mathewhe/aqua_rat huggingface dataset:
Question: If a(a + 2) = 48 and b(b + 2) = 48, where a ≠ b, then a + b =
(A) -10
(B) -9
(C) -5
(D) -4
(E) -2
Rationale: i.e. if a = 6 then b = -8
or if a = -8 then b = 6
But in each case a+b = -8+6 = -2
Answer:B
Answer: (B) -9
Question: There are 76 persons. 54 can read Hindu, 43 can read Times, 37 can read Deccan and 15 can read all. If 24 can read Hindu and Deccan and 27 can read Deccan and Times then what is the number of persons who read only Times and Hindu.
(A) 21
(B) 22
(C) 23
(D) 24
(E) 25
Rationale: Let 'A'can be read Hindu,
Let 'B'can be read Times,
Let 'C'can be read Deccan,
From the given data:n(AuBuC)=76,n(A)=54,n(B)=43,n(C)=37,n(AnBnC)=15,n(AnC)=24,n(BnC)=27,n(AnB)=?
n(AuBuC)= n(A)+n(B)+n(C)-n(AnB)-n(BnC)-n(AnC)+n(AnBnC)
==> 76=54+43+37-n(AnB)-24-27+15
==> n(AnB)= 54+43+37+15-24-27-76
==> n(AnB)= 149-127
==> n(AnB)= 22
ANSWER:B
Answer: (B) 22
Question: The difference between the exterior and interior angles at a vertex of a regular polygon is 150 degree. The number of sides of the polygon is
(A) 20
(B) 21
(C) 22
(D) 23
(E) 24
Rationale: I+E= 180 deg
I-E= 150 deg
I= 165 deg
E= 15 deg
If there are n vertices (or sides ), then
n*15 = 360 deg ( sum of all external angles)
n= 360/15 = 24
ANSWER:E
Answer: (E) 24
Question: If 40% of a number is equal to two-third of another number, what is the ratio of first number to the second number.
(A) 5 : 3
(B) 2 : 5
(C) 4 : 7
(D) 5 : 2
(E) None of these
Rationale: Explanation:
Let the first number is A and second number is B.
As per question
(40/100)A = (2/3)B
A/B = 2/3 x 100/40
A/B = 5/3
=>A:B = 5:3
Answer: Option A
Answer: (A) 5 : 3
Question: At a certain laboratory, chemical substance are identified by an unordered combination of three different colors. If no chemical may be assigned the same three colors as any other, what is the maximum number of substances that can be identified using eight colors?
(A) 21
(B) 56
(C) 105
(D) 135
(E) 210
Rationale: The prompt tells us that substance is identified by an UNORDERED combination of 3 colors and that no chemical may be assigned the same 3 colors as any other chemical.
As an example, a chemical with the colors A/B/C means that the following combinations CANNOT be used by any other chemical:
ABC
ACB
BAC
BCA
CAB
CBA
By extension, the first part of your calculation would be the number of possible substances that could be identified with 7 colors: 8c3 = 56 possible substances
B
Answer: (B) 56
Question: what is rate of interest if principal.amount be 400,simple interest 80 and time 2year.
(A) 10
(B) 12.5
(C) 25
(D) 12
(E) 14.5
Rationale: s.i=(p*r*t)/100
80=800r/100
r=80/8=10%
answer A
Answer: (A) 10
Question: A, B, C subscribe Rs. 50,000 for a business. A subscribes Rs. 4000 more than B and B Rs. 5000 more than C. Out of a total profit of Rs. 35,000, A receives:
(A) Rs. 8400
(B) Rs. 11,900
(C) Rs. 13,600
(D) Rs. 14,700
(E) None of these
Rationale: Explanation:
Let C = x.
Then, B = x + 5000 and A = x + 5000 + 4000 = x + 9000.
So, x + x + 5000 + x + 9000 = 50000
3x = 36000
x = 12000
A : B : C = 21000 : 17000 : 12000 = 21 : 17 : 12.
A's share = Rs.(35000 x	21/50)=Rs. 14,700.
