Which of the following is one less than square of a prime number?

Question

A. 1295
B. 2303
C. 5220
D. 6560
E. 7920

Abhishek009 · Answer

Option + 1 = Prime^2

Now, Check the options -

(A)  \sqrt{1296 } = 36 
(B)  \sqrt{2304} = 48 
(C)  \sqrt{5221} = 72.xx 
(D)  \sqrt{6561} = 81 
(E)  \sqrt{7921} = 89  (Prime Number)

Thus, Answer must be (E)

GMATBusters · Answer

N = p^2-1
= (6n+/-1)^2 -1 
= 6n(n+2)

so the N must be divisible by 6, hence 3
adding the digits and checking divisibility by 3, only C & E are divisible by 3.

for C , N = 5221 72..something
for E, N = 7921 = 89^2

Hence E is the right answer

CareerGeek · Answer

Any prime number more than 3 can be written in the form  6n ± 1

Let  x  =  6n ± 1 
Square of a prime number =  x^2 = (6n ± 1)^2 = 36n^2 ± 12n + 1

One less than the square of prime number =  x^2 - 1 = 36n^2 ± 12n = 12n(3n ± 1)

Note that  12n(3n ± 1)  is always divisible by  24 .
  Case 1: If  n  is odd,  12n(3n ± 1)  =  12 *odd*even --> always divisible  24 
Case 2: If  n  is even,  12n(3n ± 1)  =  12 *even*odd --> always divisible  24

--> All the options are divisible by  24 
--> They must be divisible by factors of 24 also = { 1, 2, 3, 4, 6, 8, . . .  }

Check for 3 --> {C, E} are divisible & {A, B, D} are NOT divisible. So, Eliminate {A, B, D}
Both C & E are divisible by 4

--> Check for 8 [Last 3 digits should be divisible by 8
C. 220/8 --> NOT divisible
E. 920/8 --> Divisible

Option E

Fdambro294 · Answer

Add + 1 to each option and then see if it can be a Perfect Square Prime

A 1296

(Prime)^2 ——To get a units digit of 6, the Number being squared must end in a 4 or 6

In any of the cases, the root can not be a prime number

B 2304

The base, if it were Prime, would need a Units Digit of 2 in order to have a result (when squared) that has a units digit of 4

The root can not be a prime number with a units digit of 4

C, D, and E will all have a units digit of 1 after the Prime is squared.

Thus the Prime can have a Units Digit of either 1 or 9

Can test prime values around the given answer choices:

Answers C thru E would lie between (70)^ 2 and (90)^2 ———- 4,900 and 8,100

The prime numbers between 70 and 90 are:

71, 73, 77, 79, 83 and 89

71, 79, and 89 are the only possible primes that would result in a units digit of 1 when squared. 
 
Since (79)^2 will be a little less than 6,400

And

(71)^2 will be a little more than 4,900

The closest one based on inspection night by 89 ——- at this point, you can multiply 89 * 89

(89)^2 = 7,920

E

Posted from my mobile device

Regor60 · Answer

Adding 1 to each of the answer choices is then equal to the prime number squared.

Since odd times odd = odd, answers A & B are eliminated.

Answer D is also eliminated because with 1 added to it, the digits sum to 18, which is divisible by 3.

For the units digit to be 1 of the squared prime, the prime has to have a units digit of 1 or 9.

Inspecting answer C, the tens digit has to be 7, leaving the prime options of 71 and 79.

79 is obviously too big because of its squared proximity to 6400.

Squaring 71 yields 5041. Incorrect.

Leaving only answer E with no further work required.

Which of the following is one less than square of a prime number?

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

Which of the following is one less than square of a prime number?

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards