Display of goods for sale Kit Question

Sir the below scenario which I posted on 29 Nov:

Alvin runs a business selling expensive cars. Last Monday he mistakenly placed a notice on one car indicating that it was for sale of $5000
when in fact its real price was $25000. Bert later noticed the sign and recognizing what a bargain it was immediately
indicated to Alvin that he accepted the offer and would take the car for the indicated amount. Alvin, however, told bert
that there had been a mistake and that the true price of the car was $25000.. Bert insisted that he was entitled to get
the car at the lower price , and when alvin would not give to him at that price Bert said he would sue Alvin.

After Bert had left, Alvin chnaged the price on the car to $25000 and subsequently Cat came in and said she would like
to buy the car, but that she would have to arrange the finance.

On tuesday Del came by and offered Alvin the full $25000 cash there and then and Alvin sold it to him.

Sir I asked you on 29 Nov that whether there is a binding contract between Alvin and Cat?

You replied ” Yes, there is a contract with Cat and the fact that Alvin has sold the car to Del means that Alvin will now probably have to find a similar car to sell to Cat for the agreed price”

HOWEVER, in the kaplan kit the answer is cat as follows:

“A promise to keep the offer open is only binding where there is a separate contract to that effect. This is known as option contract , and the offeree must provide additional consideration for the promise to keep the offer open. As Cat did not provide any consideration to form an option contract. Alvin is not bound to wait for her to return and can sell the car to anyone else if he so chooses.”