ANSWER IS D
Answer: (D) Rs. 14,700
Question: A sum was put at simple interest at a certain rate for 10 years . Had it been put at 5% higher rate , it would have fetched Rs.600 more. What was the Sum?
(A) Rs.1200
(B) Rs.1300
(C) Rs.1400
(D) Rs.1500
(E) None of these
Rationale: Explanation:
At 5% more rate, the increase in S.I for 10 years = Rs.600 (given)
So, at 5% more rate, the increase in SI for 1 year = 600/10 = Rs.60/-
i.e. Rs.60 is 5% of the invested sum
So, 1% of the invested sum = 60/5
Therefore, the invested sum = 60 × 100/5 = Rs.1200
Answer: A
Answer: (A) Rs.1200
Question: A train speeds past a pole in 15 seconds and a platform 100 m long in 25 seconds. Its length is?
(A) 187 m
(B) 768 m
(C) 237 m
(D) 150 m
(E) 287 m
Rationale: Let the length of the train be x meters and its speed be y m/sec.
They, x / y = 15 => y = x/15
x + 100 / 25 = x / 15
x = 150 m.
Answer: D
Answer: (D) 150 m
Question: The average of 11 numbers is 10.9. If the average of first six is 10.5 and that of the last six is 11.4 the sixth number is?
(A) 21.8
(B) 17.9
(C) 16.8
(D) 11.5
(E) 18.1
Rationale: Explanation:
1 to 11 = 11 * 10.9 = 119.9
1 to 6 = 6 * 10.5 = 63
6 to 11 = 6 * 11.4 = 68.4
63 + 68.4 = 131.4 â€“ 119.9 = 11.5
6th number = 11.5
Answer:D
Answer: (D) 11.5
Question: 4685 * 999
(A) 4680250
(B) 4685850
(C) 4680315
(D) 4685975
(E) None of these
Rationale: Explanation:
4685 * (1000 - 1)
= 4685000 - 4685
= 4680315
Option C
Answer: (C) 4680315
Question: The L.C.M. of two numbers is 54. The numbers are in the ratio 2 : 3. Then sum of the number is:
(A) 28
(B) 32
(C) 40
(D) 45
(E) 54
Rationale: Let the numbers be 2x and 3x.
Then, their L.C.M. = 6x.
So, 6x = 54 or x = 9.
The numbers are 18 and 27.
Hence, required sum = (18 + 27) = 45.
Answer: Option D
Answer: (D) 45
Question: A, B and C can do a work in 60, 30 and 45 days respectively. If they work together, in how many days will they complete the work?
(A) 12 4/5 days
(B) 13 4/5 days
(C) 13 1/5 days
(D) 13 2/5 days
(E) 12 4/5 days
Rationale: One days's work of A, B and C = 1/60 + 1/30 + 1/45
= (3+6+4)/180 =13/180
A, B and C together can do the work in 13 4/5 days.
ANSWER:B
Answer: (B) 13 4/5 days
Question: If x/4 + 24/x = 5, what are the values of 3x - 4?
(A) 8 And 9
(B) 20 and 32
(C) 17 and 19
(D) 12 and 29
(E) 17 and 29
Rationale: I got the same thing B is the answer 20 or 32
Answer: (B) 20 and 32
Question: Two trains each 250 m in length are running on the same parallel lines in opposite directions with the speed of 80 kmph and 70 kmph respectively. In what time will they cross each other completely?
(A) 19 sec
(B) 22 sec
(C) 12 sec
(D) 42 sec
(E) 32 sec
Rationale: Explanation:
D = 250 m + 250 m = 500 m
RS = 80 + 70 = 150 * 5/18 = 125/3
T = 500 * 3/125 = 12 sec
Answer: Option C
Answer: (C) 12 sec
Question: Evaluate: |5 - 8(3 - 12)| - |5 - 11| = ?
(A) 40
(B) 50
(C) 60
(D) 71
(E) 80
Rationale: According to order of operations, inner brackets first. Hence
|5 - 8(3 - 12)| - |5 - 11| = |5 - 8*(-9)| - |5 - 11|
According to order of operations, multiplication within absolute value signs (which may be considered as brackets when it comes to order of operations) next. Hence
= |5 + 72| - |5 - 11|
= |77| - |-6|
= 77 - 6 = 71
correct answer D)71
Answer: (D) 71
Question: Find the 25% of Rs. 200.
