Question

H.C.F. of two numbers is 23. Find the smaller of the two numbers.
(I) The product of the two numbers is 6348.
(II) The L.C.M. of the two numbers is 276

• A. Statement (I) ALONE is sufficient, but statement (II) alone is not sufficient
• B. Statement (II) ALONE is sufficient, but statement (I) alone is not sufficient
• C. BOTH statements TOGETHER are sufficient, but NEITHER statement alone is sufficient
• D. EACH statement ALONE is sufficient

Answer 1

The correct option is D EACH statement ALONE is sufficient

Let the number be 23x and 23y
∵∵ Product of two numbers = Product of their HCF & LCM
∴∴ (I) & (II) imply the same thing i.e, xy = 12
Now possible value of x & y for which xy is 12are (1, 12), (2, 6) & (3,4). Hence we can find the smaller of two numbers by using either statement alone.