1. Number System :
Number systems problems includes basic arithmetic, decimals, percentages, ratios, H.C.F & L.C.M and discounts.
Examples:
1. Sum of a rational number and its reciprocal is 13/6. Find the number
A) 2
B) 3/2
C) 4/2
D) 5/2
Answer: B
2. The LCM of two numbers is 280 and their ratio is 7:87:8. The two numbers are
A) 70, 80
B) 35, 40
C) 42, 48
D) 28, 32
Answer: B
2. Percentages :
a percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", or the abbreviations "pct.", "pct"; sometimes the abbreviation "pc" is also used.
Examples:
What percentage of numbers from 1 to 70 have 1 or 9 in the unit's digit?
A) 1
B) 14
C) 20
D) 21
Answer: C
Solution:
Clearly, the numbers which have 1 or 9 in the unit's digit, have squares that end in the digit 1. Such numbers from 1 to 70 are 1, 9, 11, 19, 21, 29, 31, 39, 41, 49, 51, 59, 61, 69.
Number of such number = 14
Required percentage = (14/70 x 100)% = 20%.
3. Probability :
A table or an equation that links each outcome of a statistical experiment with its probability of occurrence is known as a probability distribution.The topics covered in Probability Distribution are
• Probability Distribution
• Cumulative Probability Distribution
• Uniform Probability Distribution
Examples:
1)
Quantity A:The probability that a word selected from the set of all rearrangements of the letters of the word "Math" results in "Math"
Quantity B:The probability that a word selected from the set of all rearrangements of the letters of the word "Good" results in "Good"
A. Quantity A is greater
B. Quantity B is greater
C. The two Quantities are equal
D. The relationship cannot be determined
E. None of these
Answer: B
Solution:
Quantity A: Compute the number of ways the letters of the word 'Math' can be reordered .
All 4 letters of the word 'Math' are distinct.
The letters of the word 'Math' can therefore, be reordered in 4! Ways = 24 ways.
Therefore, the probability that a word selected out of the 24 turns out to be 'Math'
Quantity B: Two of the 4 letters of the word 'Good' repeat.
The letters of the word 'Good' can therefore, be reordered in = 12 ways.
Therefore, the probability that a word selected out of the 12 turns out to be 'Good' is 1/12
4. Relationship between numbers :
This one of the simple concept in mathematics and candidate can easily get good score in this area.
Examples:
1) If one-third of one-fourth of a number is 15, then three-tenth of that number is:
A. 35
B. 36
C. 45
D. 54
Answer: D
2) Three times the first of three consecutive odd integers is 3 more than twice the third. The third integer is:
A. 9
B. 11
C. 13
D. 15
Answer: D
4. Time and Distance :
Distance = Speed * TimeWhich implies →
Speed = Distance / Time and
Time = Distance / Speed
Let us take a look at some simple examples of distance, time and speed problems.
Example:
1. A boy walks at a speed of 4 kmph. How much time does he take to walk a distance of 20 km?
Solution:
Time = Distance / speed = 20/4 = 5 hours.
2. A cyclist covers a distance of 15 miles in 2 hours. Calculate his speed.
Solution:
Speed = Distance/time = 15/2 = 7.5 miles per hour.
5. Ratios :
To express the relative sizes, the ratio of one quantity to another is used. Ratio is often expressed in the form of a fraction.
Examples:
1. There are 12 oranges and 20 apples. What is the ratio of oranges to apples?
Solution: Ratio = of/to
12/20 = 6/10 = 3/5 = 3 :: 5 = Oranges :: Apples
2. The ratio of boys to girls is 3 to 4. If there are 135 boys, how many girls are there?
Solution: Use cross multiplication
3/4 = 135/girls
(4 x 135) = (3 x girls) = 540
540 / 3 = girls
girls = 180
There are 180 girls.
6. Arithmetic sequence :
A arithmetic progression is a succession of numbers such that the distinction between the continuous terms is steady.
Examples:
1)Find the common difference and the next term of the following sequence:
3, 11, 19, 27, 35,__________.
Answer: To find the common difference, I have to subtract a successive pair of terms. It doesn't matter which pair I pick, as long as they're right next to each other. To be thorough, I'll do all the subtractions:
11 – 3 = 8
19 – 11 = 8
27 – 19 = 8
35 – 27 = 8
=> The difference is always 8, so the common difference is d = 8.
=> They gave me five terms, so the sixth term of the sequence is going to be the very next term. I find the next term by adding the common difference to the fifth term:
35 + 8 = 43
Then my answer is:Common difference: d = 8
Sixth term: 43
2)Find the next term in the sequence 7, 15, 23, 31, __ ?
Answer: First, find the common difference among each pair of consecutive numbers.
15−7 = 8
23−15 = 8
31−23 = 8
Since the common difference is 8 or written as d = 8, we can find the next term after 31 by adding 8 to it.
Therefore, we have 31 + 8 = 39.