If T is a set of integers that contains every number of the form 4n, where n is a positive integer, which of the following options must be true about T?
-
Solution
Ans: A, C
In other words, T contains all the multiples of 4. So it will contain all the power of 4 and all the positive multiples of 8. But it will not necessarily contain all the multiples of 2 (for example it will not contain 6, 10 and such numbers).
The possible values of x that satisfy both “x – 12 < -4 & x + 12 > 3″ are;
-
Solution
Ans: B, C, D, E
Equations are
x - 12 < -4 ⇒ x < - 4 + 12 ⇒ x < 8 x + 12 > 3 ⇒ x > 3 - 12 ⇒ x >-9
Combining; the range of values of x is -9 < x < 8
If x is an even number which of the following must be odd?
-
Solution
Ans: A, C
x is even
Consider 'A' → 3x + 1 ⇒ 3 (even) + 1
= odd + 1
= odd
Consider '8' → 5x2 + 2 = 5 (even)2 + 2
= even + 2
= even
Consider 'C' ⇒ (x + 1)2 = (even + 1)2
= (odd)2 = odd
Which of the following integers have a divisor greater than 1 which is square of an integer?
-
Solution
Ans: A, C, D, E
Consider options individually
'A' → t 75 = 25 × 3(5) × 3
'B'→ t 42 = 2 × 21
'C' → t 32 = 2x 16 = (4)2 × 2
'D' → t 12 → t 4 x 3 = (2)2 × 3
'E' → t 512 → t 256 x 2 = (16)2 × 2
If n is an integer between 0 and 100, then 3n + 3 could be? Indicate all the values possible
-
Solution
Ans: A, B, D, E
3n + 3 is a positive integer
Consider the options A, B, D, E.
Option A ⇒ 3n + 3 = 300 ⇒ 3n = 297 ⇒ n = 99
Option B ⇒ 3n + 3 = 297 ⇒ 3n = 294 ⇒ n = 98
Option C ⇒ 3n + 3 = 63 ⇒ 3n = 60 ⇒ n = 20
Option D ⇒ 3n + 3 = 6 ⇒ 3n = 3 ⇒ n = 1
For option E:
3n + 3 = 208 ⇒ 3n ⇒ 205 ⇒ n ⇒ \(\frac{205}{3}\)
Which of the following could be the measures of the sides of a single triangle
-
Solution
Ans: A, C, D
Consider option 'A' = 5.5, 30 and 30.5
Multiply by 2 = 11, 60 and 61
11, 60, 61 is a Pythagorean triplet.
Consider 'E' = 5, 12, 18
For a Δ,sum of any two sides must be greater than the third side.
AB + BC > AC
12 + 5 < 18 Hence,S, 12, 18 cannot be the measures of sides of a A. Consider 'C' →t 3,4,5 is a Pythagorean triplet. Consider 'D' →t 3, 3, 3 →t an equilateral triangle.
If P↑ and P↓,are defined by the equations;
p↑ = P + 1
p↓, = P – 1
Then (4↑) (3↓) is equal to which of the following options
-
Solution
Ans:A,C
4 ↑ = 4 + 1 = 5
3↓ = 3-1 = 2
∴ (4↑)(3↓) = 5 × 2 = 10
∴ 10 = 9↑ = 11↓
Paul bears a loss of 25% by selling 40 safety pins for $3. How many safety pins should he sell for 1 dollar in order to earn a profit of 25% or more? Indicate all the amounts.
-
Solution
Ans:A,B,C,E
Since loss is 25%, selling price is 75% of cost price
If selling price is $3, Cost price is $4.
∴ Each pin will cost him 10 cents.
Now Paul wants to earn 25% profit. Selling price of 1 pin = 12.5 cents.
∴ For $1,8 pings are to be sold in order to get a profit of 25% for profit greater than 25% the number of pins he should sell must be less than 8.
3⁄4 of the number of women attending a certain party is equal to 1⁄3 of number of men attending and is also exactly equal to 1⁄2 of the number of children attending it. Which of the following can be either the number of men, women or children attending the party? Indicate all such number.
-
Solution
Ans: A, C, D
Let,
W → t Number of Women
M → t Number of Men
C → t Number of Children
According to information given
3⁄4W=1⁄3M=1⁄2C
⇒ 9W = 4M = 6C
∴ The ratio of W : M : C = 1⁄9 :1⁄4 : 1⁄6
W : M : C = 4 : 9 : 6
∴ The Number of W, M or C must be divisible by 4,9,6 respectively.
The expression (3y + 7) (2y – 5) is equivalent to which of the following expressions? Indicate all of them.
-
Solution
Ans: A, B, C
The expression (3y + 7) (2y - 5) is equivalent to all three