(A) Rs. 50
(B) Rs. 70
(C) Rs. 100
(D) Rs. 80
(E) Rs. 60
Rationale: Explanation :
25% of 200
=> 25/100 *200 = Rs. 50
Answer : A
Answer: (A) Rs. 50
Question: The elementary school has 19 fourth graders, 23 fifth graders, and 29 six graders. Fourth graders have 30 minutes of homework per night, fifth graders have 40 minutes of homework per night, and six graders have 60 minutes of homework per night. How many minutes per night does the average student with homework have?
(A) about 30 minutes
(B) about 40 minutes
(C) about 45 minutes
(D) about 50 minutes
(E) about 60 minutes
Rationale: Explanation:
19 23 29
30 40 60
570 + 920 + 1740 = 3230/71 = about 45 minutes
C
Answer: (C) about 45 minutes
Question: One fast typist type some matter in 5hrs and another slow typist type the same matter in 6hrs. If both do combine in how much time they will take to finish.
(A) 2 hr 44 mins
(B) 11 hr 40 mins
(C) 2hr 14 mins
(D) 3 hr 44 mins
(E) 4 hr 44 mins
Rationale: Fast's 1 hr work = 1/5
slow's 1 hr work = 1/6
1/5 + 1/6 = 11/30
they ll finish in 30/11hrs= 2 8/11 ==> 2 hr 44 mins
ANSWER:A
Answer: (A) 2 hr 44 mins
Question: if 105 is represented as 253 in base 6,how is 253 represented in base 6?
(A) 1100
(B) 1101
(C) 1111
(D) 1011
(E) 1010
Rationale: (105)base6=253
then (253)base6=1101
because 253%6=1 and 253/6=42
then 42%6=0 and 42/6=7
then7%6=1 and 7/6 = 1
and then 1%6=1 and 1/6=0
we see remainder part in reverse order that is 1101
so ans is 1101
ANSWER:B
Answer: (B) 1101
Question: The speed of a car is 80 km in the first hour and 60 km in the second hour. What is the average speed of the car?
(A) 76 kmph
(B) 70 kmph
(C) 87 kmph
(D) 56 kmph
(E) 86 kmph
Rationale: S = (80 + 60)/2
= 70 kmph
Answer: B
Answer: (B) 70 kmph
Question: At present, the ratio between the ages of Arun and Deepak is 4:3. After 6 years, Arun's age will be 26 years. What is the age of Deepak at present?
(A) 20
(B) 15
(C) 25
(D) 18
(E) 12
Rationale: Let the present ages of Arun and Deepak be 4x and 3x years respectively.
Then, 4x + 6 = 26 => x = 5
Deepak's age = 3x = 15 years.
ANSWER B
Answer: (B) 15
Question: If the area of a square with sides of length 5 centimeters is equal to the area of a rectangle with a width of 4 centimeters, what is the length of the rectangle, in centimeters?
(A) 4
(B) 8
(C) 12
(D) 7
(E) 18
Rationale: Let length of rectangle = L
5^2 = L*4
=> L = 25/4 = 7
Answer D
Answer: (D) 7
Question: In Set T, the average (arithmetic mean) equals the median E. Which of the following must be true?
I. Set T consists of evenly spaced numbers.
II. Set T consists of an odd number of terms.
III. Set T has no mode.
IV. None of the above.
(A) I only
(B) I and II
(C) II and III
(D) I, II, and III
(E) IV only
Rationale: This is a very good 'trap question'.
Consider Set A= { 0,0,0,0 } Mean=Median=Mode=0- Eliminates 1,2 and 3 OR
Consider Set B= {1,2,2,3 } Mean=Median=Mode=2- Eliminates 1,2 and 3
If you think that only in 'consecutive integers' the average is equal to the median E you might fall for 'D'.
