When looking for work, you should carry a business card for the following reasons:
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It makes you look like a professional. - A business card can enhance your professional image and show that you are serious about your job search.
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It reinforces your personal brand. - A well-designed business card can communicate your personal brand and make a memorable impression about who you are and what you do.
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It may prompt someone to call you. - Having your contact information readily available on a business card makes it easy for people to reach out to you, potentially leading to job opportunities.
Therefore, the best answers would be the first three options. The option "You shouldn't. They don't matter" is not a valid reason to avoid carrying business cards in a job search context.