4. Responde: ¿Cuántos números primos de la forma [tex]\( a5a \)[/tex] existen y son menores que 400?

A. 1
B. 2
C. 3
D. 4

Question

13-07-2024
Mathematics

Answered

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4. Responde: ¿Cuántos números primos de la forma [tex]\( a5a \)[/tex] existen y son menores que 400?

A. 1
B. 2
C. 3
D. 4

Sagot :

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GinnyAnswer GinnyAnswer · Answer 1 · 2024-07-13T18:04:50-04:00

Para responder a la pregunta de cuántos números primos de la forma [tex]\(a5a\)[/tex] existen y son menores que 400, sigamos estos pasos:

1. Entender la forma [tex]\(a5a\)[/tex]:
- Esto significa que el número tiene 3 dígitos en la forma [tex]\(a5a\)[/tex] donde [tex]\(a\)[/tex] es el primer y el tercer dígito, y el segundo dígito siempre es 5. Así, el número es de la forma [tex]\[100a + 50 + a = 101a + 50.\][/tex]

2. Determinar el rango para [tex]\(a\)[/tex]:
- Queremos que el número [tex]\(a5a\)[/tex] sea menor que 400.
- Esto nos da el intervalo de [tex]\(a\)[/tex] para: [tex]\(a5a < 400.\)[/tex]
- El valor máximo que [tex]\(a\)[/tex] puede tomar en este intervalo es 3 (ya que si [tex]\(a = 4\)[/tex], el número sería 454, que es mayor que 400).

3. Explorar valores de [tex]\(a\)[/tex]:
- Posibles valores de [tex]\(a\)[/tex] son 1, 2 y 3.

4. Formar los números a partir de estos valores de [tex]\(a\)[/tex]:
- Si [tex]\(a = 1\)[/tex]: el número será [tex]\(151.\)[/tex]
- Si [tex]\(a = 2\)[/tex]: el número será [tex]\(252.\)[/tex]
- Si [tex]\(a = 3\)[/tex]: el número será [tex]\(353.\)[/tex]

5. Verificar si estos números son primos:
- Para [tex]\(151\)[/tex]: es un número primo.
- Para [tex]\(252\)[/tex]: no es un número primo (es divisible por 2).
- Para [tex]\(353\)[/tex]: es un número primo.

6. Conclusión:
- Los números [tex]\(a5a\)[/tex] que son menores que 400 y que son primos son [tex]\(151\)[/tex] y [tex]\(353\)[/tex].
- Por lo tanto, existen 2 números primos de la forma [tex]\(a5a\)[/tex] menores que 400.

Entonces, la respuesta correcta es:

b) 2

Sagot :

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