Ans: E
Answer: (E) IV only
Question: Two numbers are less than third number by 25% and 37% respectively. How much percent is the second number less than by the first
(A) 6%
(B) 8%
(C) 9%
(D) 11%
(E) 12%
Rationale: Let the third number is x.
then first number = (100-25)% of x
= 75% of x = 75x/100
Second number is (63x/100)
Difference = 75x/100 - 63x/100 = 3x/25
So required percentage is, difference is what percent of first number
(3x/25 * 100/75x * 100 )% = 6% ANSWER :A
Answer: (A) 6%
Question: What is the sum of all possible solutions to |x + 3|^2 + |x + 3| = 20 ?
(A) -1
(B) 6
(C) 7
(D) 12
(E) 14
Rationale: Denote |x + 3| as y: y^2 + y = 20 --> y = -5 or y = 4. Discard the first solution since y = |x + 3|, so it's an absolute value and thus cannot be negative.
y = |x + 3| = 4 --> x = 7 . The sum = 7.
Answer: C.
Answer: (C) 7
Question: Given a two-digit number, the unit's digit exceeds its ten's digit by 5 and the product of the given number and the sum of its digits is equal to 90, which of the options is the number?
(A) 27
(B) 16
(C) 38
(D) 61
(E) 83
Rationale: Using the elimination method the option that fits this description is 27
7-2 = 5 (unit's digit that exceeds its ten's digit by 3)
27*9 = 243 (the product of the given number and the sum of its digits is equal to 175)
answer :A
Answer: (A) 27
Question: Find the value of (2 − 1/3) (1 − 1/4)(1 − 1/5)……… (1 − 1/99)(1 − 1/100)
(A) 1/20
(B) 1/18
(C) 1/21
(D) 3/5
(E) 4/21
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: A man sold 18 toys for Rs. 23100, 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. 1100
Rationale: Let the cost of one toy = X.
Then, cost of 18 toys = 18X.
Gain = 3X.
SP of 18 toys = Rs. 23100.
Gain = SP â€“ CP
3X = 23100 â€“ 18X
21X = 23100
X = Rs. 1100.
ANSWER : OPTION E
Answer: (E) s. 1100
Question: In how many B ways can the wordGMATbe arranged so that no such arrangement has A as the first letter?
(A) 6
(B) 12
(C) 18
(D) 24
(E) 30
Rationale: Number of ways of arranging the word GMAT = 4! = 24
Number of ways of arranging the word GMAT so that A is always in the first = 3! = 6
Number of ways of arranging GMAT so that A is not in the beginning B= 24 - 6 = 18
Answer: C
Answer: (C) 18
Question: Raj invests a part of Rs. 12,000 in 12% stock at Rs. 120 and the remainder in 15% stock at Rs. 125. If his total dividend per annum is Rs. 1360, how much does he invest in 12% stock at Rs. 120?
(A) 3000
(B) 4000
(C) 5000
(D) 5500
(E) 6000
Rationale: investment in 12% stock be X
Then investment 15% stock = (12000-x)
12/120*x+15/125*(12000-x) = 1360
x=4000
ANSWER B
Answer: (B) 4000
Question: If a - b =6 and
a2+b2=48
, find the value of ab.
(A) 6
(B) 8
(C) 10
(D) 12
(E) 2
Rationale: Explanation:
We know
2ab=(a2+b2)âˆ’(aâˆ’b)2
2ab=48âˆ’36=12
=>ab=6
Option E
Answer: (E) 2
Question: At what price must an article costing Rs.47.50 be marked in order that after deducting 10% from the list price. It may be sold at a profit of 25% on the cost price?
(A) 65.9
(B) 62.3
(C) 62.7
(D) 62.2
(E) 62.9
Rationale: CP = 47.50
SP = 47.50*(125/100)
= 59.375
MP*(90/100)
= 59.375
MP = 65.9
Answer:A
Answer: (A) 65.9
Question: A palindrome is a number that reads the same forward and backward, such as 242. How many odd seven-digit numbers are palindromes?
(A) 40
(B) 400
(C) 500
(D) 5,000
(E) 100,000
Rationale: 7th digit 1,3,5,7,9
6th digit 0 through 9
5th digit 0 through 9
4th digit 0 through 9
i.e 10*10*10*5 = 5000 numbers
first and second digit and third digit is going to be same as 4th and 5th and 6th. so it would still be 5000 numbers.
