a, b and c are positive integers. If b equals the square root of a, an

Question

a, b and c are positive integers. If b equals the square root of a, and if c equals the sum of a and b, which of the following could be the value of c?

I. 21
II. 30
III. 72

A. I only
B. II only
C. III only
D. II and III only
E. I, II and III

chetan2u · Accepted Answer

b=\sqrt{a}..............a=b^2 ..
and  c=a+b = b^2+b =b(b+1) 
so C is PRODUCT of two consecutive integers
21=3*7 or 1*21 ......NO
 30 = 5*6  ................YES
 72 = 8*9  ................ YES

D

TaN1213 · Answer

c=  \sqrt{a}  + a
a= 25, c= 5+25 = 30
a= 64, c= 8+ 64 = 72
a= 16, c= 4+16 = 20 (1 eliminated)
II and III only possible
--D--

luffy_ueki · Answer

Option D.
a,b,c
=> b2, b, c
c=b*(b+1)

Product of 2 consecutive +ve integers
30 &72

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ScottTargetTestPrep · Answer

We have the following equations:
 
b = √a
 
b^2 = a
 
and 
 
c = a + b
 
Thus, 
 
c = a + a^2
 
So c is the sum of an integer + that integer squared. 
 
Statement I is not true, since 4^2 + 4 = 20 and 5^2 + 5 = 30; thus the value of a that satisfies a^2 + a = 21 is not an integer, but some real number between 4 and 5. 
 
Looking at the answer choices we see that II and III can work since 30 = 5 + 25, and 72 = 8 + 64.
 
Answer: D

MathRevolution · Answer

If b equals the square root of a =>  b^2 = a

If c equals the sum of a and b =>  c = a + b = b^2 + b = b ( b + 1)

Therefore, c is the product of two consecutive integers

I. 21 = 4 * 5 = 20 - NOT POSSIBLE

II. 30 = 5 * 6 = 30 - POSSIBLE

III. 72 = 8 * 9 = 72 - POSSIBLE

Only Option II and III are possible.

Answer D

bumpbot · Answer

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a, b and c are positive integers. If b equals the square root of a, an

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