) 2/7
Rationale: S = {H,T}
E = {T}
P(E) = 1/2
Answer is A
Answer: (A) 1/2
Question: How many positive integers less than 160 are there such that they are multiples of 13 or multiples of 12 but not both?
(A) 18
(B) 19
(C) 20
(D) 23
(E) 25
Rationale: for 13: 13...160=13*12
for 12: 12...156=12*13
but there is one integer 13*12. so
N=(12-1)+(13-1)=23
D
Answer: (D) 23
Question: The area of a circle is increased by 800%. By what percent has the diameter of the circle increased?
(A) 100%
(B) 200%
(C) 300%
(D) 600%
(E) 800%
Rationale: A diameter of 2
it's radius = 1
it's area = (1^2)pi = 1pi
Answer A:
If we increase that diameter 100%, we have....
A diameter of 4
it's radius = 2
it's area = (2^2)pi = 4pi
This area has increased (4 pi - 1pi)/1pi = 3pi/1pi = 3 = 300%
Answer B:
If we increase the diameter 200%, we have...
A diameter of 6
it's area = 3
it's area = (3^2)pi = 9pi
This area has increased (9pi - 1pi)/1pi = 8 pi/1pi = 8 = 800%
ANSWER:E
Answer: (E) 800%
Question: A cycle is bought for Rs.900 and sold for Rs.1080, find the gain percent?
(A) 16 2/3%
(B) 20%
(C) 18%
(D) 25%
(E) 35%
Rationale: Explanation:
900 ---- 180
100 ---- ? => 20%
ANSWER IS B
Answer: (B) 20%
Question: A certain list consists of 21 different numbers. If n is in the list and n is 6 times the average (arithmetic mean) of the other 20 numbers in the list, then n is what fraction of the sum of the 21 numbers in the list?
(A) 1/20
(B) 3/13
(C) 1/5
(D) 4/21
(E) 5/21
Rationale: series : a1, a2....a20,n
sum of a1+a2+...+a20 = 20*x (x = average)
so, n = 6*x
Hence, a1+a2+..+a20+n = 26x
So, the fraction asked = 6x/26x = 3/13
Answer B
Answer: (B) 3/13