Answer is D.
Answer: (D) 5,000
Question: If a certain sample of data has a mean of 33.0 and a standard deviation of 2.0, which of the following pairs contain two values that are each at least 2.5 standard deviations from the mean?
(A) (26.0; 39.5)
(B) (32.5; 34.0)
(C) (30.0; 36.5)
(D) (31.5; 38.5)
(E) (29.0; 36.0)
Rationale: The standard deviation is 2, so 2.5 standard deviations would be (2.5)(2) = 5.
The values between 28 and 38 are within 2.5 standard deviations from the mean.
The answer is A.
Answer: (A) (26.0; 39.5)
Question: If the number 97215 * 6 is completely divisible by 11, then the smallest whole number in place of * will be:
(A) 3
(B) 2
(C) 1
(D) 5
(E) 0
Rationale: Answer: Option A
Given number = 97215x6
(6 + 5 + 2 + 9) - (x + 1 + 7) = (14 - x), which must be divisible by 11.
x = 3
Answer: (A) 3
Question: A fort of 2000 soldiers has provisions for 50 days. After 10 days some of them left and the food was now enough for the same period of 50 days as before. How many of them left?
(A) 400
(B) 992
(C) 878
(D) 665
(E) 211
Rationale: 2000 ---- 50
2000 ---- 40
x ----- 50
x*50 = 2000*40
x=1600
2000
-------
400
Answer:A
Answer: (A) 400
Question: A shopkeeper expects a gain of 22.5% on his cost price. If in a week, his sale was of Rs. 490, what was his profit?
(A) s. 64
(B) s. 69
(C) s.72
(D) s.75
(E) s.90
Rationale: C.P. = Rs. (100/122.5)x490
= Rs. (1000/1225)x490
= Rs. 400
Profit = Rs. (490 - 400) = Rs. 90.
Answer:E
Answer: (E) s.90
Question: 5n + 2 > 12 and 7n - 19 < 44; n must be between which numbers?
(A) 1 and 8
(B) 2 and 6
(C) 2 and 9
(D) 2 and 7
(E) 2 and 9
Rationale: 5n+2 > 12
5n > 10
n > 2
7n-19 < 44
7n < 63
n < 9
So n must be between 2 and 9
2 < n < 9
correct answer C
Answer: (C) 2 and 9
Question: A and B complete a work in 8 days. A alone can do it in 16 days. If both together can do the work in how many days?
(A) 3.75 days
(B) 3.78 days
(C) 5.3 days
(D) 3.15 days
(E) 2.75 days
Rationale: 1/8 + 1/16 = 3/16
16/3 = 5.3 days
Answer: C
Answer: (C) 5.3 days
Question: 40 = a + 3b
5 = |–a|
If a and b are both integers, What is the only possible value that b can take?
(A) 14
(B) 15
(C) 13
(D) 12
(E) 10
Rationale: First understand the meaning of 5 = |-a|
1) when we write |-x| this means the same as |x|.
2) Mod is very easy concept if you solve mod question by considering as a distance. when a mod is written as |x-(a)| = b, this means the distance from point 'a' (both side left and right of 'a' on number line) is b (This is same as given case). |x-(a)| < b means the distance is between the two extreme distance(left and right side of 'a' on number line, considering the max distance is 'b' from 'a’. |x-(a)| > b means the distance is greater than the distance of 'b'..i.e the value of a could be anywhere more than 'b'.
Now come to the question. First its given|-a| = 5 ==> |a| = 5 ===> |a-0| = 5 ==> the distance from zero is equal to 5. So the point will be -5 or 5, as distance from 0 to (-5) is 5 and distance from 0 to 5 is 5. Thus, the value of a will be either 5 or -5.
Now, lets move to equation a + 3b = 40 ==> b = (40 - a)/3. According to question, b is an integer, hence to make b integer (40 - a) must be divisible by 3. Now remove the value which can’t make (40-a) divisible by 3 from the possible values of a (i.e. 5, -5). It will remain with -5 which makes the value of b = (40 - (-5))/3 = 45/3 ==> b = 15...hence answer is B.
