Which of the following statement(s) must be true if $a, b, c, d, e, f$ are odd integers such that $a > b > c > d > e > f$ .
I. $a . b . c . d . e . f$ is odd.
II. $a + b + c + d + e + f$ is odd.
III. $a (b + c + d + e + f)$ is odd.

I

only

No worries! We‘ve got your back. Try BYJU‘S free classes today!

I I

only

No worries! We‘ve got your back. Try BYJU‘S free classes today!

I I I

only

No worries! We‘ve got your back. Try BYJU‘S free classes today!

I

and

I I I

only

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

I, I I,

and

I I I

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is E $I$ and $I I I$ only
Since $a$ , $b$ , $c$ , $d$ , $e$ and $f$ are odd integers such that $a > b > c > d > e > f$ , therefore,

Let $a = 11$ , $b = 9$ , $c = 7$ , $d = 5$ , $e = 3$ and $f = 1$ .

Consider the product of these integers that is:

$11 \times 9 \times 7 \times 5 \times 3 \times 1 = 10395$ which is an odd number.

Now consider the addition of these integers that is:

$11 + 9 + 7 + 5 + 3 + 1 = 36$ which is not an odd number.

Finally, we calculate,

$a (b + c + d + e + f) = 11 (9 + 7 + 5 + 3 + 1) = 11 (25) = 275$ which is an odd number.

Suggest Corrections

Similar questions

Q. In the given figure, which of the following statements must be true?
(i) a + b = d + c

(ii) a + c + e = 180°

(iii) b + f = c + e

(a) (i) only

(b) (ii) only

(c) (iii) only

(d) (ii) and (iii) only

Q. Look at the statements given below:
I. If AD, BE and CF be the altitudes of a ∆ABC such that AD = BE = CF, then ∆ABC is an equilateral triangle.
II. IF D is the mid-point of hypotenuse AC of a right ∆ABC, then BD = AC.
III. In an isosceles ∆ABC in which AB = AC, the altitude AD bisects BC.
Which is true?
(a) I only
(b) II only
(c) I and III
(d) II and III

Q. Match the following:
(A) (i)-a, (ii)-c,(iii)-d,(iv)-e,(v)-b,(vi)-f
(B) (i)-b,(ii)-c,(iii)-a,(iv)-f,(v)-e,(vi)-d
(C) (i)-f,(ii)-e,(iii)-b,(iv)-c,(v)-a,(d)- d
(D) (i)-b,(ii)-c,(iii)-d,(iv)-a,(v)-e,(vi)-f

A(a,b), B(c,d) and C(e,f) are the vertices of a triangle.
i) AB + BC > AC
ii) Area of the triangle = ( $\frac{1}{2}$ ) [a (c-e)+c (f-b)+e (b-d)]
Which of the following are true?

D and E are points on the sides AB and AC respectively of a $△$ ABC such that DE || BC. Which of the following statement is true?

(i) $△$ ADE ~ $△$ ABC

(ii) $\frac{a r e a o f △ A D E}{a r e a o f △ A B C}$ = $\frac{A D^{2}}{A B^{2}}$

(iii) $\frac{a r e a o f △ A D E}{a r e a o f △ A B C}$ = $\frac{A B^{2}}{A C^{2}}$

Join BYJU'S Learning Program

Which of the following statement(s) must be true if a,b,c,d,e,f are odd integers such that a>b>c>d>e>f.I.a.b.c.d.e.f is odd.II. a+b+c+d+e+f is odd.III.a(b+c+d+e+f) is odd.

Which of the following statement(s) must be true if $a, b, c, d, e, f$ are odd integers such that $a > b > c > d > e > f$ .
I. $a . b . c . d . e . f$ is odd.
II. $a + b + c + d + e + f$ is odd.
III. $a (b + c + d + e + f)$ is odd.