ANS:-The answer is simple. But one needs to understand Islamic standpoint about previous scriptures.
Undoubtedly we Muslims believe as the Quran tells us, that previous scriptures have been corrupted. But still there is a chance that may be some words of God or the Holy Prophets may have survived and transmitted down to this day. Thus we take Quran as a criterion to judge. Whatever is in consonance with Quran and Authentic Ahadith (sayings and deeds of Prophet Muhammad) we believe and else we don’t. We are told in the Holy Quran;
"To thee We sent the Scripture in truth, confirming the scripture that came before it, and guarding it in safety: so judge between them by what Allah hath revealed, and follow not their vain desires, diverging from the Truth that hath come to thee. To each among you have we prescribed a law and an open way." (Al-Quran 5:48)
Abdullah Yusuf Ali in his commentary to this word writes;
"After the corruption of the older revelations, the Quran comes with a twofold purpose: (1 to confirm the true and original Message and (2 to guard it, or act as a check to its interpretation. The Arabic word 'Muhaimin' is very comprehensive in meaning. It means one who safeguards, watches over, stands witness, preserves, and upholds. The Quran safeguards "the Book", for it has preserved within it the teachings of all the former Books. It watches over these Books in the sense that it will not let their true teachings to be lost. It supports and upholds these Books in the sense that it corroborates the Word of Allah which has remained intact in them. It stands a witness because it bears testimony to the Word of Allah contained in these Books and helps to sort it out from the interpretations and commentaries of the people which were mixed with it: what is confirmed by the Quran is the Word of Allah and what is against it is that of the people."
So as the Quran says that Holy Prophet Muhammad (PBUH) has been mentioned in the previous scriptures so we try to find those from whatever is with Jews and Christians today. Thus our endeavor is in this regard.
INDEED ALLAH KNOWS THE BEST!