Answer: (B) 15
Question: Of the total amount that Jill spent on a shopping trip, excluding taxes, she spent 45 percent on clothing, 45 percent on food, and 10 percent on other items. If Jill paid a 5 percent tax on the clothing, no tax on the food, and an 10 percent tax on all other items, then the total tax that she paid was what percent of the total amount that she spent, excluding taxes?
(A) 3.5
(B) 3.35
(C) 3.45
(D) 3.25
(E) 3.55
Rationale: Assume she has $200 to spend.
TAX
Clothing = 45% = $90= $4.5
Food = 45% = $ 90 = $0.00
Items = 10% = $ 20 = $ 2.00
Total tax = $6.50
% of total amount = 6.5/200 * 100 = 3.25%
Answer D
Answer: (D) 3.25
Question: A and B are two partially filled buckets of water. If 4 liters are transferred from A to B, then A would contain one-third of the amount of water in B. Alternatively, if 5 liters are transferred from B to A, B would contain one-half of the amount of water in A. Bucket A contains how many liters of water?
(A) 47/5
(B) 13
(C) 17
(D) 21
(E) 23
Rationale: Let A contains A, B contains B liters
so, (A-4)/(B+4)= 1/3.......(1)
again, (B-5)/(A+5)= 1/2..........(2)
from (1)(2) we find A= 47/5
ans: (A)
Answer: (A) 47/5
Question: A bag contains 6 red, 2 green balls. 3 balls are drawn randomly. What is the probability that balls drawn contain exactly two green balls?
(A) 1/7
(B) 2/9
(C) 3/11
(D) 3/28
(E) 2/3
Rationale: Total number of balls = 6+2 = 8
n(S) = 8C3 = 8*7*6 / 3*2 = 56
n(E) = 2C2* 6C1 = 6
Probability = 6/56 = 3/28
Answer is D
Answer: (D) 3/28
Question: How many 4 digit numbers can be formed with the digits 0, 1, 2, 3, 4, 5, 6 and 5?
(A) a. 220
(B) b. 249
(C) c. 432
(D) d. 216
(E) e. 288
Rationale: Taking Question with it's same language as given
To make number divisible by 5, the unit digit should be either 0 or 5 only
Case 1: If unit digit is fixed as zero
With two6s The choice to fill the remaining three digits = 3C2 x 5 = 15
With all remaining 3 digits different, The choice to fill the remaining three digits = 6 x 5 x 4= 120
Total Such cases = 120+15 = 135
Case 2: If unit digit is fixed as Five
With two6s and one0The choice to fill the remaining three digits = 2 [6605 or 6065]
With two6s and without0The choice to fill the remaining three digits = 3C2 x 4 = 12
With all remaining 3 digits different, and one0The choice to fill the remaining three digits = 2 (ways to place zero) x 5 x 4= 40
With all remaining 3 digits different, and without0The choice to fill the remaining three digits = 3 x 5 x 4= 60
Total Such cases = 2+12+40+60 = 114
Total numbers = 135+114 = 220
ANSWER OPTION A
Answer: (A) a. 220
Question: 12.5 * 6.2 * 8.8 = ?
(A) 352
(B) 435
(C) 224
(D) 682
(E) 742
Rationale: D
682
? = 12.5 * 6.2 * 8.8 = 682
Answer: (D) 682
Question: A pipe takes a hours to fill the tank. But because of a leakage it took 6 times of its original time. Find the time taken by the leakage to empty the tank
(A) 50 min
(B) 60 min
(C) 72 min
(D) 80 min
(E) 70 min
Rationale: pipe a can do a work 60 min.
lets leakage time is x;
then
1/60 -1/x=1/360
x=72 min
ANSWER:C
Answer: (C) 72 min
Question: Rs.8000 become Rs.10720 in a certain interval of time at the rate of 5% per annum of C.I. Find the time?
(A) 6 YEARS
(B) 7
(C) 5
(D) 3
(E) 4
Rationale: Explanation:
10720 = 8000(21/20)N
(21/20)6 = (21/20)N => N = 6
Answer: Option A
Answer: (A) 6 YEARS
Question: A train traveling at 72 kmph crosses a platform in 31 seconds and a man standing on the platform in 18 seconds. What is the length of the platform in meters?
(A) 240 meters
(B) 260 meters
(C) 420 meters
(D) 600 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 * 31 = 620 m.
So, length of platform = 620 - 360 = 260 m
IMO, Answer
B
Answer: (B) 260 meters
Question: Kiran travels from A to B by car and returns from B to A by cycle in 7 hours. If he travels both ways by car he saves 3 hours. What is the time taken to cover both ways by cycle?
(A) 11 hours
(B) 10 hours
(C) 15 hours
(D) 17 hours
(E) 14 hours
Rationale: B
10 hours
Let the time taken to cover from A to B in car and cycle be x hours and y hours respectively.
x + y = 7 --- (1) ; 2x = 4 --- (2)
solving both the equations, we get y = 5
So, time taken to cover both ways by cycle = 2y hours = 10 hours.
Answer: (B) 10 hours
Question: A computer wholesaler sells 11 different computers and each is priced differently. If the wholesaler chooses three computers for display at a trade show, what is the probability (all things being equal) that the two most expensive computers will be among the three chosen for display?
(A) 15/56
(B) 3/28
(C) 1/28
(D) 1/56
(E) 3/55
Rationale: Since, two of the choices are prefixed, we are free to choose 1 from the rest of the 9 avilable. so 9C1 is the numerator.
Total no of ways we can choose 3 from 11 is 11c3, which is the denominator.
So, the probability: 9c1/11c3= 3/28 ans is E.
Answer: (E) 3/55
Question: Let A be the event that a randomly selected two digit number is divisible by 3 and let B be the event that a randomly selected two digit number is divisible by 10. What is P(A and B)?
(A) 1/30
(B) 1/15
(C) 1/5
(D) 1/3
(E) 1/2
Rationale: P(A and B) = 1/3*1/10 = 1/30
The answer is A.
Answer: (A) 1/30
Question: The price of food in the area where the Sims family lives is scheduled to increase by 50% next year. Since the Sims family cannot afford an increase in their food bill, how much will they have to reduce consumption to keep their cost the same?
(A) 17%
(B) 25.6%
(C) none%
(D) 33.3%
(E) 50%
Rationale: Solution: Let the current food expense be represented by Rs. 100.
The cost of food rises 50%. So, to buy same amount of food, they need to increase their expense,
= (100 + 50% of 100) = Rs. 150.
But, they want to keep food expense the same, so they have to cut Rs. by 50 to keep it to Rs. =100.
The % decrease in consumption is,
(50/150)*100 = 33.3%.
Mental Calculation Method;
100-----50%↑---→150------X%↓---→100.
Here, X = (50/125)*100 = 33.3%.
Answer: Option D
Answer: (D) 33.3%
Question: A committee of three people is to be chosen from 6 married couples. What is the number of different committees that can be chosen if two people who are married to each other cannot both serve on the committee?
(A) 167
(B) 190
(C) 140
(D) 180
(E) 160
Rationale: Total no of ways of choosing a committee = 12C3 = 220
No of ways to choose first couple = 6C1 = 6
No of ways to choose 1 person from remaining 10 = 10C1 = 10
Total number of ways of choosing a married couple to be in the same committee = 6*10=60
So, no of ways not choosing a married couple = 220-60 =160
ANS:E. 160
Answer: (E) 160
Question: Two trains of equal lengths take 10 sec and 12 sec respectively to cross a telegraph post. If the length of each train be 120 m, in what time will they cross other travelling in opposite direction?
(A) 11
(B) 12
(C) 10.9
(D) 14
(E) 15
Rationale: Speed of the first train = 120/10 = 12 m/sec.
Speed of the second train = 120/12 = 10 m/sec.
Relative speed = 12 + 10 = 22 m/sec.
Required time = (120 + 120)/22 = 10.9 sec.
Answer: Option C
Answer: (C) 10.9
Question: Which is equal to 11?
(A) 1.1
(B) -11
(C) 11/11
(D) 11/1
(E) 1/11
Rationale: 11/1 is equal to 11.
Answer: D
Answer: (D) 11/1